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Null-field approach for piezoelectricity problems with arbitrary circular inclusions

机译：具有任意圆形夹杂物的压电问题的零场方法

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摘要

In this paper, we derive the null-field integral equation for piezoelectricity problems with arbitrary piezoelectric circular inclusions under remote anti-plane shears and in-plane electric fields. Separable expressions of fundamental solutions and Fourier series for boundary densities are adopted to solve the piezoelectric problem with circular inclusions. Four gains are obtained: (1) well-posed model, (2) singularity free, (3) boundary-layer effect free and (4) exponential convergence. The solution is formulated in a manner of semi-analytical form since error purely attributes to the truncation of Fourier series. Two piezoelectric problems with two piezoelectric circular inclusions are revisited and compared with the Chao and Chang's solutions to demonstrate the validity of our method. The limiting case that the two inclusions separate far away leads to the Pak's solution of a single inclusion. Stress and electric field concentrations are calculated and are dependent on the distance between the two inclusions, the mismatch in the material constants and the magnitude of mechanical and electromechanical loadings. The results for the shear and electric loadings in two directions are also compared well with the Wang and Shen's results.
机译：在本文中，我们推导了在远程反平面剪切和面内电场作用下具有任意压电圆形夹杂物的压电问题的零场积分方程。采用基本解和边界密度的傅里叶级数的可分离表达式来解决圆形夹杂物的压电问题。获得了四个增益：（1）适定模型，（2）无奇点，（3）无边界层效应和（4）指数收敛。由于误差纯粹归因于傅立叶级数的截断，所以该解决方案以半分析形式制定。再次讨论了带有两个压电圆形夹杂物的两个压电问题，并将其与Chao和Chang的解决方案进行了比较，以证明我们方法的有效性。两个夹杂物分开很远的极限情况导致了Pak对单个夹杂物的解决方案。计算应力和电场浓度，取决于两个夹杂物之间的距离，材料常数的不匹配以及机械和机电负载的大小。在两个方向上的剪切载荷和电载荷的结果也与王和沉的结果进行了很好的比较。

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