TY  - GEN
AU  - de Benito Delgado,Miguel
TI  - Effective two dimensional theories for multi-layered plates
SN  - 4984
PY  - 2019///
CY  - Berlin/Germany
PB  - Logos Verlag Berlin
KW  - Integral calculus & equations
KW  - bicssc
KW  - elastic plates
KW  - effective model hierarchy
KW  - gamma convergence
KW  - non-conforming penalty method
KW  - Kirchhoff
N1  - Open Access
N2  - 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
UR  - https://www.logos-verlag.de/ebooks/OA/978-3-8325-4984-8.pdf
UR  - https://directory.doabooks.org/handle/20.500.12854/64424
ER  -