Browsing by Subject "elliptic surfaces"

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    The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
    (2008-10-14) Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza
    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.