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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| Format: | Online |
| Langue: | anglais |
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Logos Verlag Berlin
2022
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| Accès en ligne: | OCN: 1226215216 |
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| _version_ | 1869518990668201984 |
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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-84308 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-843082025-07-31T13:39:17Z Effective two dimensional theories for multi-layered plates de Benito Delgado, Miguel Mathematics 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. 2022-06-19T04:06:32Z 2022-06-19T04:06:32Z 2022-06-18T05:34:36Z 2019 book OCN: 1226215216 https://library.oapen.org/handle/20.500.12657/56755 9783832549848 https://directory.doabooks.org/handle/20.500.12854/84308 eng open access image/jpeg image/jpeg image/jpeg image/jpeg image/jpeg n/a n/a n/a n/a n/a https://library.oapen.org/bitstream/20.500.12657/56755/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56755/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56755/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56755/1/external_content.pdf https://library.oapen.org/bitstream/20.500.12657/56755/1/external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/4984 https://doi.org/10.30819/4984 04b263a1-7fba-4491-9eae-1c394ac42fc3 Knowledge Unlatched 9783832549848 Knowledge Unlatched (KU) KU Open Services Logos Verlag Berlin open access |
| spellingShingle | Mathematics 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 | Mathematics |
| topic_facet | Mathematics |
| url | OCN: 1226215216 |
| work_keys_str_mv | AT debenitodelgadomiguel effectivetwodimensionaltheoriesformultilayeredplates |