Static Analysis of Functionally Graded Plate Using Nonlinear Classical Plate Theory with von Karman Strains: A Complex Solution Analysis

Abstract

The present study is based on the nonlinear bending analysis of Functionally Graded Material (FGM) plate with von Karman strain based nonlinear classical plate theory with in-plane displacement and moderate rotation subjected to thermal loading in the transverse direction. The equations of motion and boundary conditions are obtained using the Principle of Minimum Potential Energy (PMPE) method and material property is graded in thickness direction according to simple power-law distribution in terms of volume fractions of the constituents. The temperature is varying linearly through the thickness while temperature dependent material properties are nonlinear function of temperature. The effect of temperature-dependent material property is studied. It is observed that dependency of material property on the temperature cannot be neglected for analyzing the inhomogeneous FGM plate subjected to thermomechanical loading. The complex solution is obtained using analytical method, viz., Navier’s Method which assures minimum error in the solution for simply supported plate. The results show that the response is transitional with respect to ceramic and metal and the complex solution predicts the real behavior of stresses and deflections in the FGM plate. The transverse deflection is in-between to that of metal and ceramic rich plates for FGM plates. The complex form of solution also gives information about the stress distribution in the thickness direction. The effect of temperature rise, side-to-thickness ratio and volume fraction exponent on nondimensional maximum central deflection and axial and transverse shear stresses of an FGM plate is studied.