Improved implicit integrators for transient impact problems—geometric admissibility within the conserving framework

Abstract

AbstractThe value of energy and momentum conserving algorithms has been well established for the analysis of highly non‐linear systems, including those characterized by the nonsmooth non‐linearities of an impact event. This work proposes an improved integration scheme for frictionless dynamic contact, seeking to preserve the stability properties of exact energy and momentum conservation without the heretofore unavoidable compromise of violating geometric admissibility as established by the contact constraints. The physically motivated introduction of a discrete contact velocity provides an algorithmic framework that ensures exact conservation locally while remaining independent of the choice of constraint treatment, thus making full conservation equally possible in conjunction with a penalty regularization as with an exact Lagrange multiplier enforcement. The discrete velocity effects are incorporated as a post‐convergence update to the system velocities, and thus have no direct effect on the non‐linear solution of the displacement equilibrium equation. The result is a robust implicit algorithmic treatment of dynamic frictionless impact, appropriate for large deformations and fully conservative for a range of geometric constraints. Copyright © 2001 John Wiley & Sons, Ltd.