Motion analysis of structures (MAS) for flexible multibody systems: planar motion of solids

In this paper, an approach named Motion Analysis of Structures (MAS) is introduced to analyze planar motion of solids. The theoretical basis of MAS is constructed on vector mechanics instead of analytical mechanics. Four procedures are involved to embody this approach. Namely, (a) discretization of structure, (b) discretization of particle path, (c) evaluation of deformations and internal forces, and (d) time integration. The first three procedures are not involved in solving the governing equations of continuum, instead directly formulating the equations of motion of a particle set via Newton’s law. Therefore, MAS is a particle approach. In procedure (c), the vector form intrinsic finite element (VFIFE) is employed, where a description of kinematics to dissect rigid body motion and deformation, a set of deformation coordinates for each time increment to describe element deformation, and the convected material frame solution procedure are included. The algorithms of coupling with rigid bodies and modeling of constraints are presented as well. Numerical examples for large rotation and benchmark verifications are performed to demonstrate the capability and accuracy of the approach in analysis of multibody system dynamics.