An explicit algorithm for geometrically nonlinear transient analysis of spatial beams using a corotational total Lagrangian finite element formulation

Abstract

An explicit method for nonlinear transient dynamic analysis of spatial beams with finite rotations using a corotational total Lagrangian finite element formulation is presented. The kinematics of the beam element is described in the current element coordinate system constructed in the current configuration of the beam element. The element deformation and inertia nodal forces are derived by the virtual work principle, the d'Alembert principle, and the consistent linearization of the geometrically nonlinear beam theory. A nodal rotation vector is used to represent the finite rotation of a base coordinate system rigidly attached to each node of the discretized structure. A numerical procedure of explicit method is proposed for the solution of the nonlinear equations of motion. The standard central difference method is applied to the incremental displacement vector and the incremental rotation vector, and the time derivatives of displacement vector and rotation vector. The nodal orientations are updated by the incremental nodal rotation vectors. The values of nodal rotation vectors are reset to zero in the current configuration.In order to assess the efficiency and the accuracy of the proposed method, numerical examples are studied and compared with the results obtained using the implicit method based on the Newmark method.