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Some variational problems for a Foppl-von Karman plate subject to generalequilibrated loads are studied. The existence of global minimizers is provedunder the assumption that the out-of-plane displacement fulfils homogeneousDirichlet condition on the whole boundary while the in-plane displacementfulfils nonhomogeneous Neumann condition. If the Dirichlet condition isprescribed only on a subset of the boundary, then the energy may be unboundedfrom below over the set of admissible configurations, as shown by severalexplicit conterexamples: in these cases the analysis of critical points isaddressed through an asymptotic development of the energy functional in aneighborhood of the flat configuration. By a $\Gamma$-convergence approach weshow that critical points of the Foppl-von Karman energy can be stronglyapproximated by uniform Palais-Smale sequences of suitable functionals: thisproperty leads to identify relevant features for critical points ofapproximating functionals, e.g. buckled configurations of the plate. Eventuallywe perform further analysis as the plate thickness tends to 0, by assuming thatthe plate is prestressed and the energy functional depends only on thetransverse displacement around the given prestressed state: by this approach,first we identify suitable exponents of plate thickness for load scaling, thenwe show explicit asymptotic oscillating minimizers as a mechanism to relaxcompressive states in an annular plate.

Variational Problems for Foppl-von Karman plates