横观各向同性功能梯度圆板弯曲问题的精确解

对周边为弹性支承边界条件下的横观各向同性功能梯度材料圆板轴对称弯曲问题进行了分析.将位移函数写成傅里叶-贝塞尔级数的形式,根据横观各向同性功能梯度材料基本方程,并针对指数函数形式的梯度分布情况,对功能梯度圆板轴对称弯曲问题的位移和应力进行了精确分析.并通过具体算例,分析了在圆板上、下表面荷载作用下,材料性质的不同梯度变化对圆板结构响应的影响.分析结果表明,材料性质的梯度变化对圆板的力学性能有显著影响.

The Exact Solution to Bending of Transversely Isotropic Functionally Graded Circular Plate

This paper presented an exact analysis of the axisymmetric bending of the transversely isotropic functionally graded circular plate under the elastically supported edge boundary condition. The displacement function of the functionally graded circular plate was expanded as Fourier-Bessel series. Based on the basic equations of transversely isotropic functionally graded materials under the assumption that all of material properties have the same exponential dependence on the thickness-coordinate, exact solutions to displacement and stress field were obtained for a circular plate subject to axisymmetric normal and shearing loading on its upper and lower surfaces. The obtained exact solutions show that the gra- ded material properties have significant effects on the mechanical behavior of the plate.