Published Paper

Inserted: 28 dec 2022
Last Updated: 28 sep 2023

Journal: Mathematics in Engineering
Volume: 5
Pages: 1--21
Year: 2023
Doi: https://doi.org/10.3934/mine.2023092

Abstract:

We consider elastic thin shells without through-the-thickness shear and depict them as Gauss graphs of parametric surfaces. (We use the term shells in a sense including plates and thin films.) We consider an energy depending on the first derivative of the Gauss map (so, it includes curvatures) and its second-rank minors. For it we prove existence of minimizers in terms of currents carried by Gauss graphs. In the limiting process we adopt sequences of competitors that satisfy a condition that prevents self-penetration of matter.

Keywords: Geometric measure theory, Thin films, Plates, shells, Curvature effects, Gauss graphs

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