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A note on convergence of low energy critical pointsof nonlinear elasticity functionals,for thin shells of arbitrary geometry
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 2 / April 2011
- Published online by Cambridge University Press:
- 24 March 2010, pp. 493-505
- Print publication:
- April 2011
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- Article
- Export citation
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We prove that the critical points of the 3d nonlinear elasticity functionalon shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0to the critical points of the vonKármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)].This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ. 33 (2008) 1018–1032], derived for the case of plates when $S\subset\mathbb{R}^2$
.The convergence holds provided the elastic energies of the 3d deformations scale like h4 and the external body forces scale like h3.
