Closed-form solution for postbuckling of composite flanges

Abstract

This paper presents closed form approximate solutions for the postbuckling behavior of orthotropic composite flanges under longitudinal compression. The lay-up is balanced and symmetrical. Regarding the boundary conditions, the two transversal edges are simply supported, one longitudinal edge is free and the other one rotationally restrained. Solutions of high computational efficiency are derived from an approach which uses shape functions with only few variables. It allows for a closed form solution of Airy’s stress function using the compatibility condition of in-plane strains. With the Galerkin procedure the equilibrium condition is approximately satisfied yielding a load-deflection relationship. From the deflection other quantities such as in-plane displacements, stresses and strains can be calculated. For typical flange geometries the derived method shows excellent agreement with results obtained from detailed finite element analyses.