Lower Bounds of Optimal Exponentials of Thickness in Geometry Rigidity Inequality for Shells

Abstract

The optimal exponentials of the thickness in the geometry rigidity inequality of shells represent the geometry rigidity of the shells. We obtain that the lower bounds of the optimal exponentials are $4/3,$ $3/2,$ and $1,$ for the hyperbolic shell, the parabolic shell, and the elliptic shell, respectively, through the construction of the Ansätze.

arXiv comment20. arXiv admin note: text overlap with arXiv:1203.1138 by other authors

References in corpus (4)

• Scaling instability of the buckling load in axially compressed circular cylindrical shells
• Space of Infinitesimal Isometries and Bending of Shells
• Optimal exponentials of thickness in Korn's inequalities for parabolic and elliptic shells
• Linear Strain Tensors and Optimal Exponential of thickness in Korn's Inequalities for Hyperbolic Shells