Rigidity of a thin domain depends on the curvature, width, and boundary conditions
| Autor: | Zhirayr Avetisyan, Narek Hovsepyan, Davit Harutyunyan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
0209 industrial biotechnology Pure mathematics Control and Optimization Applied Mathematics 010102 general mathematics Zero (complex analysis) Order (ring theory) 02 engineering and technology Curvature 01 natural sciences symbols.namesake 020901 industrial engineering & automation Mathematics - Analysis of PDEs Differential Geometry (math.DG) Dirichlet boundary condition Domain (ring theory) Ribbon symbols FOS: Mathematics Boundary value problem 0101 mathematics Scaling Mathematics Analysis of PDEs (math.AP) |
| Popis: | This paper is concerned with the study of linear geometric rigidity of shallow thin domains under zero Dirichlet boundary conditions on the displacement field on the thin edge of the domain. A shallow thin domain is a thin domain that has in-plane dimensions of order $O(1)$ and $\epsilon,$ where $\epsilon\in (h,1)$ is a parameter (here $h$ is the thickness of the shell). The problem has been solved in [8,10] for the case $\epsilon=1,$ with the outcome of the optimal constant $C\sim h^{-3/2},$ $C\sim h^{-4/3},$ and $C\sim h^{-1}$ for parabolic, hyperbolic and elliptic thin domains respectively. We prove in the present work that in fact there are two distinctive scaling regimes $\epsilon\in (h,\sqrt h]$ and $\epsilon\in (\sqrt h,1),$ such that in each of which the thin domain rigidity is given by a certain formula in $h$ and $\epsilon.$ An interesting new phenomenon is that in the first (small parameter) regime $\epsilon\in (h,\sqrt h]$, the rigidity does not depend on the curvature of the thin domain mid-surface. Comment: 24 pages |
| Databáze: | OpenAIRE |
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