Benchmark cases for robust explicit time integrators in non-smooth transient dynamics

Abstract

Abstract This article introduces benchmark cases for time integrators devoted to non-smooth impact dynamics. It focuses on numerical properties of explicit integrators. Each case tests one necessary numerical property in computational impact dynamics: energy behaviour at impact, angular momentum conservation, non-linear behaviour. The cases are easy to implement and analyse, providing a benchmark well-suited to first numerical studies. We rewrite explicit schemes for non-smooth impact dynamics with unified notations, and analyse them with the benchmark cases.

Keywords

• Structural transient dynamics
• Non-smooth dynamics
• Explicit time integrators
• Symplectic schemes
• Impact dynamics