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Effective two dimensional theories for multi-layered plates

Augsburger Schriften zur Mathematik, Physik und Informatik , Bd. 37

Miguel de Benito Delgado

ISBN 978-3-8325-4984-8
139 pages, year of publication: 2019
price: 38.00 €

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 Γ-convergence and compactness results, minimising configurations are characterised. Finally, the interpolating theory is numerically approximated using a discrete gradient flow and the relevant Γ-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.

Keywords:
  • elastic plates
  • effective model hierarchy
  • gamma convergence
  • non-conforming penalty method
  • Kirchhoff

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