Constrained shell Finite Element Method, Part 2: application to linear buckling analysis of thin-walled members

In this paper a novel method is employed for the buckling analysis of thin-walled members. The method is basically a shell finite element method, but constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanical criteria, e.g., to force the member to buckle in flexural, or lateral torsional or distortional mode. The method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, and longitudinal discretization is used, which transform the finite strip into multiple finite elements, that is why the new method can readily be termed as constrained (shell) finite element method. In the companion to this paper a band of finite elements is discussed in detail, where 'band' is a segment of the member with one single finite element longitudinally. In this paper the constraining procedure is applied on thin-walled members discretized both in the transverse and longitudinal direction. The possible base systems for the various deformation spaces are demonstrated here, as well as numerous buckling examples are provided to illustrate the potential of the proposed method.