A review of temporal and spatial dispersions of linear and quadratic finite elements in linear elastic wave propagation problems
| Autor: | Radek Kolman, Miloslav Okrouhlík, Alena Kruisová |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Proceedings of the Estonian Academy of Sciences, Vol 73, Iss 3, Pp 279-316 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1736-6046 1736-7530 |
| DOI: | 10.3176/proc.2024.3.11 |
| Popis: | The dispersion behaviour of the finite element method, applied to the treatment of stress wave propagation tasks in an elastic solid continuum, is reviewed and complemented with the authorsâ contributions in the field, along with substantial details of finite element technology. It is shown how finite element dispersion disqualifies to a certain extent the stress wave propagation modelling and, as such, cannot be completely eradicated. The paper, however, reveals the ways how the dispersion effect (actually, modelling errors) could be minimized. The effects of spatial and temporal dispersions of the finite element method are treated. 1D and 2D linear and quadratic finite elements and their suitability are analysed for use with implicit and explicit integration methods. Historical as well as new, up-to-date approaches are also reviewed. The paper closes with recommendations for values of mesh size and timestep size, mass matrices and direct time integrations with respect to dispersion errors in finite element modelling of elastic wave propagation problems in solids. |
| Databáze: | Directory of Open Access Journals |
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