CHARACTERISTIC ORTHOGONAL POLYNIMIAL APPLICATION TO GALERKIN INDIRECT VARIATIONAL METHOD FOR SIMPLY SUPPORTED PLATE UNDER IN PLANE LOADING

J. C. Ezeh, Ibearugbulem M. Owus, H. E. Opara, O. A. Oguaghamba

Abstract: This study considers the application of characteristic orthogonal polonomial to Galerkin indirect variational method for buckling analysis elastic of thin rectangular plates with all edges simply supported. The Galerkin method has been used to solve problems in structural engineering such as structural mechanics, dynamics, fluid flow, heat and mass transfer, acoustics, neutron transport and others. The Galerkin method can be used to approximate the solution to ordinary differential equations, partial differential equations and integral equations with a polynomial involving a set of parameters called characteristic orthogonal polynomials. The buckling loads from this study were compared with those of previous researches. The results showed that the average percentage differences recorded for SSSS plates are 0.014% to 0.055%. These differences showed that the shape functions formulated by COP has rapid convergence and is very good approximation of the exact displacement functions of the deformed thin rectangular plate under in-plane loading when applied to Galerkin’s buckling load for isotropic plates. An indirect variation principle (based on Galerkin’s method) could be used in confidence to satisfactorily analyze real time rectangular thin plates of various boundary conditions under in- plane loadings. The results obtained herein are very close to the results obtained by previous research works that used different methods of analysis.

Keywords: Indirect Variational Method; Galerkin Method; Buckling loads; Characteristic Orthogonal Polynomials; Approximate solution; Non linear functional; Convergence; Boundary conditions

DOI: https://doi.org/10.15623/ijret.2014.0304127