Numerical Analysis of Constrained Dynamical Systems, with Applications to Dynamic Contact of Solids, Nonlinear Elastodynamics and Fluid-Structure Interactions

摘要

This project considers the development of robust time-stepping algorithms for the temporal integration of dynamical systems in nonlinear solid mechanics. We have developed new algorithms for the contact/impact of solids that preserve the conservations laws of momenta and of energy conservation for the normal contact interactions and of energy dissipation for the tangential frictional laws. We have also developed new arbitrary Eulerian-Lagrangian finite element methods with a direct application to the Lagrangian treatment of viscous fluids. This extension allows the analysis of fluid-structure interfaces through the Lagrangian contact logic previously developed. Similarly, we have developed new integration algorithms for nonlinear elastodynamics that exhibit the controllable high-frequency dissipation required to handle the high numerical stiffness of the mechanical systems of interest. Additional tools, like the formulation a new contact sorting/search data structure for the efficient analysis of multi-body elastic systems, have also been developed.