Buckling analysis of thick isotropic rectangular ssfs plates using polynomial displacement functions

Abstract

This research study focuses on the buckling analysis of an elastic thick isotropic rectangular plate with three edges simply supported and the third edge free (SSFS). The Ritz energy method was employed using Orthogonal Polynomial Displacement Functions (OPDF) and polynomial shear deformation function, denoted as f(z). The general governing Equation of the rectangular thick plate was formulated which was further analysed to deduce the non-dimensional critical buckling load parameters of the plate under uniaxial in-plane compressive load Nx. The meticulous consideration of the SSFS plate involved satisfying pertinent boundary conditions.  The stiffness coefficient values were deduced from the employed Orthogonal Polynomial Displacement Functions. The resultant direct governing equation was solved to yield a concise analytical expression, subsequently utilized to generate non-dimensional critical buckling load parameters for the plates. This process was conducted across varying values of the span-depth ratio (a/h) and aspect ratios (b/a). To ensure the robustness and accuracy of the findings, the results obtained in this study were meticulously compared with the works of other esteemed researchers. This comparative analysis serves to validate the present results, contributing to the scholarly discourse on the buckling behaviour of isotropic thick rectangular plates