Ritz Method-Based Formulation for Analysis of FGM Thin Plates Undergoing Large Deflection with Mixed Boundary Conditions

The analysis of functionally graded material (FGM) plates undergoing large deflection involves lengthy mathematical computations which makes the adoption of an automated procedure of practical importance. The aim of this study is to propose a generalized matrix form formulation capable of tackling the problem of FGM plates undergoing large deflection in a systematic automated approach. The proposed formulation is based on Ritz method and the classical plate theory (CPT) with von Karman assumptions. The trial functions for the three displacements u, v and w are represented by general polynomials capable of handling all classical plate boundary conditions, namely simply supported, clamped and free edges as well their possible combinations that lead to mixed boundary conditions. Substitution of the trial functions in the developed matrix form yields a nonlinear system of algebraic equations which can then be used to solve for the unknown constants and, hence, the solution of the plate displacements and other plate internal forces thereafter. Three numerical examples are presented to illustrate the applicability of the proposed formulation for different combinations of mixed boundary conditions including free edges. In addition to its accuracy, the proposed method is easy to code and yields functional form solutions.