On the enforcing energy conservation of time finite elements for discrete elasto‐dynamics problems |
| |
| Authors: | Q. V. Bui |
| |
| Affiliation: | Continuum and Thermodynamic Mechanics Department, Laboratory of Aeronautic and Spatial Technique (LTAS), University of Liège, 1 Chemin des Chevreuils, B‐4000, Liège‐1, BelgiumContinuum and Thermodynamic Mechanics Department, Laboratory of Aeronautic and Spatial Technique (LTAS), University of Liège, 1 Chemin des Chevreuils, B‐4000, Liège‐1, Belgium |
| |
| Abstract: | In the context of the time‐finite element method, algorithmic stresses, which enable the conservation of energy, are designed for temporal integrators derived from the midpoint and trapezoidal schemes. This is achieved through an appropriate modification of the standard midpoint and trapezoidal quadrature rules used for the numerical integration of time integrals. Either scalar scaling or vectorial adjustments can be employed for the modification, and well‐designed simple tests allow to investigate the quality of these different strategies of energy‐conserving enforcements. Numerical examples with semi‐discrete elasto‐dynamics problems are presented to show the superior stability of energy‐conserving schemes. Copyright © 2006 John Wiley & Sons, Ltd. |
| |
| Keywords: | Galerkin finite element method temporal integrators non‐linear dynamics energy conservation energy– momentum conservation |
|
|
