Singularities and wrinkling: The case of a concentrated force

The edge wrinkling of a uniformly stretched circular elastic plate subjected to a central concentrated load is considered within the framework of the Föppl–von Kármán nonlinear plate theory. Singular perturbation methods are employed to obtain a three-term asymptotic formula for the critical load in terms of a non-dimensional quantity that depends on the initial pre-stress. Comparisons between the analytical predictions and direct numerical simulations of the full bifurcation eigenproblem provide further insight into the accuracy and limitations of the derived results.