Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells

2018/07/29 by Peng‐Fei Yao, Yao, Pengfei
Engineering · #Composite Material Mechanics #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1807.11115

openalex publication_date 2018/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain L² regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the L² regularity for non-characteristic regions. Finally, we obtain the optimal constant in the first Korn inequality scales like h^4/3 for hyperbolic shells, generalizing the assumption that the middle surface of the shell is given by a single principal system in the literature.

Citations

• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity
• A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence

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