功能梯度压电材料反平面裂纹问题

基于三维弹性理论和压电理论，导出了材料系数在横观各向同性平面内梯度分布的压电体的状态方程，进而对材料系数指数函数规律分布的半无限大压电体中的反平面裂纹问题进行了求解，利用Fourier变换给出了半无限大压电体中位移，应力，电势及电位移的解析表达式，并求得了裂纹尖端的应力强度因子和电位移强度因子，分析了不同的非均匀材料系数及几何尺寸对它们的影响。

Anti-plane Crack Problem in Functionally Graded Piezoelectric Materials

Based on the three-dimensional theory of piezoelectric elasticity, the governing equations were deduced for the functionally graded piezoelectric materials; and the anti-plane fracture problems for half-infinite piezoelectric medium was solved in the case of the material quality being in the form of exponential functions. We got the displacement, stress, electric potential and electric displacement around the crack in the half-infinity piezoelectrical medium by the way of Fouriel Transforms, and then the stress intensity factor and the electric displacement intensity factor near the crack tip were easily obtained. Finally, the influence of different nonhomogeneous material properties and geometrical size on SIF and EDIF was analyzed.