Bifurcations of the von Kármán equations with Robin boundary conditions

We study buckling of a rectangular plate with elastic support and restraint along two edges and simple support along the other two edges. This corresponds to a bifurcation analysis of the von Kármán equations with Robin boundary conditions. Of special interest is the phenomenon of mode jumping in deformation of the plate. We discretize the von Kármán equations with the finite difference methods. The solution curves branching from the first two simple bifurcation points, resulted from splitting of a double bifurcation point, are numerically traced with respect to the increase of the load by using the continuation methods. Our numerical results show that mode jumping depends on length of the plate and stiffness of the elastic support.