Generalized constrained finite strip method for thin-walled members with arbitrary cross-section: Primary modes

In this paper the generalization of the constrained finite strip method (cFSM) is discussed. cFSM is a special version of the semi-analytical finite strip method (FSM), where carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanics, e.g., to allow buckling only in flexural, lateral–torsional, or a distortional mode. In the original cFSM only open cross-section members are handled, here the method is extended to cover any flat-walled member, including those with closed cross-sections or cross-sections with open and closed parts. Moreover, in the original cFSM only 4 deformation classes are defined, here the deformation field is decomposed into additional, mechanically meaningful, sub-fields. Formal mechanical criteria are given for the deformation classes, and implementation of the criteria regardless of cross-section topology is illustrated. In this paper, the primary deformation classes are presented in detail. Primary deformations are associated with minimal cross-section discretization, i.e. nodal lines located at folds and ends only. This paper is accompanied by a companion, where secondary modes and additional practical aspects in the selection of base vectors for the deformation classes are discussed. With the proposed modifications the powerful cFSM capabilities of buckling mode decomposition and identification are extended to essentially arbitrary thin-walled cross-sections.

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