Föppl–von Kármán equations

Summary

The Föppl–von Kármán equations describe thin elastic plates whose deflections are large compared with their thickness but still small compared with their width. They couple the bending of the plate with the stretching of its mid-plane, which the linear biharmonic plate equation ignores. The stretching is encoded by an Airy stress function, and it is driven by the Gaussian curvature of the deflected surface. They explain the buckling of plates, wrinkling and crumpling of sheets, and the stiffening of a plate as it bends.