A combined force/displacement-based constrained finite strip method for modal stability analysis of thin-walled members

Abstract

The objective of this study is to develop a new constrained finite strip method based on a combined force/displacement approach (fFSM) for thin-walled members with closed, cylindrical, and rounded cornered cross-sections. The classic constrained finite strip method (cFSM) is limited to members with cross-sections consisting of flat plate elements (i.e., polygonal sections). The developed fFSM herein aims to overcome this limit and broaden the computational analysis capability for thin-walled members to aid design. The method is implemented in the semi-analytical FSM by incorporating a new set of mode definitions of the fundamental deformation mode classes: global, local, distortional, warping-only, and transverse extension. The new definitions utilize the appropriate force and displacement relationships based on the transverse local coordinates suitable for both polygon and curved sections, which is different from the current generalized beam theory (GBT) or cFSM definitions, although some of the core mechanics are the same. This implementation is applicable to members with arbitrary cross-sections, including closed and curved cross-sections and sections with rounded corners. The constraint matrices for the fundamental mode classes are constructed using a series of linear mapping of the defined subspaces of the mode classes. Hence, the modal decomposition and identification of the method can be enabled. Numerical examples are presented to compare the solutions with those of the current cFSM from the CUFSM software for open-branch sections. The results show consistent agreement between the two approaches, although slight differences do exist. Then, additional numerical examples are provided to demonstrate the capabilities of the new fFSM in modal decomposition and identification for closed and curved sections and sections with rounded corners.