Linking the von Karman equations to the design of steel plates

In this paper the von Karman system of partial differential equations describing the nonlinear postbuckling response of plates is simplified into a single equation, while taking caution to preserve the main mechanisms through which plates develop post-buckling reserve capacity. The resulting equation is solved for the case of a perfect plate using a single Fourier term, and for the case of an imperfect plate using two Fourier terms. Good agreement with finite element simulations, used as a benchmark, is obtained. The theory is further used to derive a closed form expression for the plate capacity as a function of the slenderness, which agrees very well with the well-known Winter equation.