Analytical Solutions For Axisymmetric Bending Of Functionally Graded Circular/Annular Plates

Based on the first-order shear deformation plate theory, governing equationsfor the axisymmetric bending of functionally graded circular/annular platesare derived in terms of displacements. Then, analytical solutions for thedisplacements, force and moment resultants are obtained by directly solvingthe governing equations. It is assumed that the temperature field variesthrough the plate thickness only, and the mechanical and thermal propertiesof the plate vary continuously through the plate thickness and obey a simplepower law related to the volume fraction of the constituents. As examples,solutions for the clamped and simply supported circular plates are derived. Effects of the gradient constant of material, sheardeformation and boundary conditions on the deflection of the plate arediscussed in details. The following conclusions can be reached.(1) The effect of transverse shear deformation on the axisymmetric bendingof functionally graded circular plate can be effectively considered by useof the first-order shear deformation plate theory.(2) The method used in the present paper is simple and effective. If thethermal loading is neglected, the present solutions reduce to the solutionsobtained by Reddy et al. If the gradientconstant of material is equal to zero, then the present solutions reduce tothe solutions for isotropic plates. Moreover, if one neglects the gradientconstant of material and the transverse shear deformation, the presentsolutions reduce to the solutions based on the classical plate theory.(3) The material constant n and boundary conditions have important effectsonthe bending behavior of functionally graded circular plates. Thermal loadinghas no effect on the deflection of the clamped plate, but has significanteffect on the deflection of the simply supported circular plate.