Constrained Finite Strip Method for Thin-Walled Members with General End Boundary Conditions

The objective of this paper is to provide the theoretical background and illustrate the capabilities of the constrained finite strip method (cFSM) for thin-walled members with general end boundary conditions. Based on the conventional finite strip method (FSM), cFSM provides a mechanical methodology to separate the deformations of a thin-walled member into those consistent with global, distortional, local, and other (e.g., shear and transverse extension) modes. For elastic buckling analysis, this enables isolation of any given mode (modal decomposition) or quantitative measures of the interactions within a given general eigenmode (modal identification). Existing cFSM is only applicable to simply supported end boundary conditions. In this paper, FSM is first extended to general end boundary conditions, including simply-simply, clamped-clamped, simply-clamped, clamped-guided, and clamped-free. Next, with the conventional FSM for general end boundary conditions in place, the derivation of the constraint matrices for global, distortional, local, and other modes that play a central role in cFSM are summarized. Several bases (i.e., the constraint matrices) are presented for general end boundary conditions involving, in particular, different orthogonalization conditions. For modal identification, normalization schemes for the base vectors as well as the summation method employed for the modal participation calculation are also provided. Numerical examples of modal decomposition and identification are illustrated for a thin-walled member with general end boundary conditions. Recommendations on the choice of basis, orthogonalization, and normalization are provided.