【摘要】 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状态方程,进而对材料系数按指数函数规律分布的半无限大压电体中的反平面Yoffe型运动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、电位移的解析表达式,并求得了裂纹尖端动应力强度因子、电位移强度因子,分析了不同的非均匀材料系数、几何尺寸及裂纹运动速度对它们的影响．更多还原

【Abstract】 Based on the three-dimensional theory of piezoelectric elasticity,the governing equations were deduced for the functionally graded piezoelectric materials and the anti-plane Yoffe fracture problems for half-infinite piezoelectric medium were solved for the material quality in the form of exponential functions. The displacement,stress,electric potential and electric displacement around the crack in the half-infinite piezoelectric medium were obtained by way of Fourier transform and then the dynamic stress intensity fac- tor,the electric displacement intensity factor near the crack tip were obtained as well.Finally,the influence of different nonhomogeneous material properties,geometrical size and the moving velocity of the crack on SIF and EDIF was analyzed.更多还原