The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
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The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells
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2008-10-14
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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^\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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Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza. (2008). The matching property of infinitesimal isometries on elliptic surfaces and elasticity of thin shells. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/44216.
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