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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 wi...
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Logos Verlag Berlin
2022
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oapen-20.500.12657-567552023-02-01T09:01:43Z Effective two dimensional theories for multi-layered plates de Benito Delgado, Miguel Mathematics bic Book Industry Communication::P Mathematics & science::PB 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. 2022-06-18T05:34:36Z 2022-06-18T05:34:36Z 2019 book 9783832549848 https://library.oapen.org/handle/20.500.12657/56755 eng application/pdf n/a external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/4984 https://doi.org/10.30819/4984 1059eef5-b798-421c-b07f-c6a304d3aec8 b818ba9d-2dd9-4fd7-a364-7f305aef7ee9 9783832549848 Knowledge Unlatched (KU) Logos Verlag Berlin Knowledge Unlatched open access |
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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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2022 |
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