Existence, uniqueness, and numerical simulations of Foppl-von Karman equations for simply supported plate

Abstract : In this paper, we consider the Foppl-von Karman equations in the case of a simply supported thin plate. We introduce a nonlinear Gauss-Seidel fixed point scheme which allows to obtain a constructive proof of the existence and the uniqueness, when a small nonzero source term is considered. Numerical simulations are given using finite elements approximation. We point out the important role of a parameter which allows to select situations in which a buckling phenomena is observed numerically.