Conservation properties of a time FE method - part II: Time-stepping schemes for non-linear elastodynamics

In the present paper one-step implicit integration algorithms for non-linea r elastodynamics are developed. The discretization process rests on Galerki n methods in space and time. In particular, the continuous Galerkin method applied to the Hamiltonian formulation of semidiscrete non-linear elastodyn amics lies at the heart of the time-stepping schemes. Algorithmic conservat ion of energy and angular momentum are shown to be closely related to quadr ature formulas that are required for the calculation of time integrals. We newly introduce the 'assumed strain method in time' which enables the desig n of energy-momentum conserving schemes and which can be interpreted as tem poral counterpart of the well-established assumed strain method for finite elements in space. The numerical examples deal with quasi-rigid motion as w ell as large-strain motion. Copyright (C) 2001 John Wiley & Sons, Ltd.