Effective two dimensional theories for multi-layered plates

By (author) Miguel de Benito Delgado

Extent: 139 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Series: Augsburger Schriften zur Mathematik, Physik und Informatik

Series volume number: 37

Language: English

Paperback (Published)

(December 2019)

ISBN: 9783832549848

5.71 x 8.27 inches

Price: $57.00

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Synopsis
Contributing Authors

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 Karman one. An intermediate von Karman-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.

By (author) Miguel de Benito Delgado

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