Buckling of Columns and Plates

Abstract

The governing equations for a thin plate subjected to both in-plane and lateral loads have been derived previously. In those equations, there was one governing equation describing the relationship between the lateral deflection and the laterally distributed loading,

$$ D{\nabla ^4}w = p\left( {x,y} \right) $$

and other equations dealing with in-plane displacements, related to in-plane loads

$$ {{\nabla }^{4}}{{u}_{0}} = {{\nabla }^{4}}{{v}_{0}} = 0. $$

.