Rigid-flexible body analysis without rotation parameters

Abstract

This paper addresses the coupled flexible and rigid body response of solids undergoing large motions and deformations. The formulation is presented in a form which is free of rotation parameters and thus avoids the need of finding compatible integration formulae for translations and rotations. The motion of each rigid body is represented in terms of the nodal parameters of a simplex element subject to constraints which ensure rigid motions. Flexible structural members for rods and shells are then expressed in terms of displacement and relative displacement parameters leading to total system of equations involving only translation degrees of freedom.

The motions are integrated using classical energy and momentum conserving schemes, thus leading to systems which are unconditionally stable for Hamiltonian (elastic-rigid) systems. The only requirement for absolute stability is that the non-linear algebraic equations representing the solution at each time step must converge.

The formulation is illustrated in two dimensions by representative numerical problems which involve both rigid and flexible parts or multi-rigid body situations. In all cases the conservation properties are observed.