功能梯度压电板条中的电渗透型运动裂纹

基于三维弹性理论和压电理论 ,研究了功能梯度压电板条中的电渗透型运动裂纹问题 .利用Fourier积分变换方法 ,将混合边值问题化为对偶积分方程 ,并进一步归结为易于数值求解的第二类Fredholm积分方程 .通过渐近分析 ,获得裂纹尖端应力、应变、电位移和电场的解析解 ,给出裂纹尖端场各个变量的角分布函数 ,并求得裂纹尖端场的强度因子 .结果表明 ,对于电渗透型裂纹 ,功能梯度压电板条中运动裂纹尖端附近的各个场变量都具有 - 1/ 2阶的奇异性 ,而且与固定于裂纹尖端的运动坐标有关 ;当裂纹运动速度增大时 ,裂纹扩展的方向会偏离裂纹面 .

Permeable Moving Crack in Functionally Graded Piezoelectric Strip

Based on the three-dimensional theory of piezoelectric elasticity,the permeable moving crack problem was solved for a functionally graded piezoelectric strip.By using the Fourier transform,the mixed boundary-value problem is first reduced to dual integral equations and then into Fredholm integral equations of the second kind.The closed forms of the singular stress,strain,electric displacement and electric field are obtained by using asymptotic expansion,and we also got the angular distribution function of the field variables and the intensity factors of relevant quantities near the crack tip.The results obtained for permeable crack show that the field variables near the crack tip in a functionally graded piezoelectric strip all possess the square root singularity,and they are in terms of the local coordinates attached to the moving crack tip; the moving crack has a tendency to turn away from the crack face when the velocity is increased.