Convergence of equilibria of thin elastic plates in a discrete model - The von Kármán case
- We contribute to the mathematical rigorous derivation of the von-Kármán plate theory starting from an atomistic interaction model. We cover two different regimes: Thin and ultrathin films. The latter are extremely thin only consisting from a few layers of atoms. We show the convergence of equilibrium points of 3-dimensional nonlinear atomistic energy functionals to an equilibrium points of the von-Kármán functional. Since the atomic distance as well as the height of the plate tend to zero this includes two small parameters. A similar result is also shown for the time-dependent version of the equation.
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| Author: | David Buchberger |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1152994 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/115299 |
| Advisor: | Bernd Schmidt |
| Type: | Doctoral Thesis |
| Language: | English |
| Date of Publication (online): | 2024/09/16 |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2024/07/17 |
| Release Date: | 2024/09/16 |
| Tag: | discrete-to-continuum, dimension reduction, elasticity |
| GND-Keyword: | Plattentheorie; Elastische Platte; Elastizität; Dünne Schicht; Konvergenz; Dimensionsreduktion |
| Page Number: | 106 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
