Effective two dimensional theories for multi-layered plates

Erscheinungsjahr 2019
ISBN: 978-3-8325-4984-8
Verlag: Logos

Buch, Englisch, Band 37, 139 Seiten, PB, Format (B × H): 145 mm x 210 mm

Reihe: Augsburger Schriften zur Mathematik, Physik und Informatik

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.

Autoren/Hrsg.

Delgado, Miguel de Benito

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Nichtlineare Wissenschaft
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Über Autor(innen)

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.