From kinematics to forces: A novel constrained finite strip method for thin-walled member modal analysis

In this paper, a new set of mechanical criteria is employed to define the fundamental mode classes of thin-walled members: global, distortional and local, for use in modal analysis methods such as the Generalized Beam Theory (GBT) and constrained Finite Strip Method (cFSM). The objective of this work is to employ force characteristics, orthogonality, and completeness for defining the fundamental mode classes of thin-walled members, instead of using kinematic constraints, as in current modal decomposition methods. In this new framework the three basic mode classes span the entire deformation space of thin-walled members (i.e., they are inclusive of shear, transverse extension, and all other modes that conventional kinematic-based constraint methods separate out) and the mode classes are orthogonal to each other. Based on these criteria, this new method is implemented in the context of the Finite Strip Method (FSM) and termed fcFSM, i.e., force-based constrained finite strip method. The paper demonstrates buckling mode decomposition and identification results with fcFSM as well as the methods applicability for open/closed and polygonal/curved thin-walled cross-sections. In addition, the differences between the newly proposed fcFSM and the current kinematic-based constrained finite strip method (kcFSM) and GBT are highlighted and discussed through several specially selected examples.