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
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.