BUCKLING ANALYSIS OF THIN PLATES

Abstract

ABSTRACT In the this project, buckling loads of rectangular plates having different sets of boundary conditions and subjected to uniform and linearly varying inplane loading are analyzed. Using the stress distribution as per the variation of inplane edge loading, the plate buckling equations are derived. Adopting Galerkin’s approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to linearly varying inplane loading are found. Buckling mode shapes of plate for simply supported conditions with non-uniform inplane loadings are also presented. 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 and transverse load distributions was investigated. For each case, the weak form of the governing differential equation was solved via the Galerkin’s method.