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

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

2008-11-13

arxiv.org/abs/0811.2238v1

Mathematics

Analysis of PDEs

21 pages

Scientific paper

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 $h^\beta$ with $2<\beta<4$. 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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