Postbuckling analysis of beams of arbitrary cross section using BEM

In this paper, the postbuckling analysis of beams of arbitrary cross section is presented taking into account moderate large displacements, large angles of twist and adopting second order approximations for the deflection–curvature relations. The beam is subjected to the combined action of the arbitrarily distributed or concentrated axial, transverse and torsional loading, while it is supported by the most general boundary conditions including elastic support or restraint. Starting from a displacement field without any simplifying assumptions about the angle of twist amplitude and based on the total potential energy principle, four highly coupled nonlinear governing differential equations are derived taking into account the shortening and warping effects and the Wagner’s coefficients due to the asymmetric character of the cross section. The arising four boundary value problems with respect to the transverse displacements, to the axial displacement and the angle of twist are solved using the Analog Equation Method, a BEM based method. The geometric, inertia, torsion and warping constants of the arbitrary beam cross section are evaluated employing only boundary integrals. 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. Numerical examples are worked out to illustrate the efficiency, accuracy and range of applications of the developed method. Conclusions of great practical interest are drawn.