Effective two dimensional theories for multi-layered plates
- This work introduces a family of effective plate theories for multilayered materials with internal misfit. This is done for scaling laws ranging from Kirchhoff's theory to the linearised von Kármán one. An intermediate von Kármán-like theory is introduced to play a central interpolating role with a new parameter which switches between the adjacent regimes. After proving the necessary Gamma-convergence and compactness results, minimising configurations are characterised. Finally, the interpolating theory is numerically approximated using a discrete gradient flow and the relevant Gamma-convergence and compactness results for the discretisation are proved. This provides empirical evidence for the existence of a critical region of the parameter around which minimisers experience a stark qualitative change.
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| Author: | Miguel de Benito Delgado |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-887229 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/88722 |
| ISBN: | 978-3-8325-4984-8OPAC |
| ISSN: | 1611-4256OPAC |
| Publisher: | Logos |
| Place of publication: | Berlin |
| Advisor: | Bernd Schmidt |
| Type: | Doctoral Thesis |
| Language: | English |
| Year of Creation: | 2019 |
| Year of first Publication: | 2019 |
| Publishing Institution: | Universität Augsburg |
| Granting Institution: | Universität Augsburg, Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Date of final exam: | 2019/07/02 |
| Release Date: | 2021/08/24 |
| GND-Keyword: | Niederdimensionales System; Mathematische Physik; Laminat; Mathematische Modellierung; Plattentheorie |
| Page Number: | 147 |
| Note: | Zugl.: Dissertation, Universität Augsburg, 2019 |
| Series: | Augsburger Schriften zur Mathematik, Physik und Informatik ; 37 |
| DOI: | https://doi.org/10.30819/4984 |
| 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): |  CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand) |
