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...
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| 格式: | Online |
| 語言: | 英语 |
| 出版: |
Logos Verlag Berlin
2021
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| 主題: | |
| 在線閱讀: | ONIX_20210408_9783832549848_66 |
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| _version_ | 1869523110389088256 |
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| author | de Benito Delgado, Miguel |
| author_browse | de Benito Delgado, Miguel |
| author_facet | de Benito Delgado, Miguel |
| author_sort | de Benito Delgado, Miguel |
| collection | Directory of Open Access Books |
| description | 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. |
| format | Online |
| id | doab-20.500.12854ir-64424 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-644242024-04-04T14:41:10Z Effective two dimensional theories for multi-layered plates de Benito Delgado, Miguel elastic plates effective model hierarchy gamma convergence non-conforming penalty method Kirchhoff thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations 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. 2021-04-08T15:34:37Z 2021-04-08T15:34:37Z 2019 book ONIX_20210408_9783832549848_66 9783832549848 https://directory.doabooks.org/handle/20.500.12854/64424 eng Augsburger Schriften zur Mathematik, Physik und Informatik image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=4984&lng=eng&id= https://www.logos-verlag.de/ebooks/OA/978-3-8325-4984-8.pdf Logos Verlag Berlin Logos Verlag Berlin 10.30819/4984 10.30819/4984 04b263a1-7fba-4491-9eae-1c394ac42fc3 9783832549848 Logos Verlag Berlin 37 139 Berlin/Germany open access |
| spellingShingle | elastic plates effective model hierarchy gamma convergence non-conforming penalty method Kirchhoff thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations de Benito Delgado, Miguel Effective two dimensional theories for multi-layered plates |
| title | Effective two dimensional theories for multi-layered plates |
| title_full | Effective two dimensional theories for multi-layered plates |
| title_fullStr | Effective two dimensional theories for multi-layered plates |
| title_full_unstemmed | Effective two dimensional theories for multi-layered plates |
| title_short | Effective two dimensional theories for multi-layered plates |
| title_sort | effective two dimensional theories for multi layered plates |
| topic | elastic plates effective model hierarchy gamma convergence non-conforming penalty method Kirchhoff thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations |
| topic_facet | elastic plates effective model hierarchy gamma convergence non-conforming penalty method Kirchhoff thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKL Integral calculus and equations |
| url | ONIX_20210408_9783832549848_66 |
| work_keys_str_mv | AT debenitodelgadomiguel effectivetwodimensionaltheoriesformultilayeredplates |