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

Citation
P. Betsch et P. Steinmann, Conservation properties of a time FE method - part II: Time-stepping schemes for non-linear elastodynamics, INT J NUM M, 50(8), 2001, pp. 1931-1955
Citations number
35
Categorie Soggetti
Engineering Mathematics
Journal title
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN journal
00295981 → ACNP
Volume
50
Issue
8
Year of publication
2001
Pages
1931 - 1955
Database
ISI
SICI code
0029-5981(20010320)50:8<1931:CPOATF>2.0.ZU;2-J
Abstract
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.