Flexural–torsional postbuckling analysis of beams of arbitrary cross section

In this article, the postbuckling analysis of axially compressed elements of arbitrary cross section is presented taking into account moderately large displacements, moderately large angles of twist and employing nonlinear relationships between bending moments and curvatures. The elements are supported by the most general boundary conditions including elastic support or restraint. Based on Galerkin’s method and approximating the displacement field of the element by polynomial expressions the governing differential equations lead to a nonlinear algebraic system. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing the boundary element method. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross section’s torsional rigidity is evaluated exactly without using the so-called Saint–Venant’s torsional constant. Both the Wagner’s coefficients and the shortening effect are taken into account, while their influence is examined and discussed. Numerical examples are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method.