Linking the von Karman Equations to the Practical Design of Plates

Abstract

The Föppl-von Karman equations describe the highly nonlinear postbuckling behavior of elastic plates but are notorious for their unwieldiness. Owing to the lack of a sufficiently general solution, the practical design of plates against local buckling is instead based on the empirical Winter equation. This paper aims to connect both concepts by analytically deriving a Winter-type equation, taking the Föppl-von Karman equations as a starting point. The latter equations are first simplified in a way that preserves the main mechanics of the postbuckling behavior of plates and are combined with a failure criterion based on von Karman’s effective width concept. The resulting equation is solved by means of a truncated Fourier series. This yields excellent predictions of the plate behavior over an ever more extended range of postbuckling behavior as the number of Fourier terms increases, both for geometrically perfect and imperfect plates. As a crowning result, a closed-form expression is presented as an equivalent to the empirical Winter equation. This new expression agrees closely with the Winter curve and allows an analysis of the various factors affecting the local buckling capacity of plates.