A large torsion beam finite element model for tapered thin-walled open cross sections beams

Abstract

A 3D finite element beam element model is investigated for the behavior, the buckling and the post-buckling analyses of thin-walled tapered beams with open cross sections. For the purpose, a non-linear model is performed in large torsion context according to a new kinematics that accounts for large torsion, flexural–torsional coupling and the presence of tapering terms in bending and torsion. The equilibrium equations are carried out and new tapering stress resultants are then present. This model is extended to finite element formulation in the same circumstances. 3D beams elements with two nodes and seven degrees of freedom per node are adopted. Due to large torsion assumption and flexural–torsional coupling, new matrices are established in both the geometric and the initial stress parts of the tangent stiffness matrix. The Arclength method is adopted as solution strategy of the non-linear equations. Many applications are presented that deal with the behavior, the buckling and the post-buckling equilibrium. Comparisons are made with some available solutions and with shell elements of a commercial code. The bifurcation points are in accordance with non-linear stability solutions. Moreover, the present element is also compared to similar tapered beam finite element without the new tapering terms. The proposed beam element is efficient and accurate in both linear and non-linear behavior analyses. It follows a non negligible gain in computation time especially when the post-buckling behavior is performed.