Geometrically nonlinear dynamic analysis of 3-D beam

A co-rotational finite element formulation for the geometrically nonlinear dynamic analysis of spatial beam with large rotations but small strain is presented. The deformation nodal forces and inertia nodal forces are derived by using the d'Alembert principle and the virtual work principle. The gyroscopic effect is considered here. The beam element developed here has two nodes with six degrees of freedom per node. Some angular velocity coupling terms, which are so called gyroscopic forces, are obtained in inertia nodal force. 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 dynamic equilibrium equations. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.