Gross, M., Betsch, P. and Steinmann, P. (2005) Conservation properties of a time FE method. Part IV: Higher order energy and momentum conserving schemes. International Journal for Numerical Methods in Engineering, 63(13), pp. 1849-1897. (doi: 10.1002/nme.1339)
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Abstract
In the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite‐dimensional Hamiltonian systems with symmetry is shown. The result of this development is the enhanced Galerkin (eG) finite element method in time. The conservation of the eG method is generally related to its collocation property. Total energy conservation, in particular, is obtained by a new projection technique. The eG method is, moreover, based on objective time discretization of the used strain measure. This paper is concerned with particle dynamics and semi‐discrete non‐linear elastodynamics. The related numerical examples show good performance in presence of stiffness as well as for calculating large‐strain motions.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Steinmann, Professor Paul |
| Authors: | Gross, M., 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: | 21 April 2005 |
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