Non-Uniform Modal Decomposition of Thin-Walled Members by the Constrained Finite Element Method

In this paper a new method, the constrained finite element method is applied for the modal decomposition of thin-walled members. With the help of this method the thin-walled member can be enforced to deform in accordance with some predefined criteria. In stability analysis, thus, it becomes straightforward to directly study various buckling types, for example flexural buckling, flexural-torsional buckling, distortional buckling, etc., as desired by the user. The main focus of the paper is on the special feature of the method that modal decomposition can be performed for non-uniform members, too, more specifically, for any members built of from prismatic segments. The connecting segments can have different cross-sections. Moreover, the segments can be constrained into different deformation modes, that is the enforced deformations may vary from segment to segment. In the paper the constrained finite element method is briefly presented first, then numerical examples are shown where either the cross-section and/or the constraining is changing along the member length.

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