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

Betsch, P. and Steinmann, P. (2001) Conservation properties of a time FE method--part II: Time-stepping schemes for non-linear elastodynamics. International Journal for Numerical Methods in Engineering, 50(8), pp. 1931-1955. (doi: 10.1002/nme.103)

Abstract

In the present paper one‐step implicit integration algorithms for non‐linear elastodynamics are developed. The discretization process rests on Galerkin methods in space and time. In particular, the continuous Galerkin method applied to the Hamiltonian formulation of semidiscrete non‐linear elastodynamics lies at the heart of the time‐stepping schemes. Algorithmic conservation of energy and angular momentum are shown to be closely related to quadrature formulas that are required for the calculation of time integrals. We newly introduce the ‘assumed strain method in time’ which enables the design of energy–momentum conserving schemes and which can be interpreted as temporal counterpart of the well‐established assumed strain method for finite elements in space. The numerical examples deal with quasi‐rigid motion as well as large‐strain motion.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul
• Authors: Betsch, P., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• Publisher: Wiley
• ISSN: 0029-5981
• ISSN (Online): 1097-0207
• Published Online: 06 February 2001