Schlüter, Alexander ; Müller, Henning ; Yan, Sikang ; Faust, Erik ; Müller, Ralf (2022)
A Lattice Boltzmann Method for Elastic Solids Under Plane Strain Deformation.
doi: 10.48550/arXiv.2301.00228
Report, Bibliographie
Kurzbeschreibung (Abstract)
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the above interpretation of the LBM as a general numerical tool, allows the LBM to be extended to solid mechanics as well. In this spirit, the LBM has been studied in recent years. First publications [3], [4] presented an LBM scheme for the numerical solution of the dynamic behavior of a linear elastic solid under simplified deformation assumptions. For so-called anti-plane shear deformation, the only non-zero displacement component is governed by a two-dimensional wave equation. In this work, an existing LBM for the two-dimensional wave equation is extended to more general plane strain problems. The proposed algorithm reduces the plane strain problem to the solution of two separate wave equations for the volume dilatation and the non-zero component of the rotation vector, respectively. A particular focus is on the implementation of types of boundary conditions that are commonly encountered in engineering practice for solids: Dirichlet and Neumann boundary conditions. Last, several numerical experiments are conducted that highlight the performance of the new LBM in comparison to the Finite Element Method.
| Typ des Eintrags: | Report |
|---|---|
| Erschienen: | 2022 |
| Autor(en): | Schlüter, Alexander ; Müller, Henning ; Yan, Sikang ; Faust, Erik ; Müller, Ralf |
| Art des Eintrags: | Bibliographie |
| Titel: | A Lattice Boltzmann Method for Elastic Solids Under Plane Strain Deformation |
| Sprache: | Englisch |
| Publikationsjahr: | 31 Dezember 2022 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | ArXiv.org |
| Kollation: | 16 Seiten |
| DOI: | 10.48550/arXiv.2301.00228 |
| URL / URN: | https://arxiv.org/abs/2301.00228 |
| Kurzbeschreibung (Abstract): | The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the above interpretation of the LBM as a general numerical tool, allows the LBM to be extended to solid mechanics as well. In this spirit, the LBM has been studied in recent years. First publications [3], [4] presented an LBM scheme for the numerical solution of the dynamic behavior of a linear elastic solid under simplified deformation assumptions. For so-called anti-plane shear deformation, the only non-zero displacement component is governed by a two-dimensional wave equation. In this work, an existing LBM for the two-dimensional wave equation is extended to more general plane strain problems. The proposed algorithm reduces the plane strain problem to the solution of two separate wave equations for the volume dilatation and the non-zero component of the rotation vector, respectively. A particular focus is on the implementation of types of boundary conditions that are commonly encountered in engineering practice for solids: Dirichlet and Neumann boundary conditions. Last, several numerical experiments are conducted that highlight the performance of the new LBM in comparison to the Finite Element Method. |
| Freie Schlagworte: | Lattice Boltzmann Method, solids, plane strain, computational engineering, computational solid mechanics |
| ID-Nummer: | arXiv:2301.00228 [math.NA] |
| Zusätzliche Informationen: | Preprint |
| Fachbereich(e)/-gebiet(e): | 13 Fachbereich Bau- und Umweltingenieurwissenschaften 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik 13 Fachbereich Bau- und Umweltingenieurwissenschaften > Fachgebiete der Mechanik > Fachgebiet Kontinuumsmechanik |
| Hinterlegungsdatum: | 12 Jul 2024 07:09 |
| Letzte Änderung: | 11 Okt 2024 10:44 |
| PPN: | 522183042 |
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