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 $S\subset {\mathbb{R}}^{2}$.
The convergence holds provided the elastic energies of the 3d deformations scale
like...

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 $S\subset {\mathbb{R}}^{2}$.
The convergence holds provided the elastic energies of the 3d deformations scale
like...

Recall that a smooth Riemannian metric on a simply connected domain can be realized as the pull-back metric of an orientation preserving deformation if and only if the associated Riemann curvature tensor vanishes identically. When this condition fails, one seeks a deformation yielding the closest metric realization. We set up a variational formulation of this problem by introducing the non-Euclidean version of the nonlinear elasticity functional, and establish its -convergence under the proper scaling....

Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.

Recall that a smooth Riemannian metric on a simply connected domain can
be realized as the pull-back metric of an orientation preserving deformation if
and only if the associated Riemann curvature tensor vanishes identically.
When this condition fails, one seeks a deformation yielding
the closest metric realization.
We set up a variational formulation of this problem by
introducing the non-Euclidean version of the nonlinear
elasticity functional, and establish its -convergence under the proper
scaling....

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