中文摘要：

为了研究各向异性功能梯度夹层圆环在内外压作用下的弹性问题,假设功能梯度过渡层的材料性质为沿径向呈幂函数连续变化的形式,泊松比为常量,基于弹性力学理论,采用逆解法,引入变量φ,将轴对称问题的控制方程转化为关于φ的欧拉方程,从而由边界条件以及连续性条件求得整体结构平面应力问题的封闭解。最后通过算例分析了材料的非均匀特性和各向异性对应力和位移分布的影响。研究结果表明,梯度参数的增大,可改善结构内径向应力以及径向位移分布,但同时也会增大靠近外层区域、尤其是过渡层与外层材料交界处的环向应力。各向异性参数的增大,会导致结构内环向应力的最小和最大值由过渡层和内外层材料交界处逐渐向内外边界转移。

英文摘要：

The elastic problem of sandwich circular ring with polar orthotropic functionally gradient transition layer which is subjected to the internal and external pressures is studied.Based on the theory of elastic mechanics,we assume that the elastic moduli of the radial and circumferential of functionally gradient transition layer vary continuously with power-law along the radial direction and Poisson＇s ratio is constant.Using the inverse method and introducing the variableφ,the governing equations of axisymmetric problems are transformed to the Euler equations ofφ,the closed-form solutions of plane stress problem of the overall structure are obtained by the boundary conditions and continuity conditions.Finally,numerical examples are preserted to indicate the influence of inhomogeneous property and orthotropy of materials on the stress distribution and displacement distribution.Obtained results show that,bigger gradient parameters can improve the distribution of the radial stress and radial displacement of the structure,and increase the circumferential stress of areas near the outer layer,especially at the edge of the transition layer and outer layer.The increase of the orthotropy parameter can lead to that the minimum and maximum value of cir-cumferential stresses transfers from the edges of the transition layer with inner and outer layer to the inner and outer boundaries.