Analytical Solutions Using a Higher-Order Refined Theory for the Static Analysis of Functionally Graded Material Plates

Abstract

Analytical formulations and solutions to the static analysis of simply supported Functionally Graded Material (FGM) plates hitherto not reported in the literature based on a higher-order refined shear deformation theory with nine degrees-of-freedom already reported in the literature are presented. This computational model incorporates the plate deformations which account for the effect of transverse shear deformation. The transverse displacement is assumed to be constant throughout the thickness. In addition, another higher order theory with five degrees-of-freedom and the first order theory already reported in the literature are also considered for comparison. The governing equations of equilibrium using all the computational models are derived using the Principle of Minimum Potential Energy (PMPE) and the analytical solutions are obtained in closed-form using Naviers solution technique. A simply supported plate with SS-1 boundary conditions subjected to transverse loading is considered for all the problems under investigation. The varying parameters considered are the side-to-thickness ratio, power law function, edge ratio and the degree of anisotropy. Correctness of the formulation and the solution method is first established and then extensive numerical results using all the models are presented which will serve as a bench mark for future investigations.