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Displaying similar documents to “A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry”

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

Marta Lewicka (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness and around the mid-surface of arbitrary geometry, converge as → 0 to the critical points of the von Kármán functional on , recently proposed in [Lewicka ,  (to appear)]. This result extends the statement in [Müller and Pakzad, (2008) 1018–1032], derived for the case of plates when S 2 . The convergence holds provided the elastic energies of the 3d deformations...

A simple proof of the characterization of functions of low Aviles Giga energy on a ball regularity

Andrew Lorent (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain  ⊂ ℝ the functional is I ϵ ( u ) = 1 2 Ω ϵ -1 1 Du 2 2 + ϵ D 2 u 2 d z where belongs to the subset of functions in W 0 2 , 2 ( Ω ) whose gradient (in the sense of trace) satisfies ()·  = 1 where is...