Theories and analyses of functionally graded circular plates

Abstract This paper presents the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded axisymmetric circular plates. The classical, first-order, and third-order shear deformation theories are presented, accounting for through-thickness variation of two-constituent functionally graded material, modified couple stress effect, and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.