Geometrically Non-Linear Dynamic Analysis of Thin-Walled Beams

Abstract

A co-rotational finite element formulation for the geometrically nonlinear dynamic analysis of thin-walled beam with large rotations but small strain 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 centroid of the end cross sections of the beam element and the centroid axis is chosen to be the reference axis. The. kinematics of the beam element is described in the current element coordinate system constructed at the current configuration of the beam element. The element nodal forces are conventional forces, moments and bimoments. Both the element deformation nodal forces and inertia nodal forces are systematically derived by consistent linearization of the fully geometrically non-linear beam theory, the d'Alembert principle and the virtual work principle in the current element coordinates. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the nonlinear equations of motion. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.