Elastic Wrinkling of a Tensioned Circular Plate Using von Ka´rma´n Plate Theory

A circular elastic plate, with a uniform tension field applied at its outer edge, is acted upon by a centrally applied transverse force. As the force is increased, the tension state as determined from von Ka´rma´n plate theory, changes. In particular for sufficiently large values of the transverse force or displacement, the plate can develop a compressive circumferential membrane stress. When this compressive stress becomes sufficiently large, wrinkling can result. The corresponding value of the transverse displacement is determined by investigating an eigenvalue problem in which wrinkling is indicated by the vanishing of the lowest eigenvalue. The results are the values of the central transverse deflection which induces wrinkling for a range of in-plane tensions and are sensitive to the in-plane boundary support conditions at the outer edge.