Computational schemes for non-linear elasto-dynamics

This paper deals with the development of computational schemes for the dynamic analysis of non-linear elastic systems. The focus of the investigation is on the derivation of unconditionally stable time-integration schemes presenting high-frequency numerical dissipation for these types of problem. At rst, schemes based on Galerkin and time-discontinuous Galerkin approximations applied to the equations of motion written in the symmetric hyperbolic form are proposed. Though useful, these schemes require casting the equations of motion in the symmetric hyperbolic form, which is not always possible. Furthermore, this approaches to unacceptably high computational costs. Next, unconditionally stable schemes are proposed that do not rely on the symmetric hyperbolic form. Both energy-preserving and energy-decaying schemes are derived. Numerical examples are presented to demonstrate the accuracy and e ciency of the proposed schemes.