Large torsion finite element model for thin-walled beams

Abstract

Behaviour of thin-walled beams with open section in presence of large torsion is investigated in this work. The equilibrium equations are derived in the case of elastic behaviour without any assumption on torsion angle amplitude. This model is extended to finite element formulation in the same circumstances where 3D beams with two nodes and seven degrees of freedom per node are considered. Due to large torsion assumption and flexural–torsional coupling, new matrices are obtained in both geometric and initial stress parts of the tangent stiffness matrix. Incremental-iterative Newton–Raphson method is adopted in the solution of the nonlinear equations. Many applications are presented concerning the nonlinear and post-buckling behaviour of beams under torsion and bending loads. The proposed beam element is efficient and accurate in predicting bifurcations and nonlinear behaviour of beams with asymmetric sections. It is proved that the bifurcation points are in accordance with nonlinear stability solutions. The convenience of the model is outlined and the limit of models developed in linear stability is discussed.