A Newton-GMRES Approach for the Analysis of the Postbuckling Behavior of the Solutions of the von Kármán Equations

We propose a Newton-GMRES type algorithm to solve the discrete von Kármán problem. We show that this algorithm is efficient both in memory and computation time and robust in the neighborhood of the singular points of the bifurcation diagrams. Placing ourselves in the context of the Schaeffer and Golubitsky theory, we use this algorithm to study the post-buckling behavior of a rectangular plate clamped and compressed along its four sides.