A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

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A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry

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Lewicka, Marta

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2008-11-26

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Abstract

We prove that the critical points of the $3$d nonlinear elasticity functional over a thin shell of arbitrary geometry and of thickness $h$, as well as the weak solutions to the static equilibrium equations (formally the Euler Lagrange equations associated to the elasticity functional) converge, in the limit of vanishing thickness $h$, to the critical points of the generalized von Karman functional on the mid-surface, recently derived in [14]. This holds provided the elastic energy of the $3$d deformations scale like $h^4$ and the magnitude of the body forces scale like $h^3$.

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shell theories

nonlinear elasticity

equilibria

calculus of variations

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Lewicka, Marta. (2008). A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/45458.

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