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 .
This holds provided the elastic energy of the $3$d deformations scale like $h^4$ and
the magnitude of the body forces scale like $h^3$.
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry.
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