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arXiv · 0811.2238

The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells

Marta Lewicka·Maria Giovanna Mora·Mohammad Reza Pakzad
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Abstract

Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales like $h^β$ with $2<β<4$. We establish that, for the given scaling regime, the limiting theory reduces to the linear pure bending. Two major ingredients of the proofs are: the density of smooth infinitesimal isometries in the space of $W^{2,2}$ first order infinitesimal isometries, and a result on matching smooth infinitesimal isometries with exact isometric immersions on smooth elliptic surfaces.

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Marta Lewicka, Maria Giovanna Mora, Mohammad Reza Pakzad. 2008-11-13. The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. https://arxiv.org/abs/0811.2238

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