A co-rotational formulation for thin-walled beams with monosymmetric open section

Abstract

A consistent co-rotational total Lagrangian finite element formulation and numerical procedure for the geometric nonlinear buckling and postbuckling analysis of thin-walled beams with monosymmetric open section is presented. The element developed here has two nodes with seven degrees of freedom per node. The element nodes are chosen to be located at the shear centers of the end cross-sections of the beam element and the shear center axis is chosen to be the reference axis. The deformations of the beam element are described in the current element coordinate system, which is constructed at the current configuration of the beam element. In element nodal forces, all coupling among bending, twisting, and stretching deformations of the beam element is considered by consistent second-order linearization of the fully geometrically nonlinear beam theory. However, the third-order term of the twist rate of the beam axis is considered in element nodal forces. An incremental-iterative method based on the Newton–Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A parabolic interpolation method of the arc length is used to find the buckling load. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.