Formulation of Two Nodes Finite Element Model for Geometric Nonlinear Analysis of RHS Beams Accounting for Distortion and Shear Deformations

In this paper, the nonlinear buckling analysis of rectangular hollow sections (RHS) beams considering distortional and the shear flexibility deformation effects is investigated. The kinematic model is based on the incorporation of non-classical terms, related to shear flexibility, according to Timoshenko model and distortion and warping. This analysis is carried out by proposing a new 3D finite element, formulated in the context of large torsion, incorporating flexural torsion, and distortion coupling effects. A 3D RHS beam element with two nodes and eleven degrees of freedom per node is proposed to perform the nonlinear buckling analysis. For this aim, the arc-length method is employed as a solution strategy to solve the nonlinear equilibrium equations, established as a function of the trigonometric functions of the twist angle. Many examples are proposed to check the validity of the proposed 3D finite element and the numerical procedure, either in pre-and post-buckling states. The present numerical results are compared to those of the commercial software ABAQUS using the brick finite elements. The incidences of the compressive load and the incorporated lateral stiffeners in the RHS beams in pre- and post-buckling behaviour are studied.