A beam finite element for non-linear analyses of thin-walled elements

The aim of the present paper is to investigate a theoretical and numerical model which is able to study the behaviour of thin-walled beams with open cross section in presence of large torsion. The presented model takes into account for large torsion, linear and non-linear warping currently named shortening effects, pre-buckling deformation and flexural–torsional coupling. In numerical analysis, a 3D beam with two nodes and seven degrees of freedom per node is adopted. The equilibrium equations and the material behaviour are derived in discrete form without assumption on torsion angle amplitude. Due to large torsion context, all the equilibrium equations are non-linear and highly coupled. The linear behaviour is made possible by disregarding non-linear terms. For non-linear behaviour and stability, the tangent stiffness matrix is carried out. Due to large torsion context, new matrices are present. The element is incorporated in a homemade finite element code. Newton–Raphson iterative methods are used with different control parameters. In order to prove the efficiency of the model many examples are presented in linear and non-linear behaviour with presence of bifurcations.