Title: Covered Wooden Bridges: An Experimental and Numerical Investigation of System and Component Behavior
Covered wooden bridges and the principles of heavy timber framing by which they were built represent both a significant chapter in this country's civil engineering heritage, and a subclass of bridges that are in immediate need of repair and rehabilitation. This study attempts to increase the information available to engineers who perform design work on wooden truss bridges by exploring their system and component behaviors through experimental tests and numerical models. Four bridges were considered as case studies: Morgan Bridge, a queen post truss; Pine Grove Bridge, a Burr arch-truss; Taftsville Bridge, a multiple king post truss with arch; and Contoocook Bridge, a Town lattice truss.
Title: Probabilistic Construction and Numerical Analysis of Verification and Validation in Predictive Science
It this presentation, some recent developments in verification and validation (V&V) of predictive models are introduced. Verification is a mathematical concept which aims at assessing the accuracy of the solution of a given computational simulation compare to sufficiently accurate or analytical solutions. Validation, on the other hand, is a physics-based issue that aims at appraising the accuracy of a computational simulation compare to experimental data.
The proposed developments cast V&V in the form of an approximation-theoretic representation that permits their clear mathematical definition and resolution. In particular, three types of problems will be addressed. First, a-priori and a-posteriori error analysis of spectral stochastic Galerkin schemes, a widely used tool for uncertainty propagation, are discussed. Second, a statistical procedure is developed in order to calibrate the uncertainty associated with parameters of a predictive model from experimental or model-based measurements. An important feature of such data-driven characterization algorithm, is in its ability to simultaneously represent both the intrinsic uncertainty and also the uncertainty due to data limitation. Third, a stochastic model reduction technique is proposed in order to increase the computational efficiency of spectral stochastic Galerkin schemes for the solution of complex stochastic systems.
While the second part of this research is essential in model validation phase, the first part is particularly important as it provides one with basic components of the verification phase.
Title: Probabilistic Calibration of a Soil Model
A constitutive model is a relationship between material stimuli and responses. Calibration of model parameters within well-defined constitutive models is thus key to the generation of accurate model-based predictions. One limitation of traditional material calibration is that only a few standardized tests are performed for estimating constitutive parameters, which makes the calibration process eminently deterministic. Moreover, measurements taken during standardized tests are usually global readings, which implicitly assume a ‘homogeneous’ material composition, smearing out the influence of any local effects. This work introduces the Functional Bayesian (FB) formulation as a probabilistic methodology for the calibration of constitutive models that incorporates material random responses and local effects into the assessment of constitutive parameters. This particular calibration process is known as the probabilistic solution to the inverse problem. Estimates of the statistics required for the Bayesian solution are obtained from a series of standard triaxial tests which are coupled with 3-Dimensional (3D) stereo digital images allowing for the capturing of material local effects. In addition, the probabilistic method includes the spatial representation of elemental ‘material’ properties by introducing spatially varying parameters within a 3D Finite Element Model (3D-FEM) to reproduce to the extent possible the actual heterogeneous response of the material. The sampling of spatial ‘material’ realizations is performed by the Polynomial Chaos (PC) method, which permits the simulation of multi-dimensional non-Gaussian and non-stationary random fields. Integration of the random parameters is performed via Markov Chain Monte-Carlo and Metropolis-Hastings algorithms. The calibration of a soil sample is presented as a case study to illustrate the applicability of the method when the soil response lies within the linear elastic domain. Calibration results show a probabilistic description of the spatially distributed parameters and of the coefficients of the chaos representation that defines it. Inferences retrieved from the MCMC sampling include the analysis of the ‘material’ properties and of the coefficients of the PC representation which enhances understanding of the randomness associated with the material composition and response.
Title: On the Characterization and Analysis of the Random Eigenvalue Problem
Observed behavior of most physical systems differs from the
behavior of their deterministic predictive models. Probabilistic methods over a
way to model and analyze a system such that the discrepancy in behavior of the
predictive model and of the actual system is minimal in some sense. Certain
parameters in these predictive models are represented as random quantities.
Random eigenvalue problem arises naturally in common procedures for analyzing
the behavior of such models.
Main contribution of this thesis is to present a new insight and method for the
analysis of random eigenvalue problem. Three methods are used here to
characterize the solution of the random eigenvalue problem, namely, the Taylor
series based perturbation expansion, the polynomial chaos expansion coupled with
Galerkin projection, and Monte Carlo simulation.
It is observed that the polynomial chaos based method gives more accurate
estimates of the statistical moments than the perturbation method, especially
for the higher modes. The difference of accuracy in these two methods is more
pronounced as the system variability increases. Moreover, the chaos expansion
gives more detailed probabilistic description of the eigenvalues and the
eigenvectors. However, currently available statistical simulation based method
of estimating the chaos coefficients is computationally intensive, and accuracy
of the estimated coefficients is influenced by the problems associated with
random number generation. To circumvent these problems an efficient method for
estimating the coefficients is proposed. This method uses a Galerkin based
approach by orthogonalizing the residual in the eigenvalue-eigenvector equation
to the subspace spanned by the basis functions used for approximation.
A new representation of the statistics of the random eigenvectors is proposed to capture the model interaction. This representation offers a more detailed description and clearer prediction model of the behavior of the mode shapes of an uncertain system. This representation can also be used in efficient and accurate system reduction. An enriched version of the chaos expansion is proposed that will be helpful in capturing the behavior of the eigenvalues and eigenvectors for the systems with repeated or closely spaced eigenvalues.
Title: A Probabilistic Micromechanical-Based Approach to the Analysis of Statistically Inhomogeneous Random Media
Due to limitations in their manufacturing stage, many composites can exhibit a considerable level of randomness in their microstructure. Such variations can affect the mechanical response of the resulting specimens, especially when localized phenomena are involved. When multi-phase materials exhibit statistically inhomogeneous characteristics, as in the case of random media with a built in gradient in composition, the analysis becomes considerably more complex as the spatial dependency of their probabilistic descriptors cannot be disregarded.
This thesis presents a probabilistic simulation approach to the issue of characterizing and generating samples of such composites. Furthermore, the effects of randomness on the mechanical properties of these materials are investigated using micromechanical-based techniques. A novel method that is capable of generating non-Gaussian, non-stationary samples through a non-linear translation technique is introduced and applied to the generation of two-phase random media.
The effect of spatial fluctuations on the local material response is measured by coupling the probabilistic framework of the analysis with micromechanical homogenization techniques. Two distinct cases are presented as an illustration of the difficulties involved in the analysis of statistically inhomogeneous composites and to measure the performance of the methods developed here.
Title: Understanding Wind and Wind-Rain-Induced Stay Cable Vibrations
Under certain wind conditions, stay cables of cable-stayed bridges have frequently exhibited large-amplitude vibrations. Such vibrations are often associated with the occurrence of rain, but large-amplitude vibrations without rainfall have also been observed. The mechanisms of these vibrations are still not well understood, and it is unclear where the vibrations occurring with and without rainfall are related. Unless fully addressed, these problems significantly hinder the rational design of effective mitigation countermeasures for the vibrations, which potentially threatens the safety and serviceability of cable-stayed bridges. This study was conducted to understand the mechanisms of wind- and rain-wind-induced stay cable vibrations based on full-scale measurements of prototype vibrations in the field and tests of sectional models in the wind tunnel.
A parametric study of the stay cables is first performed based on full-scale measurement data. The Hilbert Transform is used to estimate the modal frequencies of stay cables, revealing that stay cables can essentially be treated as taut strings. The modal damping is assessed based on both ambient vibration and forced vibration data, indicating that the level of damping is very low in stay cables and that it is affected by the dynamic energy exchange between the cables and other structural elements of the bridge. Observed characteristics of stay cable vibrations, as well as their correlation with wind and rain are presented. Based on these characteristics and correlations, several different types of vibrations are identified. In particular, important similarities between the frequently occurring large-amplitude rain-wind-induced vibrations and the classical Kármán-vortex-induced vibrations are explored and compared to a type of large-amplitude dry cable vibrations, providing significant insights to the mechanisms of these types of vibrations.
To verify the observations in the field, sectional cable models were tested in the wind tunnel, revealing the inherent vortex-induced type of instability of yawed and inclined cables over a range of high reduced velocity. The observations in the wind tunnel are also compared with the results of previous wind tunnel tests reported in the literature. Based on the understanding from both the field and the wind tunnel, a framework is proposed for modeling of the vortex-induced type large-amplitude vibrations at high reduced velocity. The potential application of this model is also discussed. The observed vibrations are also used to assess the performance of passive viscous dampers and cross-ties in mitigating wind- and rain-wind-induced stay cable vibrations. Recommendations for rational design of these mitigation devices are also provided.
Title: Distortional Buckling of Cold-Formed Steel Members in Bending
Laterally braced cold-formed steel beams
generally fail due to local and/or distortional buckling in combination with
yielding. For many cold-formed steel studs, joists, purloins, or girds,
distortional buckling may be the predominant buckling mode, unless the
compression flange is partially restrained by attachment to sheathing or
paneling. However distortional buckling of cold-formed steel beams remains a
largely unaddressed problem in the current North American Specification for the
Design of Cold-Formed Steel Structural Members (NAS). Further, adequate
experimental data on unrestricted distortional buckling in bending is
unavailable. Therefore, two series of bending tests on industry standard
cold-formed steel C and Z-sections were performed and presented in this dissertation. The testing setup was carefully designed in the first series of
tests (phase 1) to allow the form of local buckling failure while restrict distortional
and lateral-tortional buckling. The second series of bending tests
used nominally identical specimens to the first phase and a similar testing
setup. However, the corrugated panel attached to the compression flange was
removed in the constant moment region so that distortional buckling may occur.
The experimental data was used to examine current specifications and new design
method. Finite element model by ABAQUS was developed and verified by the two series
of bending tests and a number of cold-formed steel beams were analyzed by
the finite element analysis.
An analytical method was derived to determine the elastic
buckling stress of thin plates under stress gradient. The buckling coefficients for stress gradient situations were given. The stress gradient effect on the
ultimate strength of thin plates was studied by finite element analysis. It was
found that the stress gradient increases the buckling load of both stiffened and
unstiffened elements and current design provision may provide good strength
prediction if the correct elastic buckling coefficient is used.
Since distortional buckling characterizes relatively long buckling
waves thus may be subjected to significant influence by the moment
gradient. Therefore the moment gradient effect on the distortional buckling of
cold-formed steel beams was studied by the finite element analysis. The results
show that the moment gradient increases both the elastic distortional buckling
moment and the distortional buckling
strength of sections. A draft design provision was proposed for the Direct
Strength Method to account for the moment gradient effect.
The tests have demonstrated that partial restraint on the
compression flange may have significant influence on the buckling mode and
strength of cold-formed steel beams. And currently design methods lack considerations
for the partial restraint effect on the distortional buckling.
Therefore research was conducted to explore the distortional buckling behavior of cold-formed beams with partial restraint on the compression flange. A simple
numerical model was proposed to calculate the elastic buckling moment of the
sections with partial restraints and recommendation for design was given.
Simple hand solutions for calculating the elastic buckling of
cold-firmed steel sections were developed for design purpose and draft
provisions for the NAS to account for the moment gradient effect were proposed.
Title: Portfolio Optimization and Value of Information for Catastrophe
Insurance
Quantifying losses inferred from natural catastrophes is a crucial part in our ability to understand and manage the damage caused by these catastrophic events. A significant component in reducing the uncertainty present in loss estimation can be associated with the use of better information in relation with such factors as exact building geometry, construction quality, design, and vulnerability analysis. The question remains though, how to judge whether the enhancement in the losses accuracy justifies the cost of obtaining this improved information.
This study is an effort towards presenting a procedure for integrating, analyzing and evaluating the impact of improved losses information on insurance portfolio-related decisions. A conceptual methodology is proposed in the aim to help insurers decide on the optimal information resolution that is best-suited for the portfolio analysis. The sensitivity analysis emphasizes on the error between simulated losses obtained from default building data versus losses obtained from enhanced information and how this error translates into misleading insurance objectives predictions. For that matter, an insurance portfolio optimization problem is also suggested offering to maximize profit and control exposure risk. Here two new components are incorporated, the means to control the correlation among losses and the ability to reach a geographically and structurally resolved portfolio.
Title: Optimization Using Noisy Simulations: Trust Region, Surrogate Surface, and Adaptive Sampling
In engineering design, computer simulations are often used in optimization.
To enhance robustness, it is necessary to include uncertainties that may come
from physical randomness, insufficient knowledge or imperfect modeling. In this
dissertation, the problem of optimization with noisy simulations is considered.
The input parameters are separated into two groups: design variables and random
factors. The optimization goal is to find the values for the design variables
which minimize expected costs under uncertainties as quantified by the random
factors. The approach is to integrate surrogate-surface methods into a framework
of trust-region-based sequential minimization.
A significant portion of the dissertation is devoted to establishing provable
convergence. Convergence proofs are derived for unconstrained and constrained
optimization under a set of mathematical conditions for objective function
uncertainty. The conditions are in terms of probabilistic bounds on the errors
in the mean of the objective function and its gradient. If a Gaussian model is
used for the errors, then the conditions can be simplified in terms of the bias,
variance and mean-square values. These statistics can be estimated from
simulation results.
To obtain a surrogate surface, which is simply an estimate of the mean of the
objective function, local linear regression is used. This regression method is
well suited for subsequent minimization by the trust-region algorithm because
the support of the local regression kernel can be adapted to the size of the
trust-region. Furthermore, the statistics of the errors in the regression fit
can be derived in terms of a local second-order fit of the true mean function.
The analysis of such a second-order fit is theoretically consistent with the
second-order fit in the convergence proofs of the trust-region algorithm. Hence,
it is possible to show in this dissertation, that an optimization approach based
on local linear regression coupled with a trust-region algorithm is provably
convergent.
To illustrate the surrogate-based optimization approach, a well-known test
problem of truss design is analyzed. It is shown that optimization under
uncertainty leads to a significantly different solution for the truss design as
compared with an equivalent optimization problem under mean conditions.
Title: Equation-Free Particle-Based Computations in Multiple Dimensions and Multiscale Data Assimilations with the Ensemble Kalman Filter
Equation-free techniques were
recently proposed to study multiscale systems where macroscopic evolution
equations may not be explicitly available. So-call Coarse Time-Steppers were
suggested to implement the macroscale evolution via microsimulators. Temporal
derivatives can be numerically obtained based on these time-steppers instead of
computing using the macroscopically explicit equations. These derivatives can
therefore be incorporated with the traditional integration schemes to evolve the
numerical representation of the macroscale observable. These equation-free
techniques have been effectively applied in Coarse Projective Integration,
Coarse Bifurcation Analysis and Coarse Dynamic Renormalization of multiscale
systems. In my research, I extended the Coarse Projective Integration and Coarse
Dynamic Renormalization to macroscopically multidimensional particle systems.
Marginal and conditional inverse cumulative distribution functions (ICDF) were
utilized to serve as the macroscale observables and it was shown that it was
easy to find orthogonal basis for these observables. As a matter of fact, with
these observables, multidimensional problems were converted to effectively
one-dimensional problems, and Coarse Projective Integration and Coarse
Renormalization can be implemented on a reduced macroscale slow manifold. It was
also found that the Coarse Renormalization for self-similar multidimensional
multiscale systems requires only a single template condition, instead of
multiple template conditions as originally expected. The proposed technique was
applied to a Brownian particle system in a Couette flow and produced results
that had a good match to true evolutions and theoretical predictions.
Title: Reliability and Bayesian Approaches to the Probabilistic Performance Based Design of Structures
Performance based design (PBD) is emerging as the guiding principle for the next generation of structural design specifications. PBD provides the engineer with greater flexibility to select appropriate performance criteria and prediction techniques, but also demands more sophisticated analyses. The presence of uncertainty in structural analysis, behavior and design -- especially in the prediction of new performance measures -- requires a probabilistic approach to PBD.
The first component of this research considers reliability-based specifications for PBD, using the example of advanced analysis of steel frames. Design by advanced analysis uses non-linear structural analyses to predict system performance measures. Current advanced analysis proposals use the resistance factors of the load and resistance factor design (LRFD) specifications with no probabilistic justification. The probabilities of failure of sixteen, two-story, two-bay steel frames, design by both LRFD and advanced analysis are estimated using Monte Carlo simulation and importance sampling schemes. The simulated strength and load distributions are used to develop resistance factors for the limit states of first plastic hinge and plastic collapse. The results indicate that design by advanced analysis can maintain the desired reliability for system failure, but may result in unsatisfactory serviceability performance. Two particular difficulties of reliability-based specifications for design by advanced analysis are discussed -- practical calibration for system-based limit states, and the determination of resistance factors applicable to a wide class of structures.
The second component of this research applies Bayesian surrogate models to engineering design, which is viewed as an iterative process of information gathering and decision making. A Bayesian surrogate model relates individual design variables to system performance, including both aleatory and epistemic uncertainties. Bayesian surrogate models can incorporate prior knowledge, update knowledge based on evidence, and propose design revisions. A Bayesian network is used to update the parameters of the surrogate model based on information collected from trial designs. Techniques of Bayesian experimental design are applied to propose design revisions which maximize the expected information gain or relative entropy. The Bayesian surrogate framework is applied to several structural design examples. The results suggest the need to develop new information criteria specific to engineering design and PBD.
Title: Period and Damping Selection for the Design and Analysis of Building Structures
Fundamental period and damping ratio are two of the most important parameters involved in dynamic analyses of buildings. These parameters are usually assigned constant values typically through the use of simplified models or by using engineering judgment. The variability associated with these values is frequently ignored. Measurements of these parameters in the completed structure may or may not match those assumed at the design stage and the effects and implications of such differences are usually not fully explored or understood.
To develop models that reliably estimate the values of period and damping expected in actual structures, a comprehensive database of full-scale measurements was compiled and rigorously analyzed. An analysis of variance (ANOVA) identifies the number of stories for the period data and the number of stories and level of vibration for the damping data a key factors that potentially affect each parameter. Estimation models are developed for different combinations of factors and model performance, which is measured through the standard error, is observed to improve with additional factors. Models are greatly simplified through constrained variations in model coefficients and ar considered to appreciably improve the state-of-the-art in period and damping estimation.
The large quantity of data allows for a proper and careful analysis of the variability in each estimation model. Model variability is quantified through two functions: a scalar value that represents the variability among measurements made on the same building and in the same lateral direction, and a function that represents the variability observed from building to building. A rigorous form representing the model variability is provided along with a much simpler form developed for possible inclusion into standards.
The effect of parameter variability on seismic response estimates was investigated. A proposed, performance-driven design procedure identifies period and damping values that achieve a specified level of performance. For a general seismic design spectrum, the engineer can apply a level of conservatism to the performance level or to period and damping selection from regions of practical values, which are defined through the parameter distributions. The effects of variability reduction are observed and possible direction for future development is discussed.
Title: Bayesian classifiers for uncertainty modeling with applications to global optimization and solid mechanics problems
Models of uncertainty have wide application beyond reliability estimation. In this talk, a model related to computer science approaches is used to solve problems in global optimization and structural mechanics. In contrast to usual statistical methods, a classifier that uses Bayesian classification trees is adopted. In this method, human expertise is quantitatively modeled and used to construct the feature space. Knowledge functions are defined in the feature space, approximating the distribution of promising designs. Within feature space, promising designs, which can be widely scattered in the original high-dimensional design space, become concentrated in a relatively small number of discrete subregions. Knowledge function provides an efficient way to generate the starting points for multi-start global optimization strategy. Furthermore, the classifier provides an efficient knowledge transfer mechanism through reuse of the knowledge functions for solving related, more complex problems.
The method is demonstrated in the design of thin-walled steel columns, where the design space is too large to be effectively handled by common evolutionary techniques such as genetic algorithms. The method is also demonstrated with an entirely different problem of an analysis of a composite material with random properties. In the latter problem it is shown that the features, obtained by principle component analysis of spatial patterns, are closely related to Eshelby's theorem.
Title: Numerical Simulation and Uncertainty Quantification in Microfluidic Systems
Microfluidic Systems are increasingly stimulating considerable interest in both industry and academia. In the construction of high fidelity models capable of adequately predicting the behavior of these devices, uncertainty quantification (UQ) emerges as a main ingredient for resource allocation, engineering design, and model validation. This thesis demonstrates the application of a (UQ) methodology based on a spectral polynomial chaos approach to the modeling of electrokinetically and pressure-driven microchannel flow.
A numerical study of band crossing chemical reactions is first conducted and general solution trends are interpreted in terms of a reduced set of dimensionless parameters. The capability of (UQ) techniques is then illustrated in the context of reduced design models for straight and serpentine channels. Using stochastic UQ tools, deterministic design rules are converted into design envelopes, highlighting the impact of uncertainties in design and operating parameters. Finally, the UQ methodology is extended to fully coupled 2D model for electrokinetically pumped microchannel flow of a reacting mixture. Case studies are presented which investigate sample dispersive mechanisms due to buffer disturbances and random variability in zeta potential.
Title: Evaluation of Response Prediction Methodology For Long-Span Bridges Using Full-Scale Measurements
An important consideration in the design of long-span bridges is the effect of wind loading on the bridge response. Commonly used methods to assess the wind-induced response of these structures include wind tunnel testing and/or analytical approaches that require experimentally determined parameters. While these techniques have predominantly been compared with each other, there has been few opportunities to evaluate them using actual bridge responses. Motivated by this idea, a long-term full-scale measurement program was conducted on a cable-stayed bridge for measuring its response under a range of meteorological conditions. The measured responses were compared with predictions obtained from a multi-mode frequency-domain approach, which was able to capture the coupling between closely spaced modes of the structure. Where possible, input parameters used in the analysis were calibrated using measured quantities at the bridge, to ensure that they were representative. Also, vortex-induced vibrations of the bridge were investigated, and such events were carefully identified. The response comparisons showed that the predictions were in good agreement with measured values, successfully capturing the buffeting response. A parameter study identified the vertical wind spectrum to be one of the primary factors influencing bridge response, and indicated that proper calibration of spectral models used in the analysis provided improved predictions for some of the records.
Title: Stochastic Modeling of Materials with Complex Microstructure
One of the new challenges in Civil Engineering involves the analysis of uncertainty in complex engineering systems. As the accuracy of measurements increases and new composite materials are introduced, we start looking into the behavior of systems that span a wide range of scales from the atomic scale to the scale of continuum mechanics. The study on the role of uncertainty and its propagation should serve as a principal guideline that one must follow in investigation. Of particular interest to us are systems comprised of materials with microstructure that cannot be neglected in comparison to the size of the systems. In modeling such materials, the classical continuum mechanics, or the local theory, may lead to predictions deviating due to neglecting nonlocal interactions between microstructures and the accompanying effects. Basic modifications must be made to the local theory as we start to investigate the nonlocal effects.
The objective of the present research is to construct a material model that is consistent with the variability of heterogeneity and nonlocal interactions of material at the microstructure. The modeling of microstructural variability, the propagation of uncertainties across scales and the prediction of response uncertainties are the emphases in this modeling procedure.
This dissertation focuses on the theoretical treatment for the stochastic modeling of materials with random microstructures in the framework of nonlocal theories. In this work, the random microstructural interactions are represented by the integration of subscale variables and become a part of the constitutive equation for global state variables as in the classical nonlocal field theory. The integration reflects the contribution from the subscale to the global states. The Green's function associated with the integration should be calibrated as a constitutive property. The global behavior, being the overall contributions accumulated from all the scales, must satisfy the admissible condition and boundary conditions. In this manner the behavior of a multiscale system can be stated as a boundary value problem.
Title: A New Directional Method to Assess Structural System Reliability in the Context of Performance-based Design
Recent natural disasters, such as the earthquakes at Northridge, California and Kobe, Japan and hurricanes Hugo and Andrew, have inflicted enormous economic losses on the public and the insurance industry. These losses and resulting impacts have led to renewed interest in development and implementation of performance-based design (PBD). The performance levels in typical PBD recommendations are mapped to measurable structural responses and limit states. To facilitate this development, an efficient procedure to assess system reliabilities of realistic structures accurately is needed. This dissertation is dedicated to developing such a procedure.Analysis of the reliability of complex structural systems requires an efficient simulation procedure coupled with finite element analysis. Directional simulation (DS) is among the most efficient methods for system reliability analysis in the sense that every direction can yield information about system failure. However, the randomly generated directions may not represent the underlying probability distributions very well when the number of directions is limited. Various point sets, which are collectively named deterministic point sets (DPS) herein and have been developed in different domains of science and engineering, have high fidelity in representing the distribution and can reduce simulation error. DPS from the uniform distribution are emphasized herein, since the uniform distribution is commonly used in DS. DPS include spherical t-designs, Fekete points, GLP points, spiral points, and advanced hyperspace division method (AHDM) points. Extensive tests on the efficiency and accuracy of these point sets in system reliability analysis are conducted. Fekete point sets are shown to have some particularly attractive features in terms of accuracy.
Two types of neural networks, namely the feed-forward back-propagation network and the radial basis network, are utilized to further improve the efficiency in a two-phase point refinement scheme based on the Fekete method. The neural network works as a parallel concept to importance sampling in identifying the regions in hyperspace that contribute significantly to the failure probability. The Fekete point method and neural network technique form the essential statistical module denoted "FeketeNN" used to perform system reliability analyses in this dissertation.
Load space formulation has been shown to be particularly useful in limiting the number of calls to the finite element programs in system reliability analysis. These techniques are demonstrated using several realistic plane steel structures. With the help of the load space formulation, the FeketeNN method can achieve accurate estimates of the system failure probabilities efficiently.
Title: On Estimating the Error in Stochastic Model-Based Predictions
In the rational prediction of the behavior of physical systems, models are often relied upon. These predictive tools are calibrated in terms of parameters, on the basis of data. A recurrent phenomenon in this context s the random scatter in model parameters. Stochastic models have thus been developed, in which the parameters are treated as a random entity. The probabilistic characterization of the parameters is often hampered by practical limitations and induces inaccuracies in the stochastic predictions of the response.
This thesis reports a novel methodology to estimate the error in stochastic model-based predictions. It relies on the response representation in a Polynomial-Chaos basis. The error is approximated via Taylor expansion and thus hinges on the explicit computation of the stochastic response gradient. The computed error estimate sheds light on the sensitivity of particular response statistics with respect to statistics of the stochastic parameters. This helps to raise the confidence in the model predictions.
The method is demonstrated on two model problems, involving a Bernoulli beam with random bending rigidity and the potential flow in a porous medium with random conductivity. In both cases the parameters are modelled as a random field and are discretized with the Karhunen-Loeve expansion. The finite element method is used for the spatial discretization.
Title: Cross-Anisotropic Behavior of Granular Materials under Three-Dimensional Loading Conditions
This dissertation presents results of an experimental and theoretical investigation of the cross-anisotropic behavior of gravitationally deposited sands under general three-dimensional loading conditions.
The laboratory study included a series of cubical triaxial tests using a true triaxial apparatus with improved accuracy of measurements and control. The cubical tests were performed on Santa Monica beach sand under general stress conditions allowing for exploration of the entire range of Lode's angles [0°, 180°], necessary for complete description of a cross-anisotropic material. Stress-strain behavior and strength, failure patterns and shear banding, volumetric response and dilative properties were analyzed in view of the inherent material anisotropy.
A series of high-pressure isotropic compression tests were performed on Santa Monica beach and Nevada sands using four different densities and two specimen deposition methods. The evolution of the inclination of the plastic strain increment vector to the hydrostatic axis with pressure was evaluated and analyzed using different elastic models.
A principle of rotation of the principal stress coordinate system to account for the experimentally observed transverse isotropic effects was introduced. A cross-anisotropic constitutive model was derived based on the existing model for isotropic materials. A thorough analysis of response of each component of the modified model was performed. The new model was implemented to predict the results of the cubical triaxial tests producing good fits with the experimental data.
Title: Resource Allocation for Complex Systems in the Presence of Uncertainty
The objective of the present work is to quantify and manage the confidence in model-based predictions associated with complex systems as exemplified by pollution transport in a watershed system. A probabilistic framework is adopted for representing uncertainty and a constrained optimization problem is posed, the solution of which provides the strategy for resource allocation that will maximize the target confidence. The hydrologic cycle, which involves multi-physics phenomena, is the driving force behind the transport of pollutants in the watershed. Mechanisms for pollutant transport which are addressed in this work include surface runoff and advection in streams and rivers. These different modes of transport when coupled together form an integrated transport model for a given watershed. The thesis addresses the flow of data and information between the components making up this model. Given the nature of this problem which features natural variability and complex boundary conditions, the properties of the parameters of the sub-models are modeled as spatially, and sometimes temporally, varying random processes. The Karhunen-Loeve expansion is used to represent these processes in terms of a denumerable set of random variables. Then, as a result, the predicted state variables are identified with their coordinates with respect to a basis formed by the Polynomial Chaos random variables. Once the coefficients in the Polynomial Chaos representation have been computed, a complete probabilistic characterization of the state variables processes can be obtained. It is worth noting that a treatment to the interaction across the interfaces of the sub-models is essential for the proper analysis of the propagation. An optimization algorithm scheme is then developed that incorporates budget constraint component, while minimizing the uncertainty of the final prediction by selectively reducing the uncertainty of the input parameters. The thesis makes original contributions to the computational modeling of integrated uncertain systems and to the management of uncertainty in the associated predictions.
Title: Wave-Induced Migration of Grounded Ships
An improved understanding of the behavior of ships after running aground could lessen the environmental and economic damage caused by ship groundings. Wave forces often push grounded ships towards the beach, sometimes so far ashore that they become unreachable by salvage vessels. An estimate of the distance a grounded ship may migrate in a given time would help ship owners, insurers, and government officials make critical decisions in the initial hours after a ship grounding. The present study analyzes linear and nonlinear grounded ship motions, both experimentally and theoretically. Experiments were conducted to measure the motion response of an embedded ship hull at model-scale to both small-amplitude and solitary waves. The predicted oscillatory motion responses, based upon prior theoretical work on the linear motion of grounded ships, are compared to results from the small-amplitude wave experiments. A new method is presented to predict the distance a grounded ship will migrate ashore in a given time. This method shows good correlation with the migration distances observed in the solitary wave experiments.
Title: Modeling the Vibrations of a Stay Cable with Attached Damper
Many cable-stayed bridges around the world have exhibited excessive wind-induced vibrations of the main stays, inducing undue stresses and fatigue in the cables. To suppress these vibrations, fluid dampers are often attached to stays near the anchorages. To enable effective and economical design of such dampers, it is important to develop a thorough understanding of the dynamics of a stay cable with attached damper.
To investigate the dynamics of the cable-damper system, a fairly simple model is first considered: a taut string with linear viscous damper. An analytical formulation of the free vibration problem is used to explore the solution characteristics, revealing that damper-induced frequency shifts play an important role in characterizing the response of the system due to the concentrated nature of the damping force. A critical value of the damper coefficient is identified, and for a supercritical damper, certain modes of vibration are completely suppressed, while others emerge, including a non-oscillatory decaying mode.
The influence of bending stiffness is considered using a dynamic stiffness formulation of the free-vibration problem for a tensioned beam with attached damper. Many of the solution characteristics observed in this case are reminiscent of those for the taut string, and damper-induced frequency shifts are again important. The nature of the boundary conditions has a significant effect when bending stiffness is appreciable, and for a damper located near the end of a tensioned beam, significantly higher damping ratios can be achieved if the supports are not fixed against rotation.
Dampers can also have nonlinear characteristics, either unintentionally or by design, and equivalent linear solutions are developed for the vibrations of a taut string with two different types of nonlinear dampers: a power-law damper and a viscous damper with a friction threshold. Relevant nondimensional parameter groupings are identified, and asymptotic approximations are obtained relating these nondimensional parameters to the modal damping ratios for cases when the damper-induced frequency shifts are small. The nature of the dependence of nonlinear damper performance on the amplitude and mode of vibration is investigated, revealing some potential advantages that may be offered by a nonlinear damper over a linear damper.
Title: Fragility Analysis of Concrete Gravity Dams
Concrete gravity dams are an important part of the nation's infrastructure. Many dams have been in service for over 50 years, during which time important advances in the methodologies for evaluation of natural phenomena hazards have caused the design-basis events to be revised upwards, in some cases significantly. Many existing dams fail to meet these revised safety criteria and structural rehabilitation to meet newly revised criteria may be costly and difficult. A probabilistic safety analysis (PSA) provides a rational safety assessment and decision-making tool managing the various sources of uncertainty that may impact dam performance. Fragility analysis, which depicts the uncertainty in the safety margin above specified hazard levels, is a fundamental tool in a PSA.
This study presents a methodology for developing fragilities of concrete gravity dams to assess their performance against hydrologic and seismic hazards. Models of varying degree of complexity and sophistication were considered and compared. The methodology is illustrated using the Bluestone Dam on the New River in West Virginia, which was designed in the late 1930's. The hydrologic fragilities showed that the Bluestone Dam is unlikely to become unstable at the revised probable maximum flood (PMF), but it is likely that there will be significant cracking at the heel of the dam. On the other hand, the seismic fragility analysis indicated that sliding is likely, if the dam were to be subjected to a maximum credible earthquake (MCE). Moreover, there will likely be tensile cracking at the neck of the dam at this level of seismic excitation.
Probabilities of relatively severe limit states appear to be only marginally affected by extremely rare events (e.g. the PMF and MCE). Moreover, the risks posed by the extreme floods and earthquakes were not balanced for the Bluestone Dam, with seismic hazard posing a relatively higher risk. Limit state probabilities structural damage are much larger than the "de minimus" risk acceptable to society, and further investigation involving benefit-cost analyses to assess the risk posed by the Bluestone Dam appears warranted.
Title: Three-Dimensional Discrete Element Method Analysis of Cohesive Soil
The macroscopic engineering properties of soil depend on microstructure features of the soil: mineral constituent of individual soil particles, pore fluid chemistry and particle arrangements. Due to the small size of clay particles, physico-chemical interactions, mainly double-layer repulsive interaction and van der Waals attractive interaction, between clay particles are as important as mechanical interactions. This thesis attempts to study the three-dimensional behavior of cohesive soil from the microstructure point of view with the help of the discrete element method.
Rational and practical procedures to calculate the double-layer repulsive force and van der Waals attractive force between two cuboid clay particles in three-dimensional space are developed. Using cuboids to represent clay particles, a three-dimensional discrete element method program for cohesive soil is developed.
One-dimensional compression of kaolinite assembly is simulated using a randomly generated 400-particle numerical assembly. The discrete element program is capable of capturing the representative trend of the compression behavior in terms of compressibility and anisotropy. Quantitatively the numerical results are in the same range of laboratory experimental results.
A preliminary study of the influence of pore fluid chemistry on the behavior of cohesive soil is conducted using the discrete element method. Results from a change of wall pressure as well as the number of mechanical contacts are presented.
Title: Efficiency of Simulation-Based SFE Structural Analysis: Modeling and Solution Issues
Many engineering systems have parameters that demonstrate significant random variation in space or in time. The stochastic finite element method (SFEM), which incorporates the uncertainty of system parameters into the finite element formulation, has become a powerful tool in analyzing complex engineering problems. The commonly used lower-order perturbation-based SFE analysis is often limited to linear or mildly nonlinear problems with small variability. Simulation-based SFE analysis is more flexible, and is applicable to virtually all types of problems. However, the efficiency of simulation-based SFE analysis is a research issue due to the computational cost of the repetitive FE analyses involved in the simulation.
The need to properly model system uncertainties gives rise to many of the numerical difficulties in a simulation-based SFE analysis and such models must be developed to achieve computational efficiency. This study addresses the effect of uncertainties on the modeling and solution of stochastic problems from a different perspective by identifying characteristics introduced by the uncertainties that can be utilized to improve the efficiency of the SFE structural analysis. Stochastic ensemble averaging was found to have a positive impact on the efficiency of the calculation of lower-order response statistics by enabling the use of coarser mesh and/or larger time steps in SFE analyses. The process of selecting proper initializations for random samples and using the solution of the closest neighboring sample as the initialization. A computationally efficient method based on a sample tree data structure was developed to implement this optimal initialization strategy. These methods were applied in stability and modal analyses of random beam and frame structures. While uncertainty often introduces numerical complexity, it also has features that, when considered appropriately, can alleviate the numberical difficulty and improve the overall efficiency of a stochastic analysis.
Title: Modeling the Mechanical Interaction between FRP Bars and Concrete
In recent years there has been an increased interest in applying fiber-reinforced polymer (FRP) reinforcing bars for concrete, as an alternative to steel reinforcing bars. The mechanical interaction between the FRP and the concrete, commonly called the bond behavior, is not well understood and has a significant effect upon the structural behavior of FRP-reinforced concrete. While many experimental bond studies have been conducted for a variety of different bars, modeling efforts to both quantify the underlying bond mechanisms and the resulting behavior have been very limited.
Smaller scale (rib-scale) models explicitly represent the surface structure of the bar and can thus be used to characterize the underlying mechanisms associated with the mechanical interlocking and to help optimize the surface structure of a bar. Existing rib-scale models have not addressed the progressive failure of the constituent materials, an issue addressed in this study. There is also a need to model the bond behavior of these bars at a scale amenable to the analysis of structural components. Existing "structural models" do not have sufficient generality to meet this objective since they do not address the dependence of the behavior upon the stress state or allow multiple failure modes (pullout and splitting) to be predicted -- the other main issue addressed in this study.
An intermediate scale model (a bar-scale model originally developed for steel bars) is modified and applied to the bond of FRP bars. The model provides a macroscopic characterization of the bond behavior within the mathematical framework of elastoplasticity theory. The model incorporates a non-associated flow rule and elastoplastic coupling. Calibration and validation results for nine pullout specimens and one transfer length specimen demonstrate the model's ability to predict the bond strength and suggest that the model has a measure of generality.
Rib-scale models for several specimens are developed to represent the mechanisms that produce the bond behavior. A micromechanical model using the method of cells is developed for the FRP. An elastoplastic-damage model within the framework of continuum damage mechanics is developed to characterize the plastic and damage behavior of the matrix and fibers. A simple adhesion model is developed to represent the fiber-matrix interaction. The rib-scale models are able to reproduce the bond strengths of three independent experimental studies with acceptable accuracy. The predicted failure modes and surface structure damage are consistent with experimental observations.
Author: David Robert Burke Kraemer
Title: The Motions of Hinged-Barge Systems in Regular Seas
Harnessing the oceans' vast, clean, and renewable energy to do useful work is a tempting prospect. For over a century, wave-energy conversion devices have been proposed, but none has emerged as a clearly practical and economical solution. One promising system is the McCabe Wave Pump (MWP), an articulated-barge system consisting of three barges hinged together with a large horizontal plate attached below the central barge. Water pumps are driven by the relative pitching motions of the barges excited by ocean waves. This high-pressure water can be used to produce potable water or electricity.
A simulation of the motions of a generic hinged-barge system is developed. The equations of motion are developed so that the nonlinear interactions between the barges are included. The simulation is general so that it can be used to study other hinged-barge systems, such as causeway ferry systems or floating airports. The simulation is used to predict the motions of a scale model that was studied in wave-tank experiments. In the experimental study, it was observed that the plate attached to the central barge acted as a pendulum. It was also observed that the phases of the pitching motions of the barges was such that the motions were enhanced by the pendulum effect at all of the wave periods studied. Hence, the increased angular displacements produced greater relative pitching motions which would lead to higher volume rates of pumped water in the operational system. The numerical simulations are found to predict the pendulum effect. In addition, the theory predicted that the after barge motions were significantly less than those of the forward barge, as was observed in the experimental study. The good agreement between the two data sets gives confidence in the ability of the theory to predict the performance of the MWP prototype.
The motions of the MWP prototype in regular ocean waves are predicted by the simulation, and its performance is calculated. By modifying the length of the system to be compatible with the wavelength for maximum pitching excitation, the power output of the system is shown to increase by more than 150%.
Title: The Value of Information in Structural Performance Assessment
The need for improved procedures for civil infrastructure management has prompted a great deal of research in global structural condition assessment in recent years. In theory, global methods can identify damage in structures based upon changes in a small set of structural parameters obtained from full-scale measurements. Despite the fact that many new damage detection methods are being proposed, there remains a need for an objective means of estimating the utility of these new techniques.
Using a systems-based approach, a rational means was developed for evaluating the utility of structural condition assessment techniques. The approach considers both the engineering and the economic merits of damage detection methods in a unified fashion, in order to assess the value of the information that a given technique can provide to the management decision process. A Partially Observable Markov Decision Process (POMDP) provided a computationally tractable modeling framework that was readily adapted to this problem.
The POMDP modeling framework was applied in two application examples. The first example, which consisted of a hypothetical highway bridge system, demonstrated that a damage detection method must exceed a threshold of utility such that the information it provides can effect a noticeable change on management policy. The second example was a prototype problem designed to highlight each of the modeling tasks involved in applying the POMDP framework to a structural management problem. The following features were included: (1) mathematical descriptions of the dynamic mechanisms that influence the evolution of a structure, such as resistance deterioration, loading, and maintenance, (2) a means of probabilistically relating observations of damage and the resistance of a structure, and (3) a means of characterizing costs associated with inspection strategies and maintenance activities. As part of this example, a quantitative approach for assessing the expected value of information provided by damage detection measurements was demonstrated. several important lessons were learned from the application examples regarding the balance that must be achieved between accuracy and cost before a damage detection method can be considered worthy of implementation. Many of the conclusions drawn herein can be extended to systems of greater complexity.
Author: Carl Donald Liggio, Jr.
Title: Experimental Study and Modeling of Instability and Time Effects of Granular Materials
This study presents the results of experimental and numerical investigations of two factors that affect the conditions for stability and instability of granular materials. These are (1) imposed volume changes and (2) time-dependent behavior. These factors are studied in triaxial compression tests and are modeled by an existing single hardening constitutive model.
The effects of imposed volume changes on the instability of granular materials are studied in experiments on a fine sand in which water is forced into or out of a sand specimen during shearing. The effects on stress-strain behavior and stability are recorded and discussed. Specimens forced to dilate more than desired in a standard drained test exhibited a tendency toward unstable behavior. Specimens forced to contract more than desired exhibited a tendency toward stable behavior. The conditions of imposed volume changes are then simulated with a single hardening constitutive model and compared with the experimental results. It is shown that the model can predict the corresponding loading paths and sand behavior as well as the resulting stable and unstable conditions.
The experiments conducted for investigation of time effects were performed on a crushed coral sand. The testing series involved shearing at different strain rates as well as jumps between strain rates, creep and relaxation tests, and stress drop tests followed by constant stress creep or constant strain relaxation tests. The experimental results are presented and discussed as a basis for development of a time-dependent version of the single hardening model. It was found that correspondence between creep and relaxation does not necessarily exist.
Title: Analytical and Computational Modeling of the Mechanical Interlocking between Steel/FRP Reinforcing Bars and Concrete
Mechanical interaction (commonly called bond) between concrete and reinforcing bars significantly affects the structural response of reinforced concrete. This study addresses modeling issues for the bond of steel and fiber-reinforced polymer -- FRP bars. Two analysis scales are examined: the rib-scale (where the surface structure of the bar is often explicitly modeled) and the bar-scale (where the surface is idealized as smooth and an interface idealization is adopted). The study's main objective is to better understand how contact between concrete and a bar with a fabricated surface structure affects the radial elastic response and how these effects can be incorporated into bar-scale models. A limited modeling study on the local crushing near the ribs of a bar is also presented.
Experimental or analytical justifications for the radial elastic modulus (Ďe) of a bar-scale model do not exist, yet Ďe is important toward predicting bond behavior and splitting failures. A proposed analytical framework defines Ďe as characterizing the local elastic deformation resulting from mechanical interlocking. The approach enforces static and strain energy equivalencies of rib- and bar-scale idealizations. Assuming axisymmetric elastic behavior, homogeneous materials, and periodicity, closed-form analytical solutions are obtained for Ďe. Ďe's dependence on interface traction distribution, material constants and bar geometry is studied for steel and FRP bars. Ďe increases with the contact area but remains finite for full contact (assuming a nonuniform traction). For FRP bars, Ďe reproduces the radial snap-back behavior that occurs with longitudinal cracking, which helps explain the splitting behavior of some test specimens and the convergence problems in some numerical studies. For a steel bar Ďe is incorporated into a bar-scale model via a local contact model which leads to improved prediction of the radial response.
Elastoplastic constitutive relations are adopted and implemented in a rib-scale analysis to simulate the local crushing behavior near the surface structure of a bar. Numerical examples show how the crushing is concentrated near the surface structure. For a given axial load, crushing is predicted to decrease with an increase in the level of specimen confinement stress due to frictional response along the remainder of the interface.
Title: Limit Loads on Soil Media and Collapse of Soil Slopes
Slope failures, landslides and foundation failures frequently result in a significant destruction to properties. This severity raises much interest among researchers to develop methods to achieve satisfactory assessment of the danger of slope failures and foundation collapse.
Collapse mechanisms of strip footings under non-symmetrical loads were introduced and the kinematic approach of limit analysis was used to analyze the bearing capacity on footings. Inclination coefficients for surface strip footings were derived. These coefficients fit the numerical limit analysis results better than coefficients suggested earlier in the literature. The seismic effect on limit loads is also investigated. The influence of interface models between foundation and soil on bearing capacity is studied.
The stability of both uniform and reinforced slopes subject to earthquake loading was studied. The method to calculate permanent displacement of slopes under real earthquakes was developed. Displacement charts for design were developed for different earthquake levels. With these a displacement criterion rather than the factor of safety could be developed for future slope design. A limit analysis approach is applied to determine the amount of reinforcement necessary to prevent collapse of slopes due to reinforcement rupture, pullout, or direct sliding. The length of reinforcement is also calculated and both reinforcement pullout and direct sliding are accounted for. Design charts for both the required reinforcement strength and its length under different earthquakes were also produced.
Title: Regional Seismic Risk Analysis for Multi-Story Structures
Over the years, earthquake damage and the resulting catastrophe insurance losses have motivated numerous structural damage analysis studies. However, previous models tended to rely on experts’ opinions or nonphysical parameters to qualitatively estimate damages. Even in cases where quantitative estimates were conducted, the number of parameters used remained limited. The study herein, examined a stochastic, regional model that engages the mechanistic parameters of ground motion and structural response, expanding its applicability to multi-story steel and reinforced-concrete frame structures. Also, the statistical investigation and presentation of results was conducted in terms of a collection of structures which enabled the examination of standard deviations in addition to mean results for groups of varying composition.
To investigate the capabilities of this newly expanded model, simulations of the Northridge earthquake were run for four, five, six, and seven-story reinforced-concrete and steel frame structures located on soft soil sites in the City of Los Angeles. In comparison with loss data collected after the actual event, the model represented damages suffered by a group of structures mostly within one or two standard deviations, suggesting that it reasonably reflects losses to these classes of structures. Although further studies are needed, the successful results of the study presented herein, in conjunction with a previous study conducted by Liu (1995) on wood-frame residential structures, insinuate, that with the proper input of parameters, other types of structures may be modeled as well.
Title: Wavelet Analysis and Multi-Scale Pattern Classification in Wind Engineering
Wavelet analysis was used to develop a multi-scale pattern detection and classification algorithm for intermittent time series, which are characterized by large transients separated by relatively quiescent periods. The detection algorithm is based on the dyadic wavelet transform, in which regions of sharp change in the signal are detected as having locally large wavelet coefficients that are contiguous across two or more dyadically-spaced wavelet scales at a given time index. Empirically-devised criteria are used to determine if the detected edge forms a boundary of a given transient or falls between other local edges, such that it is part of a longer transient. Traditional self-organizing pattern classification techniques, which cluster patterns into classes based on their similarity in feature space, were used to enable the detection of underlying structure in the observed transients. The resulting algorithm was tested successfully using time series consisting of artificial patterns and white noise. Then, roof-corner pressure measurements from Texas Tech University were processed to explore the applicability of multi-scale pattern detection and classification to field data. Finally, synthetic time series were constructed based on the patterns extracted from one of the pressure signals. These time series are expected to be useful as excitation inputs to computational structural models in parameter studies.
Title: Seismic Reliability Evaluation of Steel Frames with Damaged Welded Connections
The numerous brittle failures observed in welded beam-to-column connections during the 1994 Northridge earthquake have raised questions and concerns about the seismic performance of welded special moment-resisting frame (WSMF) steel structures. Four WSMFs of different sizes and configurations that suffered connection damage in the Northridge earthquake are evaluated using both deterministic and stochastic approaches. In the deterministic approach, a new degraded hysteretic connection model which incorporates the effects of brittle weld failure is developed based on experimental data. Nonlinear dynamic time domain analyses of these four WSMFs are performed using ground motions representing the Northridge earthquake, and predicted behavior is compared with the actual damage observed. In the stochastic approach, an analysis of variance is performed with respect to the parameters in the degraded hysteretic connection model and the stochastic earthquake ground motion. A detailed uncertainty analysis is conducted for one of the four buildings, and probability distributions of maximum roof displacement angle and maximum inter-story drift angle are constructed. Results using degraded and bilinear connection models are compared. Building fragilities are constructed and are convolved with the seismic hazard to evaluate the reliability of the building; these results compare favorably with independent findings from concurrent research on aseismic design of steel buildings.
Title: A Damage Mechanics Based Approach to Structural Deterioration and Reliability
Structural deterioration often occurs without perceptible manifestation. However, the existing methods of modeling structural deterioration usually need measurable flaws to be applicable. Moreover, the existing methods of predicting service life are mostly empirical in nature and are generally unable to provide estimates of residual strength of a degrading structure.
Continuum damage mechanics (CDM) defines structural damage in terms of the material microstructure, and relates the damage variable to the macroscopic strength parameters of the structure. This enables one to predict the state of damage prior to the initiation of a macroscopic flaw, and allows one to estimate residual strength/service life of an existing structure.
The accumulation of damage is a dissipative process that is governed by the laws of thermodynamics. Partial differential equations for damage growth in terms of the Helmholtz free energy are derived from fundamental thermodynamical conditions. Closed-form solutions to the equations are obtained under uniaxial loading for ductile deformation damage as a function of plastic strain, for creep damage as a function of time and for fatigue damage as function of number of cycles. The proposed model uses only readily available material parameters. The proposed damage growth model is extended into the stochastic domain by considering fluctuations in the free energy, and closed-form solutions of the resulting stochastic differential equation are obtained in each of the three cases mentioned above. A reliability analysis of a ring-stiffened cylindrical steel shell subjected to corrosion, accidental pressure and temperature is performed.
Title: Numerical Calculation of Bluff Body Flutter Derivatives via Computational Fluid Dynamics
With the immense leap in computational speeds in the recent past, numerical experiments are fast maturing as a viable complement, if not an alternative, to wind tunnel investigations to study the various aerodynamic and aeroelastic phenomena. The central focus of the present study is the numerical calculation of flutter derivatives-- fluid force coefficients associated with body oscillatory motions. These aeroelastic coefficients play an important role in determining the stability or instability of long, flexible structures under ambient wind loading.
Flutter derivatives are obtained most directly by simulating cross flow across an oscillating bluff body and comparing the unsteady lift and moment forces thus determined with theoretical expressions for the same written in terms of flutter coefficients. For a numerical simulation, such an approach would entail internal boundary motion in the flow, which requires considerable computational effort in case of most Eulerian non-adaptive grid-based schemes. An alternate approach to calculation of flutter derivatives using indicial functions has been proposed in the present study. In this approach, flutter derivatives are obtained analytically from step-start flow definitions that elicit indicial or impulse response functions for the unsteady lift and moment forces. These transient responses are obtained via numerical simulation. In recent years, the finite element method (FEM) has gained considerable acceptance in the solution of problems governed by the viscous, incompressible flow equations. FIDAP, one such general fluid dynamics analysis package that employs the finite element methodology, has been used to simulate flow circumstance that produce the above-mentioned indicial responses for a variety of bluff sections.
FEM is based on an Eulerian formulation of the governing equations. For moderate-to-high Reynolds number flows, convection often dominates and the grid points required to simulate the flow can be computationally prohibitive. Vortex methods, on the other hand, offer an efficient way to track vorticity in convection dominated regions of an external flow, while grid-based finite difference schemes provide the flexibility and accuracy to capture the viscosity dominated regions of the flow. Therefore, a hybrid finite difference - vortex method flow solver has been devised in this study for two-dimensional flow across bluff sections. For calibration purposes, the bluff body of primary focus is chosen as a square cylinder. Development along these lines, internationally, is still in a nascent state. The coupled solver developed in the present study employs an Eulerian finite difference grid in the viscous region next to the bluff section boundaries and a Lagrangian vortex particle domain in flow regions away from the boundaries. Results of this portion of the study match selected results from the recent literature
Title: Limit Behavior of Fiber-Reinforced Granular Soils
Fiber reinforcement of granular materials (e.g., soils) has been tried recently as an alternative method to a traditionally engineered reinforced soil mass. Here, the micromechanics of the fiber composites is investigated. The friction decaying on the fiber-matrix interface is discussed, and it is shown to lead to a possible fiber snap-back.
Failure criteria for both isotropic and anisotropic fiber-reinforced granular soils are developed using an energy-based homogenization method. The matrix cohesion and fiber-matrix interface adhesion effects on the isotropic failure criterion are investigated.
Triaxial tests on fiber-reinforced sand specimens were performed to verify the approach used in the failure analysis. A variety of composite parameters and stress magnitudes was used to find out their effect, on the macroscopic behavior of the specimens.
The macroscopic failure stresses predicted using the criterion developed compare favorably with actual results from tests on fiber-reinforced soils. Some composite specimens exhibit kinematic hardening, which can be attributed to a change in the configuration of fibers during the deformation process. An analysis capturing the hardening effect is described, and the failure stresses calculated are compared with experimental results.
The anisotropic failure criterion for fiber-reinforced soils is implemented in solutions to boundary value problems using the slip-line approach.
Title: An Analytical Study on Flutter and Buffeting of The Akashi-Kaikyo Bridge
Flutter and buffeting are both issues of utmost concern in the wind-resistant design of long-span bridges. These aeroelastic phenomena are usually investigated by wind tunnel testing and/or an analytical approach. Since multi-mode behaviors have been reported with increased center-span length of bridges, considering the coupling effect among modes is necessary, and therefore wind-tunnel testing with an aeroelastic full-model or a multi-mode analysis method is desirable.
In this essay, multi-mode flutter and buffeting response of the Akashi-Kaikyo Bridge, which will be the world’s longest suspension bridge with a center span of 1990m, were analyzed, and the analytical results were compared with wind-tunnel test data. The multi-mode flutter analysis was in good agreement with the measurements, and there was a significant coupling among modes. The multi-mode buffeting analysis also showed excellent agreements between the analysis and measurements in vertical and torsional response. However, the analysis overestimated lateral response. Significant coupling among modes was also observed in the buffeting analysis, and the multi-mode analysis predicted the measurement better than an equivalent single-mode analysis method.
Title: System and Excitation Identification for Large Structures
With the building of large yet flexible structures from long-span bridges to high-rise buildings, improved understanding of dynamic characteristics become essential for design and analysis. Because of the complexity of modern structures, full-scale measurement is the only assured way to determine model parameters. One of the most popular techniques is the ambient vibration survey in which ambient sources such as wind and traffic loadings serve as the excitation. Common problems encountered in the ambient vibration survey are that the input excitation is generally unknown and the measurement of structural response is corrupted with ambient noise. Certain analysis assumptions including locally white noise input, have been made. Improper treatment of input excitation, however, may strongly affect the accuracy of system parameters identification, and the excitation itself (e.g., wind excitation on a long-span bridge) may be of interest in the general context of structural dynamics.
System identification techniques have been recently applied to structural identification problems. The Kalman filter, which incorporates both model and measurement uncertainties to achieve optimal estimate of state variables with minimum error covariance matrix, becomes a natural choice to address the problem of simultaneous identification of system and excitation characteristics from measurement alone. An extended Kalman filter algorithm is implemented for structural identification problems formulated in the frequency domain. The new algorithm is formulated for both discrete and continuous systems. Numerical simulations, laboratory experiments as well as field measurements are used to demonstrate the accuracy, reliability and robustness of the proposed method. Parameter studies have also been conducted to reveal the effect of Kalman filter parameters on the performance of the algorithm.
Title: A Characterization of Dynamical Systems Using Wavelets
In this essay a method for assessing the evolution of the behaviour of a structural system based on the knowledge of input-output, data is presented. In particular, the identification of the parameters involved in the differential equation governing dynamical systems is addressed. The study is carried out within the mathematical framework of wavelet theory. Given the mathematical model, the first step of the procedure consists of expanding the input and output signals in terms of wavelet bases. Then, according to the Galerkin scheme, the error associated with the expansion is forced to vanish on the subspace spanned by the chosen basis. Once the problem is reduced to an algebraic expression, the equations are rearranged in order to be solved for the unknown parameters. Firstly, the simple case of linear time invariant systems is discussed. Damping and stiffness are shown to be estimated in a straightforward manner solving for any pair of the above mentioned set of equations. Then, systems with time varying parameters are dealt with. Smooth and abrupt variation of the stiffness and damping parameters are investigated. The estimation can be carried out either considering the sequence of pairs of equations or adopting a minimization technique over subsets of sequential equations. To enhance the performance of the estimation technique, the algorithm is then modified expanding the time varying parameters in the wavelet domain. Systems characterized by material nonlinearity are addressed next. The Bouc-Wen model is selected in order to analyze hysteretic systems. The estimation is performed considering an equivalent piecewise linear elastic system. The possibility of noise corrupted signals is taken into account throughout the analysis. Finally, in analogy with the more common frequency domain approach, a time-frequency description of the evolution of dynamical systems is investigated by means of a time-varying transfer function.
Title: Experimental Determination of Aeroelastic and Aerodynamic Parameters of Long-Span Bridges
Determination of aeroelastic and aerodynamic parameters through wind tunnel investigations is an essential component of the aerodynamic modeling of bridges. With super-long span bridges being constructed and planned for future, the aerodynamic mechanisms have become even more complex than before. Recently developed multi-mode flutter and buffeting analyses have significantly advanced the capabilities of the existing analytical methods. However, availability of all the aerodynamic and aeroelastic parameters and other relevant descriptors is important for investigation of complex modal interactions and aeroelastic coupling expected in such long and flexible bridges.
A 3-DOF suspension system for wind tunnel section model tests was implemented and all the eighteen flutter derivatives were estimated for a streamlined (Tsurumi) and a bluff (Deer Isle) bridge deck sections. The experimentally obtained flutter derivatives were compared with those calculated using pseudo-steady approximations. The interrelations and approximate equivalences among the flutter derivatives of a low speed airfoil were analytically derived and the possibility of such interrelations among flutter derivatives of bridges was investigated. The sensitivity of aeroelastic parameters to seemingly small geometric changes was studied through a series of experiments on Tsurumi bridge by changing the modeling of its guard railings.
The buffeting forces on both the Tsurumi and the Deer Isle bridge deck section models were investigated in smooth and turbulent flow incoming conditions. The existing quasi-static formulation of buffeting forces was examined. Based on the observations of the effect of incident turbulence on the body-initiated or signature turbulence, a new approach to model buffeting forces and aerodynamic admittance has been suggested.
Title: Multi-Mode Aeroelastic and Aerodynamic Analysis of Long-Span Bridges
A fully coupled three-dimensional analytical model for the aeroelastic and aerodynamic analysis of long-span bridges has been developed. In the design stages it is important to be able to investigate the flutter stability, buffeting response, and vortex-induced response of a long-span bridge to wind excitation using rational and reliable procedures. These procedures must be able to estimate faithfully the response of the prototype, but allow for simple incorporation of the frequent changes that occur during the design process. The analysis procedure considers the effect of multiple modes of vibration acting simultaneously, in contrast with the single-mode approaches adopted in the past. This accounts for the complex modal interactions and aeroelastic coupling that can be expected in the superlong and flexible decks of suspended-span bridges being constructed or considered. Combined with results from a section-model test, the coupled analysis can yield valuable information on the suitability of a deck cross section and the structural configuration.
This dissertation outlines a procedure to compute the multi-mode aeroelastic and aerodynamic response of a long-span bridge to wind-induced excitation. This method was applied to evaluate the response of several long-span bridges and the results compared with those obtained from a single-mode analysis procedure. Results show that while in many cases the single-mode procedure is sufficient, in some cases consideration of the additional complexity provided by aerodynamic or aeroelastic interaction is essential.
Title: Reliability-based Optimization of Plant Precast Concrete Building Systems
A building is an investment made by owners in anticipation of some return on the investment. There are many trade-offs among initial manufacturing and construction costs, costs of recurring operations and maintenance, and building performance. The building process consists of several stages: planning, design, manufacturing, Construction and utilization. All stages should be considered in evaluating a building investment to obtain a result that is optimal for the entire process. In principle, decisions about a building‘s design, manufacturing, construction, operation. and maintenance ought to be made in such a way that the building meets all performance requirements over its service life and the total costs incurred over its life cycle are minimized. The completed building must have sufficient reliability against ultimate and serviceability limit states that are specified by the code. There is no assurance that current or proposed limit states design requirements are optimal from a minimum overall cost viewpoint. An improved basis for structural design would be obtained by relating safety and serviceability checking procedures to quality assurance programs for the building process so as to minimize the life cycle cost of structural components or systems. Realistic real life cycle cost data of plant precast concrete building systems are collected and analyzed in this research. Reliability-based life cycle cost analysis is used to assemble the existing information in a rational framework and to utilize it to improve design procedures for precast concrete elements. The decision model gives a more rational basis to the set of safety and serviceability checking requirements used in building design that result in minimum expected life cycle cost, subject to structural reliability and performance constraints.
Author: William Ralph Lewis, Jr.
Title: Dynamic Response of the Head in Boxing: Development of an Instrumental Helmet for Impact Measurements
In 1986, because of concerns and recommendations raised by the American Medical Association and other medical societies, the United States Olympic Foundation, at the request of the USA/Amateur Boxing Federation, approved and funded a proposal made by The Johns Hopkins Medical Institutions to develop a study on active amateur boxers. Other studies performed on amateur boxers conducted neurological tests to determine if boxing lead to brain dysfunction, but the studies had conflicting conclusions and all lacked quantitative data on what the head was experiencing during a bout. However, with the use of a regulation boxing helmet, the Hopkins’ study will be the first to capture head accelerations of amateur boxers during sparring and competition and use the quantitative data collected during a bout to compare with the neurological tests conducted on a boxer before and after a bout.
The research conducted for this essay involved developing and testing a prototype for collecting head acceleration data of amateur boxers during sparring. The prototype was tested at the Sugar Ray Leonard Gym in Landover, Maryland and 13 rounds of data were collected and then analyzed in the Department of Civil Engineering at the Johns Hopkins University. Calibration data was also collected in the Department of Bioengineering at the University of Pennsylvania using a side impact dummy to test the validity of the prototype. The prototype was constructed from a regulation boxing helmet.
In addition to the data collection, a proposed design for the future generations of the device was developed. The future device will be called HAT (Head Accelerometry Technology) and will be used to collect data for the Department of Epidemiology at The Johns Hopkins University School of Hygiene and Public Health to determine what accelerations cause particular head injuries. Although the direct application of the HAT is for boxing, it is certainly not limited to that sport: the HAT can easily be incorporated into any helmet.
Title: Experimental Study
of Stress-Strain and Shear Strength Behavior of Contaminated Cohesive Soils
Clay soils are commonly used as barriers in municipal or industrial waste sites to isolate ground water from contaminants. With migration of contaminated fluids, the pore water of the soil is replaced and the soil becomes contaminated. The changes in physico-chemical properties of pore fluid result in the changes in physico-chemical forces between clay particles. With the aid of existing theories on the double-layer repulsive force and the van der Waals’ attractive force, the net physico-chemical force between two clay particles immersed in a contaminant has been analysed.
As a consequence of the changes in interparticle physico-chemical forces, the geotechnical properties of a contaminated clay soil change. An experimental study has been conducted on kaolinite soil with nine organic chemicals as pore fluids and two inorganic salts as electrolytes. The test results have been compared to the theoretical analyses of interparticle forces. The mechanisms governing the behavior of a contaminated clay soil are examined based on the understanding of the relations between experimental results and analytical results concerning the interparticle physico-chemical forces.
Title: Frontiers in High Performance Computing in Finite Analysis
Two areas in high performance finite element analysis are discussed, those being
1. Finite element analysis on massively parallel and scalable supercomputers.
2. Finite element analysis using multi-time step integration schemes.
Both of these topics deal with speeding up finite element simulations. While speedup is achieved on a parallel computer by employing many CPUs concurrently on the problem, it is achieved by eliminating many computations in multi-time step methods.
High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. A methodology based on domain decomposition and force exchanges is discussed for implementing nonlinear finite element analysis on a homogeneously distributed processing network. The method can also be extended to heterogeneous networks.
Visualization techniques are developed to better understand the working of parallel algorithms and processor inter-dependency. Using these techniques, various bottlenecks are detected and their solution is discussed. Overall, performance exceeding 1 gigaflop is attained on the Intel Touchstone Delta. Due to many limitations of existing domain decomposition algorithms, a new mapping based algorithm is also developed and its effectiveness is discussed.
Over the last few years, subcycling methods have been proposed by many researchers. Such methods are typically used for meshes where critical time step is very small due to the presence of few small elements. A study is presented consisting of an accuracy analysis of subcycling schemes. The results of numerical experimentation are provided, and the error behavior of a mixed element mesh is compared with an acceptable upper bound (coarse mesh) and a lower bound (fine mesh) set of error values. In general, it is observed that a subcycling solution can decrease the accuracy otherwise achieved by a finer mesh. Further analysis shows that the use of these schemes for long simulation times can lead to instabilities in the solution. A frequency analysis is presented which shows spurious high frequencies being introduced into the solution due to subcycling. Applicability of damping is discussed for the explicit central difference method. Through numerical examples, the use of a proper amount of damping is shown to eliminate exponentially growing high frequencies.
Title: Regional Loss Estimation in Earthquakes
A new approach, which predicts the statistical distribution of the damage factor for a class of structure in an inventory by using simulated time histories of ground motion coupled with a realistic structural model, is proposed to estimate structural damage in earthquakes. The approach, while sensitive to the stochastic nature of the problem, attempts to model the physical underpinnings of the process in a manner which permits quantitative assessment of the uncertainties in each phase of the modeling process and enables evaluation of the sensitivity of the final estimates to these uncertainties. The approach is designed to reflect the incomplete nature of the knowledge available for some components, such as the structural properties of the inventory. It is therefore able to incorporate, in a physically and statistically consistent manner, additional quantitative information as it becomes available.
Case studies are presented which compare the calculated building loss with damage data for wood-frame residential buildings in the City of Watsonville affected by the Loma Prieta earthquake and in the City of Los Angeles affected by the Northridge earthquake. The ground motions are also generated from geophysical considerations and compared with those recorded.
From comparisons with observations of past earthquake damage, the modified damage factor and estimation procedure appear to reflect consistently the damage patterns in wood-frame structures. This newly defined damage factor can be ex-tended to other types of structures. The pattern of predicted damage captures in a meaningful way the distribution of damage observed in the past. The proposed model is able to treat loss estimation in different regions by changing parameters in the model.
Title: Identification of System Characteristics and Random Excitation from Output Measurements
Structural systems can be dynamically characterized by their natural frequencies, damping ratios, mode shapes and generalized masses. Identification of system characteristics can be accomplished using both input and output data from the system (e.g., in the case of earthquakes), or more conveniently (often in the context of wind engineering) by way of an ambient vibration survey. For buildings and bridges, however, only output measurements are possible under ambient vibration conditions. Under such circumstances, the input power spectral density is often assumed to be Gaussian white; the system parameters (e.g., natural frequencies and damping ratios) can then be estimated. These estimates are not reliable in the sense that the assumed input characteristics may be incorrect. Successful and reliable estimation of system dynamics properties of such structures is critical for the design of large structures, especially for dynamic (e.g., wind) loads. In this dissertation, a Kalman filter is applied to problems formulated in the frequency domain to estimate the dynamic characteristics (including confidence intervals), as well as the input excitation more reliably. The algorithm is presented, and its applicability is verified through several numerical examples and with controlled laboratory experimental
Title: Development of a Database of Aeroelastic and Aerodynamic Parameters for Long-Span Bridges
Since the flutter-induced failure of the Tacoma Narrows bridge in 1940, engineers have significantly developed their understanding of the physical mechanisms of the complex aeroelastic phenomenon which drove the Tacoma Narrows to collapse. One essential aspect of the modeling process remains strongly experimental in nature. Deck section-model wind-tunnel test has been employed worldwide to evaluate the aeroelastic stability of long-span bridges through estimation of the pertinent aeroelastic and aerodynamic parameters.
A bridge aeroelastic and aerodynamic parameter database developed in the present study provides the opportunity to conduct comprehensive critical comparison, assessment and interpretation of such data for a large number of bridge deck sections measured over the past decades. It is expected that the database will not only provide useful information as to the consistency and comparability of these data under different experimental conditions, but also help develop recommendations and guidelines for the selection of optimal cross sections for superior stability under wind.
Title: Ambient Vibration Survey and Finite Element Analysis of the Tacoma Narrows Bridge
The structural dynamic behavior of an existing suspension bridge can be used as a basis to determine the performance of the bridge under major excitation, and the stability and integrity of the structure. This information is important with respect to a major structure like the Tacoma Narrows Bridge, which is located in what is classified as a seismically active area and has a history of wind-related disaster.
The modes and frequencies of the structure can be determined by computer-aided finite element modelling and analysis. An ambient vibration survey provides a convenient verification of these results.
In September, 1993, a team from the Johns Hopkins University performed an ambient vibration survey (AVS) on the Tacoma Narrows Bridge as part of a full seismic retrofitting effort. The AVS data was compared to finite element models prepared by Arvid Grant and Associates, Inc. and OPAC Geospectra. Nine vertical and 12 lateral mode shapes were verified by the AVS data in the frequency range of 0.0 to 1.0 Hz.
A finite element model was also developed at the Johns Hopkins University. The frequencies and mode shapes from the model were consistent with the Arvid Grant and Associates and OPAC Geospectra results.
Title: Failure Criteria for Reinforced Soils and Analysis of Reinforced Soil Structures
The concept of improving soil by reinforcing it with long bars of tension-resisting material or large blankets of synthetic fabric (or geogrids) has been put into practice in the last three decades. Recently, soil reinforcement with short fibers and continuous synthetic filament has been tried and proved to have some advantages. As of yet, however, no techniques for design with such materials exist.
An attempt at describing the failure criteria for reinforced soil composites derived from the properties of the constituents is made. Two homogenization techniques are explored to derive the macroscopic failure conditions for unidirectionally and randomly reinforced soil composites. Triaxial compression tests were performed to find out how reasonable the proposed theoretical description is.
Two approaches to analysis and synthesis of reinforced soil structures are explored, one based on homogenization of the reinforced soil mass (continuum approach), and the second based on considering the soil and reinforcement as two separate structural elements (structural approach). The continuum approach was found to be more restrictive and less convenient than the structural approach. The structural approach, with the kinematical method of limit analysis as the solution technique, was found to be more convenient and more rigorous than the existing design techniques.
Title: Development of an Object-Oriented Program for Finite Element Self-Adaptive Mesh Refinement
A static linear elastic finite element program is developed using object oriented methods. The finite element code incorporates a self-adaptive algorithm for mesh refinement making use of an error estimator. Here h-type adaptivity is used which incorporates the error estimator based on nodal averaging of a gradient measure. This criterion works well for linear problems.
The role of data abstraction in finite element class design is based on the identification and separation of levels of concern in a finite element program. Since object-oriented languages provide linguistic support for data abstraction, the object oriented language C++ has rapidly gained acceptance in many scientific communities. It is used to model mathematical and numerical concepts such as vectors and matrices as well as higher level concepts such as graphs and elements.
Examples of using the resulting finite element program are demonstrated and directions for future research are discussed.
Title: A Neural Network Approach for Finite Element Domain Decomposition
The problem of domain decomposition for a parallel implementation of finite element analysis is discussed. It is posed as an unconstrained optimization problem with an objective function that has penalty terms for load imbalance and non-zero inter-processor communication. An approach similar to that for the traveling salesman problem is used to apply a Hopfield network to the minimization of the model’s objective function. This yields a decomposition of the problem domain directly into m subdomains as opposed to some neural network based approaches, as well as other conventional ones, which rely on recursive graph bisection. The problem model is mapped onto a graph, which allows for the methods of graph partitioning to be applied. Results are presented for a set of test cases. The method is found to perform successfully for the set of example problems tested. Limitations and directions for future research are outlined.
Title: STRUCTURAL SYSTEM RELIABILITY: A Study of Several Important Issues
Three important issues in structural reliability analysis and design are studied in this thesis.
A prerequisite for reliability-based code calibration is the ability to compute modal failure probabilities. Three definitions for model failure probability which are currently used by engineers, explicitly or implicitly, are shown to yield quite different results. A methodology based on mathematical programming techniques is proposed to identify systematically the dominant failure modes of a complex structure when the loads are stochastic processes.
Despite the inherent advantage of providing an upper bound on the system failure probability, Pf, the static approach for reliability analysis of rigid-plastic structures has received very limited attention compared to the kinematic approach. The static approach is studied in detail, with particular attention given to its relationship to the kinematic approach. A mathematical programming algorithm is developed to compute an upper bound for Pf. Many properties of this bound observed from numerical examples are readily explained in the basic variable space and the redundant force space. Guidelines on selecting the best starting points and redundant forces are also proposed, two of which are of particular interest. One relates to the equivalence of two redundant force sets, and the other to the possibility of obtaining better results using multiple redundant sets.
As a step toward the goal of developing general reliability methods for load path-dependent problems, some fundamental concepts such as limit state surface are recast in the context of load path-dependency. New concepts are introduced to help in the understanding of path-dependent reliability problems.
Title: Preliminary Study of the Pointing Control System for the Next Generation Space Telescope
The pointing control system of the Hubble Space Telescope (HST) represents the current state-of-the-art for the precision control of a large spacecraft. The proposed Next Generation Space Telescope (NGST) will require an order-of-magnitude increase in pointing resolution over that of HST. The use of active optics in the form of a steerable secondary mirror has been proposed for NGST in order to satisfy this requirement.
The pointing control system of this telescope relies entirely on the attitude information provided by the position of a guide star, so the sampling rate is limited by the amount of light from the star which is collected by the telescope. The primary motivation for this essay is to demonstrate the feasibility of satisfying the pointing-stability requirements by sensing the guide star position and steering the optical path of the telescope with the active secondary mirror.
In order to study the requirements of the control system, a two-degree-of-freedom model which retains the rigid-body mode of the telescope as well as its first oscillatory mode is constructed. The corresponding optimal control law is developed and implemented in a discrete manner to examine the behavior of the system subject to typical spacecraft excitations.
Title: Reliability-Based Condition Assessment and Life Prediction of Concrete Structures
Concrete structures may be exposed to aggressive environmental effects that cause their load capacity to decrease over an extended period of service. If a safety assessment of such structures were to be performed to evaluate the possibility of continued service, a major concern would be to ensure that in their current condition they are able to withstand future extreme load events during the intended service life with a level of reliability sufficient for public safety. Methodologies to perform this assessment currently do not exist. A methodology is proposed to facilitate quantitative assessments of current and future structural reliability and performance of concrete structures. This methodology takes into account the nature of past and future loads, randomness in strength and in degradation resulting from environmental factors. Changes in engineering properties of steel and concrete over the service life are identified. An adaptive Monte Carlo simulation procedure is proposed to evaluate time-dependent system reliability. The sensitivity of the reliability to various parameters describing load occurrence and strength degradation is illustrated. The reliability is sensitive to the choice of initial strength and strength degradation models. Less sensitivity is found to correlation in component strengths within a system. It is important to identify the critical components before performing system reliability analysis so that the size of the analysis can be reduced.
The evaluation of time-dependent reliability and deterioration of concrete structures provides a basis for selecting appropriate periods for continued service and/or for determining optimum intervals and extent of inspection and maintenance. Inspection/maintenance strategies are identified that minimize the expected future cost keeping the failure probability at or below an established target failure probability during the lifetime of a structure. Needs for additional data, to allow the reliability models to be fully implemented as a decision tool are identified.
Author: Sarah Elizabeth Mouring
Title: Dynamic Response of Floor Systems to Building Occupant Activities
Serviceability limit states in buildings are conditions where the use of the building is disrupted due to excessive deformations, deterioration, or motions of the structure or its components. One major serviceability consideration in modern buildings is excessive floor vibrations. Methods for accurate prediction of these vibrations and evaluation of floor systems are not readily available to the design community.
The objective of this research is to develop methods for the evaluation of floor systems subjected to occupant activities. This development requires realistic load models, an assessment of dynamic models of the floor system, and up-to-date information on human perception and tolerance of vibrations. The occupant-induced loads are modeled as moving, random loads. Two approaches are developed. The first uses finite element analysis to calculate the dynamic response of a floor to random crowd activity in the time domain. The second approach is based on random vibration analysis in the frequency domain. The response predictions from both approaches are quite close to each other and to in-situ response measurements from prior studies. However, both methods are found to be too involved to be used in routine design.
Design aids are developed in chart form for floor systems subjected to groups walking and exercising. Each chart represents a certain type of activity and floor system, and provides a limit for tolerable peak acceleration as a function of generalized mass and stiffness for the first mode of the floor. By using one of these design charts, a designer can determine whether a specific floor system may have a potential serviceability problem.
Title: New Identification Methods Applied to the Response of Flexible Bridges to Wind
Multimode analysis of flexible bridges, in particular of cable-stayed bridges, is required for accurate prediction of their response to wind. This study has endeavored to improve the methodologies for flutter and buffeting response prediction that are required for a multimode treatment. New identification methods for assessing experimental parameters from section-model tests are developed. As a vehicle for demonstration of the methods developed, the present work focuses on the Tsurumi Fairway cable-stayed twin bridges presently under construction in Japan. These parallel twin bridges, of 510 m center span, have streamlined bridge-deck sections that offer an excellent opportunity to study effects both of their sectional form and their side-by-side configuration. A system-identification (SID) method is presented that simultaneously identifies all the flutter derivatives of a bridge deck directly from section-model test results. The robustness and reliablity of this SID method under a low signal-to-noise ratio is first demonstrated through numerical simulation. Later, two-degree-of-freedom (vertical and torsional) coupled-motion tests are performed on the section model under a smooth flow in the wind tunnel to extract all eight flutter derivatives simultaneously employing the SID method developed. The effect of grid generated turbulence on the flutter derivatives is also demonstrated. Further, the present work determines static aerodynamic coefficients as well as the admittance functions pertinent to the buffeting forces. An alternate concept of aerodynamic transfer functions is introduced as an improved representation of the more common aerodynamic admittance functions, for use in buffeting-response analysis. Finally, the effect of the windward deck on the aeroelastic and aerodynamic characteristics of the leeward deck in the side-by-side configuration is demonstrated by further experiments. The work closes with a calculation of the critical flutter speed of the windward deck, which corroborates analogous results obtained in Japan.
Title: Vortex-Induced Vibration of Circular Cylinders
Dynamic interactions in the near wake of a bluff body placed in a laminar fluid stream give rise to a periodic array of vortices that are shed from the separating shear layers and convect downstream. Within a certain range of windspeeds, the shedding process can be ‘controlled’ by the dynamics of the structure, thereby tuning the fluid-structure system to a single frequency. A nonlinear feedback from the near wake to the body can then occur, leading to large amplitudes of response.
A flexibly-suspended circular cylinder was tested for such vortex-induced vibrations in a low-speed wind tunnel. The effect of mechanical damping and fluid-structure mass-ratio were investigated. Particular attention was given to the behavior of the near wake for different wind-speeds. The response of the cylinder as well as single-point velocity fluctuations in the wake were monitored and recorded digitally. Two mathematical models - a single degree of freedom model with frequency-dependent constants and parametric excitation, and a full body-wake coupled model with nonlinear coupling - were proposed and their parameters discussed in relation to the data obtained in the wind tunnel.
New insight was gained into the character of vortex-induced response of a circular cylinder outside and within the synchronization range.
Title: Computational Methods in Optimization of Structural Frames under Multiple Stress Constraints
In earlier studies of structural optimization, two design methods have been developed separately. One is optimal elastic design, which considers constraints on the elastic stresses, and the other is optimal plastic design, which considers the ultimate load constraint.
This study presents the characteristics of elastic and plastic design, combined with an iterative scheme checking both linear elastic stresses and plastic collapse load factors. Structural optimization of steel frames is achieved through material reallocation, which is governed by a. generalized stress parameter in those cases where elastic design controls, and by a reduced cost vector from a mathematical program in the case of plastic design. Regression analysis techniques among member properties are employed to reduce the number of independent design variables and to incorporate buckling and axial load effects for the elastic design.
The optimization procedure is implemented in a comprehensive computer system developed for the least-weight design of steel frames.
Author: Golam Sayeed Choudhury
Title: Data Collection Forms and Methodology for Post-earthquake Survey of Buildings and Casualties
During an earthquake, buildings which are vulnerable to seismic loads will be damaged. This damage results in property loss and casualties. Current methodologies to evaluate buildings are based purely on economic considerations. A methodology for minimizing losses in terms of deaths and injuries needs to be developed.
To reduce loss of life and injury, the relationship between earthquake-induced building failure and injury severity and distribution needs to be clarified. To this end, a series of data collection forms, referred to herein as the Hopkins forms, were developed to collect data regarding this relationship and to provide a basis for structural triage in the field shortly following an earthquake for search and rescue purposes.
The Hopkins forms were developed in four steps: (1) identifying the variables which affect the outcome of an occupant; (2) classifying the variables into three levels of priority for data collection; (3) designing the forms; and (4) applying forms to damaged buildings from past earthquakes. These forms represent a significant departure from existing forms because they consider both casualties and building damage.
By applying the forms to damaged structures from the Loma Prieta earthquake and past earthquakes, it was shown that they can be used in the field, and provide a basis for structural triage. The forms should be used during future earthquakes, for certain past earthquakes, and may possibly be developed for use in other disasters.
A database concerning the relationship between earthquake-induced building failure and injury severity and distribution could be created if the Hopkins forms are used during future earthquakes. This database would allow the first opportunity to evaluate the current beliefs and ideas which comprise the "folk wisdom" regarding earthquake-related injuries. With this analysis, the limited resources available for mitigating and responding to earthquake could be distributed in the most effective manner.
Author: Sivakolunthunathan Kesavanathan
Title: Radiation Boundary for Dynamic Soil-Structure Interaction Anaylsis in Time Domain
An effective procedure for modeling the radiation energy in time-domain finite element analysis of soil-structure interaction is presented. The radiation boundary developed herein represents the infinite extent of the layered soil stratum in time domain nonlinear analysis.
The soil domain is divided into two regions; a core region which contains the structure and irregular soil adjacent to the structure, and a semi-infinite exterior region of horizontally layered soil deposit. The core region, which may behave nonlinearly, is modelled using standard finite elements. An effective radiation boundary is developed to represent the infinite region. The displacement field within this infinitely extended region is represented by a set of admissible shape functions in terms of unknown generalized coordinates. The shape functions are selected based on the structure of the frequency-domain solution to the wave propagation problem. The interior and exterior domains are coupled by requiring displacement continuity on the boundary using the Lagrange multiplier method.
Derivation of the radiation boundary is carried through three stages: first for an axisymmetric Love-wave propagation problem; then for an axisymmetric Raleigh-wave propagation problem; and finally a three-dimensional wave propagation problem. Eigenvalue problems corresponding to the Love-wave and the Raleigh-wave propagation problems are summarized. Shape functions for the exterior region are derived from these eigen-solutions. A brief study on variation wave propagation parameters with forcing frequencies is presented for the Love wave and the Raleigh wave cases. Formulation of stiffness and mass matrices for the exterior region involves infinite integrals of products of cylindrical functions. An effective numerical procedure is developed for the evaluation these integrals.
The validity of the approach has been successfully demonstrated through a variety of simple linear cases. First axisymmetric Love wave propagation is examined. A circular footing subjected to dynamic axial torque embedded in a homogeneous half-space and a similar footing embedded in a layered half-space are presented. Then cases of axisymmetric Raleigh wave propagation are analysed. They are similar to the Love wave cases except that the dynamic axial torque is replaced by a dynamic vertical load. A parametric study on selection of waves and placement of boundary is presented for the Raleigh wave propagation case.
Eigen-solutions of Love- and Raleigh-wave propagation are utilized in the derivation of the three-dimensional radiation boundary. Three-dimensional numerical studies are presented for two problems. First a convergence study with respect to the number of elements and size in the circumferential direction for a vertical load problem is presented. Then a symmetric problem, a semi-circular domain of homogeneous stratum with an half-circular footing under horizontal load is analyzed.
The results from the radiation boundary analysis are compared with the results of conventional finite element analysis with fixed boundaries placed sufficiently far from the structure. The proposed method captures both transient and steady state responses effectively in the cases considered.
Title: The Analysis of Site-Dependent Effects on the Inelastic Response of Structural Systems Subjected to Seismic Loading
The response of structural systems to earthquake ground motion at a particular site is random, due in party to the variability of the excitation. For design purposes, it is desirable to obtain probabilistic descriptions of the response. However, the response is inelastic, so that linear random vibration methods cannot be implemented directly. The development of probabilistic ground motion models also is difficult, due to the nonstationary character of seismic shaking. The work presented herein examines probabilistic models of ground motion which attempt to account for site-specific characteristics. Equivalent linearization techniques are developed for the analysis of inelastic response to earthquake ground motion, facilitating the implementation of random vibration techniques. The results from random vibration analyses are compared to those from simulation, and the effects of nonstationarity in the excitation on the statistics of inelastic response are examined.
Title: A Graphical Surface-Navigation Technique for Multi-objective Programming Problems
This dissertation tackles the problems faced by a decision maker when confronted by the bewildering magnitude of solutions obtained from a multi-objective optimization procedure. The methodology developed is a graphical surface-navigation technique based on a spring equilibrium analogy. The whole procedure is set up in the framework of an interactive graphical session, which seeks to provide the decision maker with a ‘feel’ for the nature of the surface and the trade-offs involved in moving from one noninferior point to another. To compensate for the initial approximate nature of the method, a zooming capability is incorporated, which enables the decision maker to refine the approximation over particular areas of interest and even zoom in onto the exact noninferior set. A three-dimensional problem is used to illustrate the salient features of the methodology developed, and a higher-dimensional problem demonstrates the generality of the navigation technique.
Title: Stochastic Damage Accumulation and Probabilistic Codified Design for Wood
Wood is a naturally occurring material with large inherent variability in its structural properties. These structural properties are dependent on species, size, and grade of the structural members, as well as rate and duration of load. Reliability analyses of wood structures must account for these special characteristics. The dependence of strength on load duration implies that complete load histories are required in evaluating lifetime reliabilities. Stochastic load processes are coupled with damage accumulation models in the reliability analysis of engineered wood members and systems. A method for the treatment of duration of load effects in Load and Resistance Factor Design (LRFD) is developed. A system reliability analysis is performed using a simple model of a wood floor system fabricated with dimension lumber joists. Issues of member vs. system reliability and the coupling of the load duration and system effects are examined, and the implementation of system factors in probability-based codes is addressed.
Title: Response of Rigid Bodies to Base Excitation
The dynamic response of unrestrained rigid bodies to base excitation is investigated. This is motivated by the need to minimize damage to essential and expensive building contents during earthquakes. Behavior is studied for a rectangular block, considering all five modes of response: rest, slide, rock, slide-rock and free-flight. Impact is considered from a rock, slide-rock or free-flight mode using relations which are derived from first principles. Vertical ground acceleration is neglected.
Previous investigations to consider this behavior have generally been restricted to a single mode response: slide or rock. The validity of the assumptions made in these analyses are examined. Free and steady-state rocking solutions are shown to be generally valid for relatively tall blocks and a range of friction and restitution parameters. Slide solutions are shown to be valid, regardless of the form of ground acceleration, for friction less than the inverse aspect ratio. The study also demonstrates that a multiple mode response (slide and rock) due to harmonic ground motion is possible under certain conditions.
The method of slowly varying parameters is used to develop an approximate closed-form solution for a steady-state slide-rock response resulting from a harmonic ground acceleration. Solutions in general exist only for relatively high amplitudes of ground acceleration. The rock component of the response is sensitive to changes in aspect ratio and friction, and insensitive to changes in ground acceleration: the opposite is true for the slide component. Results compare favorably to those obtained by numerical integration.
A modified slowly varying parameter solution is developed for nonlinear systems subject to periodic loads which are impulsive in nature (e.g., rock or slide-rock). The proposed solution admits a discontinuity in velocity that is produced by the impulsive load. Examples are given which demonstrate the improvement in accuracy of the proposed solution.
A program is described which has been developed to compute the response numerically. Application of the program is demonstrated for a range of system parameters and three forms of ground acceleration: initial-value problems and the response to harmonic and recorded earthquake ground motion.
Title: Wind Response of Long-Span Flexible Bridges
The present investigation is an attempt to sharpen and corroborate the wind response prediction methodology of long-span flexible bridges to gusty winds. The study is somewhat centered around the Deer Isle-Sedgwick suspension bridge in Maine. This bridge has been the subject of an extensive field survey by the U.S. Federal Highway Administration (FHWA) since 1980. These field data consist of simultaneous measurements of wind velocity and bridge response obtained using an extensive array of anemometers and accelerometers. Some of the data acquired by FHWA at the Deer Isle bridge site were used to verify analytical results.
The Deer Isle bridge has a deck section not unlike that of the ill-fated Tacoma Barrows bridge, thus rendering it susceptible to wind-induced oscillations. After the Tacoma Narrows experience, the Deer Isle bridge was extensively modified by the addition of various stiffening systems with the aim of bracing the bridge against excessive wind response. With the aim of improving the aerodynamic response; deck section has also been provided with open-grate sidewalks for venting purposes.
The initial phase of the project consisted of a finite element modeling of the bridge structure to obtain its natural modes. The efficacy of structural modifications in stiffening the bridge, thereby significantly reducing the risk of excessive wind response was also demonstrated using the results of this modeling. The analytical results obtained from the finite element procedures were corroborated and supplemented using the field response data.
The scope of the current study was mainly the verification of the modeling procedures involving random vibrations of the bridge deck due to the turbulence in the wind flow or the so-called buffeting type wind response. A preliminary response computation study using a state-of-the-art method of buffeting response computation indicated a significant under-estimation of the observed response levels. Further research pursued with the aim of obtaining an improved level of consistency between the predicted and observed response levels, the signature or self-induced turbulence was identified as potentially one of the major mechanisms in wind driven oscillations involving bluff cross-sections such as bridge decks.
Wind-tunnel experiments were conducted to verify the significance of this self-induced turbulence and to find methods of including the effects of this in response computations. The experiments also showed the effectiveness of the open-grate sidewalks in improving the deck cross-section aerodynamically.
The improved response calculations made including the effects of signature turbulence were finally verified using the observed response of the Deer Isle bridge.
Title: Critical Ecitations of Structural Systems
The process of designing structures to resist seismic loads involves reliance on past records to provide an estimate of peak response. This may not be sufficient to ensure adequate performance during future earthquakes. The critical excitation technique attempts to do away with uncertainty in the loading by identifying the worst possible loading on the structure subject to physical constraints on the excitation. A general mathematical formulation for obtaining the critical excitations of single and multi-degree-of-freedom systems is developed using the calculus of variations. The effects of input energy, duration and system damping are investigated. Comparisons are made between peak responses obtained by the critical excitation technique and existing strong motion records. Stochastic critical excitations which maximize the response variance subject to constraints on the excitation energy are then introduced and a nonstationary earthquake model is used to obtain the stochastic critical excitation for an SDOF system. The use of the critical excitation method in the areas of equipment qualification and risk analysis is examined. An example in each area is worked out to show the use of the technique.
Title: Load Path Dependence in Structural Frames Subjected to Fluctuating Forces
The load space formulation of structural reliability provides a convenient method for calculating the reliability of structural systems. A major advantage of this method is that the dimension of the reliability analysis is kept to a manageable size. However, the limit states can be considered structural characterizations (independent of the loads) only if they are load path-independent. Although this is not the case for brittle systems, it is considered a good approximation for ductile systems, even though it is strictly true only for the first crossing of the elastic limit state. With this approximation, the limit states for ductile systems can be constructed from an analysis in which proportional loading is assumed.
In this study the dependence of system limit states on load path is investigated to understand the influence of different load path on the failure limit state. Both single story and multi-story frames are examined. For certain cyclic load cases, the strength of the structure decreases significantly and load path-dependence is apparent. In these instances, use of the proportional load failure limit state in evaluating system behavior and reliability is unconservative. A load path-independent lower bound limit state is formulated using shakedown theory.
Reliability analyses of the different limit states are performed to determine the importance of load path dependence on computed system reliability. Comparisons are made between element and system reliability in order to relate results to current design practice.
Title: In Situ Calibration of Constitutive Models – Preliminary Feasibility Study
In recent years, much research has been directed towards the development of sophisticated constitutive models, which can more accurately account for the diverse stress-strain phenomena exhibited by soils. Most of these models employ parameters whose optimal values can only be indirectly established through a trial and error curve fitting process. The objective here is to obtain the best overall fit to a given experimental relation or a set of observed responses. As a result, the accuracy and efficiency of the calibration process can be strongly dependent on the subjectivity of the analyst (or user) as well as his/her familiarity with the particular material model. In order to minimize this user dependence and thereby significantly reduce the complexity of the calibration process, the feasibility of developing a method to directly determine the model parameters has been investigated. Using in situ measurements as inputs, the method seeks to determine the model parameters by a computer-aided automated process, where a non-linear optimization technique was iteratively coupled with an incremental finite element analysis, in an attempt to identify that set of model parameters that most closely simulates the in situ soil response. Through the application to an isotropic, normally consolidated hypothetical soil, the calibration computer program has been developed and tested. The study clearly indicated the feasibility of the proposed method for the in situ calibration of constitutive models, but significant further research is necessary to fully develop this method. This study was also restricted to the bounding surface constitutive model, but can readily be adapted to other constitutive formulations. This technique attempts to reduce the dependence of calibration accuracy on user expertise, thereby significantly increasing the accessibility of sophisticated material models to the general engineering community.
Title: Lagrangian Formulation of Dynamical Equations Governing Appendage Deployment from Spacecraft
In the past, models concerned with the attitude dynamics of multi-body satellites have been developed. With NASA’s recent interest in the deployment and maintenance of large space structures, these models gain a new application. This essay presents an analysis of the deployment of a single appendage with n-hinges from an orbiter. The center of mass of the system follows an assumed circular orbit. Both rigid and flexible appendage models are considered. Principles of Lagrangian Dynamics are adapted to develop general equations of motion unlike those of previous investigations found in the area of multi-body satellite dynamics. The resulting coupled nonlinear second order differential equations are integrated numerically. Results are presented as time histories of parameters and illustrations of the system at steps in the deployment process.
Title: The Lighthill Correction to the Morison Equation
When a hydrodynamic flow field is known, the in-line force on a submerged slender structural element is usually calculated using the Morison equation. According to this expression the total in-line force consists of two components: an inertia force of potential origin and a drag force due to viscosity effects.
Primarily, this report investigates a second order correction term to the Morison equation that is of potential origin and was proposed by Sir James Lighthill. This correction is due to the horizontal gradient of the in-line velocity, which causes the dynamic pressure to vary around the cylinder. The Lighthill correction is derived theoretically for the condition of finite water depth.
Two sets of data were used to determine the effect of the Lighthill correction quantitatively. The first set consisted of periodic wave data and the second set consisted of random wave data. Each set of data was analyzed to evaluate the drag and inertia coefficients used to calibrate the Morison equation and also to determine the effect of the Lighthill correction. It was found that the inertia coefficients based on the measured flow properties were in some cases significantly greater than the ideal potential flow value of 2.0. The theoretical calculation of the force coefficients was investigated for low Keulegan-Carpenter numbers, but it was found that the normally adopted procedure of linearizing the boundary layer equation used in this calculation was not applicable for conditions experienced in these tests, and in general appears not to be applicable to ocean data. From the analysis of both the periodic and the random data it was found that the addition of the Lighthill correction term did not improve the Morison equation significantly; in most cases the Morison equation without the Lighthill correction provided a better fit to the measured forces.
Another correction, due to flow separation effects and based on Sarpkaya's 1981 work, is also investigated. The analysis suggests that a correction of the Sarpkaya type can be useful as a curve fitting device to improve the fit of the Morison equation to any given set of measured data.
Title: Modal Coupling and Wind-Induced Vibration of Tall Buildings
A general formulation based on Rayleigh-Ritz method was developed for analyzing the three-dimensional response of a building subjected is fluctuating wind forces. The formulation is general enough to be used for determining wind-induced response in the first several modes of torsionally coupled as well as uncoupled buildings. Typical mode shapes, frequencies of vibration and damping ratios used in the formulation are obtained from an extensive review of tall building ambient vibration measurement data available in the literature. Wind force spectra are developed from the results of a wind tunnel experiment performed on a model of a tall building in an urban boundary layer. Time series analysis techniques and, in particular, the "transfer function" modeling technique, are used to obtain a statistically consistent set of forces from partial records available from several nominally identical experimental observations.
The formulation is used to study the effects on building response of building stiffness, mass, damping and eccentricities of centers of rigidity and/or mass from the geometric center. The effect of statistical correlation between the acrosswind force and the torque on the acceleration response of mechanically uncoupled and coupled buildings are examined. The contributions of higher modes to the rms acceleration response are also reported.
The results obtained using this analysis are compared with the results of the more common building analysis, where the forces are assumed to be statistically uncorrelated and the components of motion uncoupled. Approximate methods have been developed for calculating the rms acceleration for uncoupled and coupled buildings.
Author: Avinash Madhukar Nafday
Title: Extremum Methods of Structural Analysis for System Reliability Assessment
Discrete extremum methods of systems analysis are demonstrated as a tool for structural system reliability assessment. Specifically, linear and multiobjective linear programming based procedures are developed for structural analysis of ductile frames under proportional and multiparameter loading, respectively. Kinematic and static approaches for rigid plastic analysis form a primal-dual pair in each of these models and have a polyhedral format. Duality relations link extreme points and hyperplanes of these polyhedra and lead naturally to dual methods for computing system reliability, depending upon the treatment of uncertainty.
Random events - based procedures require enumeration of the failure modes, and these are identified as the extreme points of the convex polytope for the kinematic model. An algorithmic procedure is used for the generation of the multiple failure modes of frames under proportional loading in ascending order of their collapse loads. The method can be used to generate a prespecified number of modes or all modes up to a specified level of significance. Modal collapse loads, failure mode expressions, bending moment distributions, modal correlations and bounds on the number of failure modes are easily available.
Random variable methods proceed from the limit surface demarcating the safe and unsafe regions. A static multiobjective programming model is formulated for frames under multiparameter loading, in which the weak noninferior sets represent the limit surfaces in load and basic variable spaces. Powerful computational procedures are utilized for generating the global n dimensional polyhedral limit hypersurfaces. The maximal facets of the polyhedra represent unique failure modes. Bending moment distributions, load combinations leading to a given mode, and modal correlations can be obtained.
A new approach for the estimation of structural system reliability based on the random variable approach is presented. The proposed method replaces the safe region of the structure with an analytically tractable region of equivalent volume, where this volume may be of different order and dimension. The system reliability can be computed from the properties of the substituted region. A hyperspherical equivalent region is used for polytopic limit surfaces, and the system reliability is directly available from probability tables.
Author: Deborah L. Nykyforchyn
Title: Stability Analysis of the Slope of an Embankment Constructed at Washington National Airport
The stability of the slope of an earthen embankment supporting the overrun of Runway 18 at Washington National Airport was examined using the finite element method. The purpose of this work was to study the applicability of the finite element method to the design of the slopes of embankments. The embankment is partially submerged, layered and reinforced with a geotextile. The embankment was designed by the Baltimore District of the U.S. Army Corps of Engineers based upon analysis results obtained using the simplified Bishop method- a version of the method of slices which is widely used for estimating the stability of slopes.
Finite element analyses were conducted considering the embankment with and without a reinforcing geotextile. The factors of safety obtained using the finite element method were compared with those obtained using the simplified Bishop method. Additionally, the development of failure within the embankment and the deformations of the embankment at failure were studied.
The finite element method was found to be capable of providing physically reasonable descriptions of the behavior of embankment slopes. Fair agreement was observed between the corresponding factors of safety obtained using the simplified Bishop method and the finite element method. The finite element method resulted in higher factors of safety. However, difficulty was encountered in precisely defining the state of failure.
It was concluded that the finite element method can provide refined estimates of behavior for complex problems but may require considerable effort, cost, and expertise. As a result, this method would appear best suited for later stages in the design of critical facilities.
Several areas toward which future work could be directed were identified. Work in these areas would be intended to advance the ability of the finite element method to describe the behavior of embankment slopes. These areas include more precise definitions of the state of failure, more realistic modeling of soil behavior, use of effective stress analysis, accounting for partial dissipation of pore water pressures and the development of boundary conditions which can describe more effectively the behavior of regions surrounding the region of interest.
Title: Shell Finite Element Kinematics for Improved Bending, Membrane and Transverse Shear Behavior
A displacement-based finite element formulation is developed for the approximate stress analysis of shells. The formulation is derived following the kinematics of the Love-Mindlin-Novozhilov theory for shells. This allows the analysis of thin to moderately-thick shells considering bending, membrane and transverse shear deformation. Attention is directed to shells made of homogeneous, isotropic, and linearly elastic materials. The extension to orthotropic and non-linear materials is direct.
Bending deformation is formulated to be kinematically independent from membrane and transverse shear deformation. This is accomplished by constructing an inextensional thin shell bending solution, referred to herein as the integrated bending field. The kinematic independence of bending deformation from the membrane and transverse shear deformation eliminates the common shear and membrane locking phenomena that adversely affect the performance of many isoparametric shell elements. Construction of the bending field in the distorted space of the element helps reduce the sensitivity of this formulation to geometric distortion.
Integrability constraints are imposed on the element to assure kinematic compatibility in an integral sense. The constraints are formulated separately for plates, single-curvature shells and double-curvature shells. The proposed integrated bending field is derived using the isoparametric interpolation basis. The method is sufficiently general, however, to work with other interpolation schemes and element types. The interpolated deflection and rotation fields are explicitly defined in the element, and local normals are constructed on the mid-surface to define the thickness direction. Full integration of the stiffness matrix is utilized, hence no spurious kinematic modes are produced. Over integration is allowed, giving practically the same solution.
Numerical results show the good accuracy, reliability and efficiency of this element for modelling bending, membrane and transverse shear deformation. Comparison with other prevalent formulations shows the advantage of the present method. The extension of this formulation to non-linear kinematics and layered materials is discussed.
Author: Venkatakrishna R. Meda
Title: A Fully-Integrated General Finite Element for Think and Layered Plates
A displacement-based formulation for thick and layered plates is presented. This is an extension of the "Integrated Bending Field" (IBF) kinematic formulation for Mindlin plates. In this formulation, independent (uncoupled) interpolations for the bending- and shear-dominant displacement fields are chosen. The resulting element can be fully integrated and is free from shear locking and other problems common to most isoparametric elements. It is also not overly sensitive to geometric distortion. As such it provides a significant improvement over existing formulations.
The displacement variation through the plate thickness is represented by a piecewise continuous polynomial function. Standard isoparametric shape functions are used to interpolate the corresponding nodal values over the plane of the element. Other interpolation bases can also be utilized. The bending displacement field is determined by integrating the thickness-varying membrane displacement field over the plane of the element. The transverse shear strain in this case is assumed to be zero. The formulation is not restricted to isotropic materials, and orthotropic materials can be used for different layers. Hence, modern plate constructions can be properly analyzed.
Better performance of the element is obtained by relaxing the internal integrability constraints. Although the element can be made fully conforming, best results are obtained by allowing some internal strain-displacement incompatibility and a degree of non-conformity across the element boundaries.
The true test of an element is its numerical performance and hence results are presented to show the accuracy, reliability and excellent performance of this element in modelling shear and bending deformations in thick and layered plates.
Title: The Effect of Upstream Gusting on the Aeroelastic Behavior of Long Suspended-Span Bridges
The effect that the presence of upstream gusting has upon the ability of long suspended-span bridges to sustain wind loads has been the subject of a certain amount of controversy among bridge designers and wind engineers. Wind tunnel studies of full bridge models, using passively-generated small-scale turbulence, have indicated that upstream turbulence exerts a stabilizing influence on the aeroelastic response of bridges. These wind tunnel studies have been criticized because the simulated gusts are usually smaller that the deck width of the model, whereas field measurements of the prototype conditions indicate that upstream gusts should be substantially larger than typical bridge deck widths. Theoretical analyses, based on stochastic parametric excitation models, have indicated that the presence of large-scale upstream gusting should have a destabilizing effect upon bridge deck sections.
This dissertation presents the results of wind tunnel experiments in which bridge deck section models were subjected to gusting flow regimes with simulated turbulence that contained gusts several times larger than the section model width. The large-scale gusting flow was produced by the novel technique of flapping-airfoil gust generation. Three section models were tested under smooth and gusting flow conditions. These experiments measured the change in the flutter derivatives, buffeting response and vortex shedding proclivities that are caused by upstream gusting. The preliminary results of this study indicates that large-scale upstream turbulence can decrease the flutter stability, increase the buffeting response and suppress the vortex-shedding action of bridge deck section models.
Title: Probabilistic Basis of Partial Resistance Factors for Use in Concrete Design
An advanced first-order, second moment reliability method is used to develop partial resistance factors for reinforced concrete design that are compatible with the load requirements of ANSI A58.1-1982. The effects on overall capacity of variability in concrete strength, steel strength, and geometry are analyzed for flexure, compression plus bending, and shear limit states. Also, the consistency of reliability levels inherent in the existing code is analyzed, and the performance, from a reliability viewpoint, of certain key code provisions is investigated.
Title: Aspects of the Natural Wind Conditions at the Golden Gate Bridge
Some aspects of the natural wind conditions at a typical suspended-span bridge site are examined using wind data obtained at the Golden Gate bridge, San Francisco. The wind at this site appears to be quite smooth . The intensity of turbulence even at moderate to high wind speeds seems to be very low. Some empirical models which attempt to represent the spectra of longitudinal fluctuations of the wind are compared with spectra obtained at the Golden Gate bridge.
Title: Three-Dimensional Dynamic Analysis of Gravity Dam and Reservoir Systems
An economical procedure for the frequency domain analysis of gravity dam and reservoir systems is developed and the three dimensional effects on their earthquake response are investigated.
The dam is modeled as a thick plate which includes shear, bending and rotatory inertia effects. The reservoir is assumed to be of constant cross-section with its far end extending to a large distance upstream. Water compressibility and a wave absorbing reservoir bed are incorporated. The system is completely linear. The substructure approach is found to be suitable.
The dam is analyzed by a Rayleigh-Ritz technique for the free vibration and by an extension of the technique for the forced vibration case that includes hydrodynamic effects. The differential equation describing the mechanics of the water is treated with a separation-of-variables approach that leads to a continuum solution in the upstream direction and necessitates a numerical solution in the cross-stream plane. A boundary element method is employed and the results compared with a finite element solution.
The free vibration study presents the natural frequencies and mode shapes. Frequency response functions for the crest acceleration and displacements are generated for all three components of ground motion. These functions are later used to determine the time-domain responses of the system to typical strong motion earthquakes. Pine Flat Dam is modeled as described above and some of the results from a full scale vibration test were compared. The agreement was found to be reasonably good.
Title: Load Space Formulation of Reliability for Nonlinear Random Structural System
A technique is proposed for determining the reliability of redundant ductile framed structures. A nonlinear structural analysis program and incremental load procedure are used to find the limit state function in load space for fixed structural properties. The failure probability of this deterministic structure is then computed by integrating the joint distribution function of loads over the failure region in load space. The procedure is extended to include randomness in the strength of the structure by introducing a random resistance variable unique to each load path. The statistics of this variable can be found by relating magnitudes of the load vector to successive component failure. The load space formulation of system reliability appears applicable to realistic structures of reasonable complexity.
By utilizing the proposed technique and several load models proposed elsewhere, the reliability of sample structures designed according to current design provisions is checked. The probabilities of failure of the limit states corresponding to first yielding, first plastic hinge, and collapse are assessed for structures with rigid and flexible connections.
A resistance space reliability formulation is also considered as an alternative to the formulation in load space. Approaches for determining the elastic limit state and collapse limit state of a deterministic structure in resistance space are proposed. Furthermore, in conjunction with the load space reliability analysis, isosafety contours in resistance space are established for probabilistic optimum design.
Author: Mostefa Djamel Boussouf
Title: Stiffened and Prestressed Composite Overwrapped Pressure Vessels
A structural analysis of a stiffened cylindrical pressure vessel closed with spherical caps is presented. This construction consists of an isotropic, stiffened inner metal layer strengthened by two unidirectional composite overwrapped layers in which the fibers have a ring winding. One layer covers the structure completely and provides reinforcement in the axial direction, while another covers the cylindrical part only with a circumferential composite overwrap. Methods are developed for deriving equivalent flexural rigidity, extensional rigidity, and interaction influence stiffnesses. Analytical solutions and numerical results for vessels with and without edge stiffeners are presented. This study is confined to the isotropic/orthotropic thin shell theory and uses load sharing liners, it also assumes that there is no adhesive between layers, thus no shear couplinq. The analysis takes into consideration the variation in the radii of individual layers. In this study, it is assumed that the fiber windinq of the composite layers are coincident with the principal directions of the structure, that is the axial and circumferential for the cylinder and only meridional for the spherical cap.
Title: Dynamic Analysis of Short-Length Gravity Dams
A three-dimensional procedure for analyzing the dynamic behavior of short-length gravity dams is developed. The method of analysis is based on the substructure concept. The motion of the dam is modeled by a general thick-plate theory incorporating both shear and bending deformations. Compressibility of water and flexibility of the reservoir boundaries are taken into consideration.
Neglecting the water compressibility, the natural frequencies of the structure and the corresponding mode shapes are found by the "Ritz-Galerkin" method. The three-dimensional effects on these dynamic properties are examined.
Based on harmonic excitation, and including compressibility of water, the "Galerkin" method is used to obtain frequency domain acceleration and displacement responses to all three components of ground motion. These are next used to evaluate time domain response to arbitrary earthquake ground motions through the use of the Fourier Integral technique. The three dimensional effects on these responses are investigated.
Title: Wind Induced Motion of Tall Buildings
The dynamic response of light and/or flexible modern tall buildings due to wind forces is analyzed, and studies are performed to identify those parameters that are most significant in determining structural motion.
Expressions for the total rms displacement and acceleration experienced at any location in a tall building are developed using random vibration theory. Force records from wind tunnel experiments performed on a model of a tall building in an urban exposure boundary layer are analyzed using a two-channel FFT analyzer. The resulting auto- and cross-spectra of the alongwind and acrosswind forces and torsional moments are used to examine the effects on building response of building stiffness, mass, and eccentricities of the centers of rigidity and/or stiffness from the geometric center of the building. Statistical correlations of the torsional moments and the acrosswind forces and the effects of these correlations on building response also are examined.
The results obtained using this analysis are compared to existing methods for checking the sensitivity of tall buildings to wind-induced motion. The acrosswind force is the most important factor in determining the acceleration response of flexible buildings. The correlation between the torque and the acrosswind force does not affect the total rms acceleration of structures significantly if the two orthogonal sideways and twisting degrees of freedom are mechanically uncoupled. Eccentricities in the centers of mass and rigidity cause the torsional accelerations and covariances between the torsional and translational accelerations to increase significantly, which cause the total rms acceleration to increase as well.
Title: Earthquake Analysis of Nuclear Power Plants
The paper is a review of the current literature on nuclear power plant seismic design. In addition, several types of analyses were performed on a typical model of a nuclear power plant reactor building. The soil model was varied between the analyses and the result compared to investigate the reaction to nonlinear behavior of the soil.
Nuclear power has steadily increased in usage since the 1950’s. However, the possible disasterous consequences of structural failure have lead to increased concern about the ability of nuclear reactors to withstand a strong motion earthquake. The term "failure" has a different meaning when applied to a nuclear power plant. It is necessary for the flow of the coolant for the reactor core to be maintained during an earthquake. It is not enough to design the containment building to remain standing or even remain structural sound. Therefore, the stresses induced by a possible earthquake must be able to be predicted with some accuracy in order to designate the design of the plant as being earthquake resistant.
The techniques involved in predicting the response of a nuclear power plant to a seismic excitation use finite element models to predict the interaction that takes place between the soil and the structure. These techniques are investigated in detail in this paper and both time history analysis and response spectra analysis are used to compare the damping effects of the soil. Damping in the soil is caused by both "radiation" of the energy away from the structure and by internal damping in the soil due to its nonlinear behavior. Both these types of damping are modeled in the soil for the analyses done for this paper. The results of the analyses are then compared to see what kinds of effects each type of damping has upon the entire response of the reactor building.
Author: Linda Keiko-Yamane Merrell
Title: Modern Culvert Design: Predicting Performance
Until recently, design of buried structures has been based more upon past experience than on knowledge of the behavior of structures when surrounded by soil. An accurate design method must take into account the soil-structure svstem as well as individual components.
Current flexible culvert design falls into three general categories: (1) equilibrium solution; (2) linear elastic solution; and (3) finite element method solution. The most popular of these methods is the equilibrium solution. Its equations are easy to use and there have been few culvert failures since they were introduced fifty years ago. The major disadvantage is their basis on a "semi-empirical" parameter--the modulus of soil reaction. Elasticity equations are theoretically sound, but calculations are extremely cumbersome, despite (sometimes questionable) simplifying assumptions made in their derivation. The finite element method is relatively expensive both in terms of time and money, and is difficult to justify for all but very large or highly specialized culvert installations.
In order to assess design reliability, culvert deflection was calculated using five methods: Iowa Formula, USBR Equation, Burns and Richard elasticity equations, a linear finite element solution, and a non-linear finite element solution (CANDE), and compared to actual field installation deflection data. Because the philosophy of the non-linear finite element method differed from the others, two separate data sets were used. The first set consisted of 77 installations, all of which were used in the equilibrium solution analysis. Due to insufficient data, only 41 and 30 of these installations were used for elasticity equations and linear finite element analyses, respectively. Data for the non-linear finite element analysis were taken from two culvert installations with a total of 14 measurements. A linear regression technique was used to obtain a measure of correlation between calculated and actual deflection values.
Of the five methods, the elasticity solutions showed the widest statistical scatter and least reliability in predicting culvert performance. The non-linear finite element method appeared to be the most accurate overall. The equilibrium solutions, though not always as accurate as the non-linear finite element method, were considerably more accurate than the elasticity solutions.