Variational principle of plastic buckling of plates

Wrinkling is one of common defects in sheet metal forming processes, which has bad effect on formed parts. Prediction and prevent of wrinkling has been considered as a hot problem for long time. Wrinkling essentially is a compressive instability phenomenon of sheet metals. In this paper, the sheet metal before and after wrinkling is assumed to be the rigid-plastic material model. During plastic wrinkling, the sheet metal satisfies all equations, including differential equations of equilibrium, strain compatibility equations, yield criteria and flow rules. Thus this problem comes as to solution of the maximum value of a variation function. In the variation function, the internal force field and the velocity field are independent variable functions, which are dependent each other. Therefore, an approximately analytical solution to the plastic wrinkling in sheet metal processes can be conveniently obtained by the direct method. As an example, the wrinkling load, the internal force and velocity field are given for annular plate with the longitudinal tensile and compressive force acting on its boundary.