A co-rotational total Lagrangian finite element formulation for the geometrically nonlinear dynamic analysis of spatial Euler beam with large rotations but small strain, is presented.
The nodal coordinates, displacements, rotations, velocities, accelerations, and the equations of motion of the structure are defined in a fixed global set of coordinates. The beam element has two nodes with six degrees of freedom per node. The element nodal forces are conventional forces and moments. The kinematics of beam element are defined in terms of element coordinates, which are constructed at the current configuration of the beam element. Both the element deformation nodal forces and inertia nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theot 3, using 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.