Dimensional analysis and asymptotic expansions of equilibrium equations in nonlinear elasticity. Part II: The two-dimensional von Kármán model

Abstract

In the second part of this article, which is a continuation of [8] which dealt with a plate subjected to large loads, we consider a plate subjected to moderate applied forces level within the framework of nonlinear elasticity. We then apply the new constructive asymptotic approach developed in the first part which needs no a priori assumption. For these moderate forces, we prove that the two-dimensional model we obtain by asymptotic expansions is the von Kármán one. Finally the two-dimensional stress field in the plate is deduced from the three-dimensional constitutive equations without any a priori assumption.