An analytical description of the post-buckling behaviour of outstand plates in compression

Abstract

A theoretical model describing the post-buckling behaviour of elastic outstand plates under uniaxial compression is presented in this study. The derivation is rooted in the Föppl-von Karman equations, which are further simplified by making a number of basic mechanical assumptions about the post-buckling stress field. An approximate solution to the emerging differential equation is obtained, which assumes a polynomial displacement profile in the transverse direction of the plate. This solution agrees eminently well with the results of finite element simulations, both for the case of a geometrically perfect plate and a plate containing an initial imperfection. By combining the obtained post-buckling stress profile with a failure criterion based on von Karman’s effective width concept, a closed-form strength equation for compressed outstand plates is derived, which is seen to be a sole function of the plate slenderness and a dimensionless imperfection factor. Based on this, a design equation is proposed which closely agrees with the available experimental data.