Strain Tensors and Matching Property on Surfaces with the Gauss curvature changing sign

2021/11/30 by Liangbiao Chen, Chen, Liang-Biao, Peng‐Fei Yao +1
Engineering · Physics and Astronomy · Mathematics · #Elasticity and Material Modeling #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2111.15189

Abstract

We prove the regularity of solutions to the strain tensor equation on a region S with the Gauss curvature changing sign. Furthermore, we obtain the density property that smooth infinitesimal isometries are dense in the W^2,2(S,ℝ³) infinitesimal isometries. Finally, the matching property is established. Those results are important tools in obtaining recovery sequences (Γ-lim sup inequality) for dimensionally-reduced shell theories in elasticity.

Citations

• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

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