功能梯度中厚圆/环板轴对称弯曲问题的解析解

基于一阶剪切变形板理论，导出了热/机载荷作用下，位移形式的功能梯度中厚圆/环板轴对称弯曲问题的控制方程，获得了问题的位移和内力的一般解析解. 作为特例，分别研究了边缘径向固定和可动的夹紧和简支的4种实心功能梯度圆板，给出了它们的解，并分析了热/机载荷作用下解的形态，讨论了横向剪切变形、材料梯度常数和边界条件，对板的轴对称弯曲行为的影响.

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

Based on the first-order shear deformation plate theory, governing equations for the axisymmetric bending of functionally graded circular/annular plates are derived in terms of displacements. Then, analytical solutions for the displacements, force and moment resultants are obtained by directly solving the governing equations. It is assumed that the temperature field varies through the plate thickness only, and the mechanical and thermal properties of the plate vary continuously through the plate thickness and obey a simple power 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, shear deformation and boundary conditions on the deflection of the plate are discussed in details. The following conclusions can be reached.(1) The effect of transverse shear deformation on the axisymmetric bending of functionally graded circular plate can be effectively considered by use of the first-order shear deformation plate theory.(2) The method used in the present paper is simple and effective. If the thermal loading is neglected, the present solutions reduce to the solutions obtained by Reddy et al. If the gradient constant of material is equal to zero, then the present solutions reduce to the solutions for isotropic plates. Moreover, if one neglects the gradient constant of material and the transverse shear deformation, the present solutions reduce to the solutions based on the classical plate theory.(3) The material constant n and boundary conditions have important effects on the bending behavior of functionally graded circular plates. Thermal loading has no effect on the deflection of the clamped plate, but has significant effect on the deflection of the simply supported circular plate.