Nonlinear Lateral Deflection Analysis of an FGM Circular Plate Whose Material Properties Vary in Transverse and Radial Directions

In the present paper, nonlinear analysis of lateral deflection of bidirectional functionally graded circular plates whose material properties vary in both transverse and radial directions is presented. The governing equations of the plate are derived based on the classical theory and von Karman’s nonlinear strain-displacement relations. Due to bidirectional variations of the material properties, influence of the radial derivatives of the material properties and the transverse variations of the properties on the rigidities have appeared in the governing equations. The governing equations are solved by the finite difference method. Incorporation of the finite difference form of the boundary conditions on various points of the boundary is also discussed. Finally, behaviors of plates fabricated from isotropic, transversely-graded, and two-directional-functionally graded materials are investigated and present results are validated against results of the special cases reported in the available well-known references and results of Abaqus software.