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arXiv · 1807.11115

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

Pengfei Yao
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Abstract

We perform a detailed analysis of the solvability of linear strain equations on hyperbolic surfaces to obtain $L^2$ regularity solutions. Then the rigidity results on the strain tensor of the middle surface are implied by the $L^2$ 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.

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Pengfei Yao. 2018-07-29. Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells. https://arxiv.org/abs/1807.11115

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