横观各向同性压电功能梯度旋转圆盘的三维解析解

从横观各向同性压电弹性力学轴对称问题基本方程出发，采用直接位移法将位移分量展开成径向坐标，的幂函数线性组合形式，其中含有7个待定的位移函数，它们是坐标z的函数，由基本方程导出关于位移函数的控制方程，结合相应的边界条件，可以积分得到位移函数，并确定积分常数，从而给出横观各向同性压电功能梯度旋转圆盘的三维解析解．并通过相应算例展示了一种特殊形式的压电功能梯度材料的梯度指标对应力场、位移场和电场的影响．

3D Analytical Solution for Rotating Disc of Functionally Graded Piezoelectric Materials with Transversely Isotropy

Based on the basic equations of axisymmetric problems identified with transversely isotropic piezoelectric materials, the displacement components are expanded and assumed to fit with polynomials of the radial coordinate with seven involved parameters, resulting with seven undetermined displacement functions in the thickness coordinate. The displacement can be obtained through integration along with the consideration of the boundary conditions of the disc. Thus a three-dimensional analytical solution is attained for the piezoelectric rotating disc made of transversely isotropic and functionally graded materials, in which the material properties are the arbitrary functions of the thickness coordinate. The effect of gradient index on the field of stress, displacement and electricity is demonstrated through presenting a special functionally graded piezoelectric material.