Shear-flexible models for spatial buckling of thin-walled curved beams

The governing non-linear finite element equations for the spatial stability analysis of curved beams, using a simple two-noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross-sectional warping and bending/twisting rotations. The formulation is valid for both open-and closed-type thin-walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural-and warping-torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second-order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral-torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations.

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