Numerical Solutions of the von Karman Equations for a Thin Plate
  In this paper, we present an algorithm for the solution of the von Karman equations of elasticity theory and related problems. Our method of successive reconditioning is able to avoid convergence problems at any ratio of the nonlinear streching and the pure bending energies. We illustrate the power of the method by numerical calculations of pinched or compressed plates subject to fixed boundaries. 
Pedro Patricio da Silva and Werner Krauth