  We prove that the critical points of the 3d nonlinear elasticity functional
on shells of small thickness $h$ and around the mid-surface $S$ of arbitrary
geometry, converge as $h\to 0$ to the critical points of the von K\'arm\'an
functional on $S$, recently derived in \cite{lemopa1}. This result extends the
statement in \cite{MuPa}, derived for the case of plates when
$S\subset\mathbb{R}^2$. We further prove the same convergence result for the
weak solutions to the static equilibrium equations (formally the Euler-
Lagrange equations associated to the elasticity functional). The convergences
hold provided the elastic energy of the 3d deformations scale like $h^4$ and
the external body forces scale like $h^3$.
