A 3D Finite Element Solver for Multibody Systems Based on Implicit Runge-Kutta Schemes

An efficient finite element (FE) formulation and a time-integration scheme for the simulation of multibody systems are derived. The absolute nodal coordinate formulation is chosen. In the discretized form, a constant mass matrix and a nonlinear stiffness matrix follow from a variational formulation. According to the classical assumptions of multibody systems, only small deformations but large rotations are taken into account. A special decomposition of the Green strain tensor leads to a stiffness matrix which is multiplicatively composed of the rotation matrix of the rigid body rotation and the small strain stiffness matrix, which has to be computed only once. Thus, Runge Kutta schemes of higher order accuracy can be solved efficiently.