Effective two dimensional theories for multi-layered plates

• मुख्य लेखक: de Benito Delgado, Miguel (auth)
• स्वरूप: इलेक्ट्रोनिक पुस्तक अध्याय
• भाषा: अंग्रेज़ी
• प्रकाशित: Berlin/Germany Logos Verlag Berlin 2019
• श्रृंखला: Augsburger Schriften zur Mathematik, Physik und Informatik 37
• विषय: Integral calculus & equations; elastic plates; effective model hierarchy; gamma convergence; non-conforming penalty method; Kirchhoff
• ऑनलाइन पहुंच: DOAB: download the publication; DOAB: description of the publication

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.