Analysis and Design of Nonlinearly Constrained Dynamic Systems

Abstract

In this manuscript, rigid body and elastodynamic systems are considered separately. A unifying formulation, i.e. one that augments rigid body formulations with flexible members, is not pursued due to that fact that the rigid body formulations described herein, exhibit recursive behavior, which augmented with flexibility effects, do not account for geometric stiffening effects. The introduction of flexibility drastically increases the number of degrees of freedom and destroys the recursive nature and fine-grain parallelism of the problem. As a result, algorithms that are best suited to the study of rigid body systems are no longer computationally efficient. Instead, a total Lagrangian approach based on constrained nonlinear elasticity is pursued to study flexible multibody systems. In the finite element formulation of this approach, domain decomposition is used to exploit course-grain parallelism.