压电半平面梯形夹杂的梯度特征应变问题

针对边界处自由和绝缘以及固定和绝缘两种不同的条件，分别计算分析了均匀和梯度特征应变下梯形夹杂内部和外部诱发产生的弹性场和电场，并且讨论了梯形夹杂角点处的奇异性．最后，计算了平均梯度特征应变为零时梯形夹杂内部产生的平均弹性场和电场．所得结果揭示了基体不同边界条件对诱导场的影响．

The Problem of Trapezoidal Inclusion with Graded Eigenstrain in a Piezoelectric Half Plane

Under freedom insulation and fixed insulation boundary conditions, the exterior and interior elastic field and electric field for a trapezoidal inclusion were calculated and analyzed, where the eigenstrain within the inclusion can be not only uniform but also graded. Furthermore, the vertex singularity issue of trapezoid was discussed. Finally, the mean interior elastic field and electric field were computed when the mean graded eigenstrain was zero. The numerical results revealed the effects of different boundary conditions on the induced fields.