Buckling mode decomposition of single-branched open cross-section members via finite strip method: Application and examples

The objective of this paper is to provide implementation details of, and practical examples for, modal decomposition of the cross-section stability modes of thin-walled members by constraining a traditional finite strip method (FSM) solution. The theoretical development of the proposed method is provided in a companion to this paper [Ádány S, Schafer BW. Buckling mode decomposition of single-branched open cross-section members via finite strip method: derivation. Thin-walled Structures, submitted for publication, companion to this paper.] The constraint matrix, which is directly applied to the elastic and geometric stiffness matrices of a traditional FSM solution in order to constrain the deformations, is provided along with all formulae necessary in its construction. In addition, a completely worked out numerical example is provided to aid in implementing the constrained FSM solution. The authors implemented the constrained FSM in the open source program CUFSM. This modified version of CUFSM is then used to provide a series of numerical examples that illustrate (i) the advantages of performing modal decomposition, (ii) the importance of understanding and defining the deformation fields related to a desired mode, and (iii) the behavior of constrained FSM stability solutions compared with classical analytical solutions, GBT, and unconstrained FSM. Decomposition of the cross-section buckling classes related to global and distortional modes is demonstrated. Further, the impact of how to select the deformation fields and perform modal decomposition for cross-section stability modes within a class, e.g., for the traditional three global modes (weak-axis flexure, strong-axis flexure and flexural-torsional buckling), is explored and the impact of the deformation field definitions demonstrated. Comparisons of the constrained FSM solutions with other available solutions demonstrate the importance of properly determining when beam theory and plate theory should apply to the cross-section stability of thin-walled members.