Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy–momentum schemes

Abstract

A multibody formulation for the nonlinear dynamics of mechanical systems composed of both rigid and deformable bodies is proposed in this work, focusing on its conservation properties for basic magnitudes such as total energy and momentum. The approach is based on the use of dependent variables (cartesian coordinates of selected points) and the enforcement of the constraints through the penalty method. This choice has the advantage of providing a simple overall structure that allows the inclusion of both rigid bodies (discrete model) and elastic bodies (continuum model discretised with the finite element method) under the same framework, in order to build a single set of ordinary differential equations. The elastic bodies are represented by general hyperelastic models and may undergo large displacements, rotations and strains. An energy–momentum time integration method has been employed, achieving remarkable stability and robustness with exact conservation of total energy. This approach effectively overcomes drawbacks associated with penalty formulations in other time integration algorithms. This important result in fact proves to be the main conclusion of this work. Some representative numerical simulations are presented for mechanical systems comprised of rigid and deformable bodies.