A mechanical model for the buckling of unilaterally constrained rectangular plates

Abstract

A mechanical model is described for the problem of buckling of unilaterally constrained, finite, rectangular plates. Due to the nature of the imposed constraint on the plate's lateral deflection, w, solving for the buckling load required the solution of a nonlinear partial differential equation in w. While the plates were modeled along the lines of classical plate theory, the nonlinearity arose from the fact that the plates were attached to nonlinear elastic foundations exhibiting a deformation sign dependent force-displacement relationship. This feature was introduced to model the unilateral constraint. The influence of different boundary conditions, material orthotropy and transverse load distributions was investigated. For each case, the weak form of the governing differential equation was solved via the Galerkin's method. Investigations of the buckling loads of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this approach for the cases investigated and compared to some previous exact results reported in the literature.