professor ben schafer's thin-walled structures research group - johns hopkins university Finite Strip Method (FSM) research page   The finite strip method (FSM) is a variant of the finite element method that has been put to highly effective use in the study of the stability of thin-walled structures. For any thin-walled structure which may effectively be modelled as "extruded" FSM provides an incredibly powerful simplification to FEM. Our research team provides open source FSM software and actively develops new research and tools related to FSM, including the following:         Our popular software for the elastic buckling analysis of thin-walled members utilizing the semi-analytical, classical, finite strip method is full detailed here.     The constrained finite strip method, or cFSM, is now implemented in our software CUFSM. Go download the software and give it a try. Using formal mechanical definitions of the buckling classes: global, distortional, local, and other deformations, the constrained finite strip method can provide both modal decomposition (see second figure below) and modal identification (see third figure below) to a conventional finite strip solution.   Modal decomposition allows the conventional finite strip solution to be focused on any buckling class (e.g., global, distortional, or local only), resulting in problems of reduced size and definitive solutions for the buckling modes in isolation, as demonstrated for an example section. Modal identification allows the results of a conventional finite strip solution to be judged with regard to the participation of the buckling classes; and thus provide a measure of buckling mode interaction. The conventional finite strip method combined with the constrained finite strip method provides a powerful tool for understanding cross-section stability in cold-formed steel members.   Journal Articles by Schafer on constrained Finite Strip Method (scopus feed)   Reports Ádány, S. (2004). “Buckling mode classification of members with open thin-walled cross-sections by using the finite strip method.” Research Report, Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA. (pdf)              In the literature on thin-walled structures two methods provide a means to formally decompose stability solutions into local, distortional, and global bucking modes: constrained Finite Strip Method (cFSM) and Generalized Beam Theory (GBT). The mechanical definitions employed in the constrained Finite Strip Method are directly motivated from Generalized Beam Theory; however the implementations of the two methods are significantly different. In essence Generalized Beam Theory enriches a beam element with additional degrees of freedom and performs the solutions in a modal deformation basis, while the constrained Finite Strip Method constrains a general purpose plate finite strip in a manner consistent with the GBT modal deformation basis. Papers discussing this further are detailed below. Also see the full list of recent papers from the research group for additional citations.   Journal Articles Ádány, S., Silvestre, N., Schafer, B.W., Camotim, D. “GBT and cFSM: Two modal approaches to the buckling analysis of unbranched thin-walled members.” International Journal of Advanced Steel Construction. (Accepted 2009). Conference Papers Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2008). “Buckling Mode Identification of Thin-Walled Members A Comparison Between the cFSM and GBT Approaches.” CIMS 2008, Fifth International Conference on Coupled Instabilities in Metal Structures, Sydney, Australia – June 23-25, 2008. 249-256. *Ádány†, S., Silvestre, N., Schafer, B., Camotim, D. (2007). “On the Identification and Characterisation of Local, Distortional and Global Buckling Modes in Thin-Walled Members using the cFSM and GBT Approaches.” ICSAS'07 - 6th International Conference on Steel and Aluminium Structures, Oxford, UK. 24-27 July, 2007. *Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2006). “Buckling Analysis of Unbranched Thin-Walled Columns using cFSM and GBT: A Comparative Study.” Proceedings of International Colloquium on Stability and Ductility of Steel Structures, Lisbon, Portugal, Ed. Camotim et al., Vol. 1, 205-212. *Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2006). “Buckling Analysis of Unbranched Thin-Walled Columns: Generalised Beam Theory and Constrained Finite Strip Method.” Third European Conference on Computational Solid and Structural Mechanics: Solids, Structures and Coupled Problems in Engineering (ECCM-2006), Lisbon, Portugal, June 5-8, 2006.     A significant advantage of the constrained Finite Strip Method is the formal identification of local, distortional, and global buckling modes. The extension of this formal identification to the finite element domain potentially provides a quantitative means to perform buckling mode classification. Papers discussing this further are detailed below. Also see the full list of recent papers from the research group for additional citations.   Conference Papers Ádány, S., Joó†, A., Schafer, B.W. “Identification of FEM buckling modes of thin-walled columns by using cFSM base functions.” CIMS 2008, Fifth International Conference on Coupled Instabilities in Metal Structures, Sydney, Australia – June 23-25, 2008. 265-272.     The classical semi-analytical finite strip method (FSM) as implemented, for instance, in CUFSM is applicable only to simply supported boundary conditions. For such boundary conditions the longitudinal shape function - the heart of the 'strip' portion of a finite strip - is sinusoidal. For a sinusoidal shape function the deformations as a function of buckling waves along the length are orthogonal and the final solutions simplifies remarkably.   The numerical efficiency and algorithmic simplicity of classical finite strip makes it a powerful tool, but limited in applicability. In particular, the inability to generate fixed-fixed solutions provides little means to bound potential stability results and thus engineering approximations are required or recourse to general purpose finite element solutions with plate/shell elements are necessary.   To alleviate this circumstance work has been completed with a set of classical longitudinal shape functions that provide an FSM implementation that can cover a variety of boundary conditions. A report on the method, including verification resutls, has been completed and is provided below.   Reports Li, Z. (2009). "Buckling analysis of the finite strip method and theoretical extension of the constrained finite strip method for general boundary conditions." Research Report. Departmenet of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA (pdf).     Current implementations of the constrained Finite Strip Method (cFSM) are married to the classical semi-analytical cFSM and thus only apply to simply supported boundary conditions. With the completion of extension to FSM solutions for any boundary conditions (Spring 2009) a framework for extended cFSM is now possible. This work is underway and recent progress reported in our research report:   Reports Li, Z. (2009). "Buckling analysis of the finite strip method and theoretical extension of the constrained finite strip method for general boundary conditions." Research Report. Departmenet of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA (pdf).    Full list of References See the online publications list for the most up to date listing of our publications. This list was last updated in Spring 2009. Journal Articles Ádány, S., Silvestre, N., Schafer, B.W., Camotim, D. “GBT and cFSM: Two modal approaches to the buckling analysis of unbranched thin-walled members.” International Journal of Advanced Steel Construction. (Accepted 2009). Ádány, S., Schafer, B.W. (2006). “Buckling mode decomposition of single-branched open cross-section members via finite strip method: derivation.” Elsevier, Thin-walled Structures. 44 (5) 563-584. Ádány, S., Schafer, B.W. (2006). “Buckling mode decomposition of single-branched open cross-section members via finite strip method: application and examples.” Elsevier, Thin-walled Structures. 44 (5) 585-600. Conference Papers Ádány, S., Joó†, A., Schafer, B.W. “Identification of FEM buckling modes of thin-walled columns by using cFSM base functions.” CIMS 2008, Fifth International Conference on Coupled Instabilities in Metal Structures, Sydney, Australia – June 23-25, 2008. 265-272. Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2008). “Buckling Mode Identification of Thin-Walled Members A Comparison Between the cFSM and GBT Approaches.” CIMS 2008, Fifth International Conference on Coupled Instabilities in Metal Structures, Sydney, Australia – June 23-25, 2008. 249-256. *Ádány†, S., Silvestre, N., Schafer, B., Camotim, D. (2007). “On the Identification and Characterisation of Local, Distortional and Global Buckling Modes in Thin-Walled Members using the cFSM and GBT Approaches.” ICSAS'07 - 6th International Conference on Steel and Aluminium Structures, Oxford, UK. 24-27 July, 2007. *Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2006). “Buckling Analysis of Unbranched Thin-Walled Columns using cFSM and GBT: A Comparative Study.” Proceedings of International Colloquium on Stability and Ductility of Steel Structures, Lisbon, Portugal, Ed. Camotim et al., Vol. 1, 205-212. Schafer†, B.W., Ádány, S. (2006). “Modal decomposition for thin-walled member stability using the finite strip method.” SMCD 2006, May 14-17, 2006, University of Waterloo, Waterloo, Ontario, Canada. *Ádány†, S., Silvestre, N., Schafer, B.W., Camotim, D. (2006). “Buckling Analysis of Unbranched Thin-Walled Columns: Generalised Beam Theory and Constrained Finite Strip Method.” Third European Conference on Computational Solid and Structural Mechanics: Solids, Structures and Coupled Problems in Engineering (ECCM-2006), Lisbon, Portugal, June 5-8, 2006. Schafer†, B.W., Ádány, S. (2005). “Understanding and classifying local, distortional and global buckling in open thin-walled members.” Proceedings of the Structural Stability Research Council Annual Stability Conference, May, 2005. Montreal, Quebec, Canada. 27-46. (pdf, ppt) Ádány†, S., Schafer, B.W. (2004). “Buckling mode classification of members with open thin-walled cross-sections.” Proceedings of the Fourth International Conference on Coupled Instabilities in Metal Structures, September 27-29, 2004. Rome, Italy. 467-476. Reports Ádány, S. (2004). “Buckling mode classification of members with open thin-walled cross-sections by using the finite strip method.” Research Report, Department of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA. (pdf) Li, Z. (2009). "Buckling analysis of the finite strip method and theoretical extension of the constrained finite strip method for general boundary conditions." Research Report. Departmenet of Civil Engineering, Johns Hopkins University, Baltimore, MD, USA (pdf). last edited on 08/13/10 - schafer@jhu.edu

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