Perturbation solution of two arbitrarily-shaped holes in a piezoelectric solid
Perturbation solution of two arbitrarily-shaped holes in a piezoelectric solid
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压电固体中两个任意形状孔的微扰解
DOI：
10.1016/j.ijmecsci.2014.06.015
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发表时间：
2014-11
影响因子：
7.3
通讯作者：
Gao Cun-Fa
中科院分区：
文献类型：
--
作者：
Dai Ming;Gao Cun-Fa
本文给出了无限大压电体中两个任意形状的孔在无穷远处承受均布力电载荷的二维问题的摄动解。特别感兴趣的是与两个孔之间的距离有关的孔周围的应力场和电场。每个孔的形状用截断映射来表征，这可以看作是带有摄动的椭圆孔的截断映射。利用微扰法和费伯级数，将压电体的复势和孔洞内的电场表示成待定系数的级数形式，由傅立叶展开法求出。给出了椭圆形、椭圆形、三角形和方孔的详细数值结果。得出的基本结论是，随着最大曲率点到另一个孔的距离的减小，孔׳-S边界上最大曲率点附近的环向应力和电场强度迅速增大。结果表明，无论两孔间的距离如何，非椭圆孔内的电场总是不均匀的，而椭圆孔内的电场则随着两孔间距离的增大而趋于均匀。此外，如果两个孔之间的距离大于孔大小的四倍，则两个孔之间的相互作用是可以忽略的，并且两个孔的问题可以分解为只有一个孔的两个单独的问题。
This paper presents a perturbation solution to a two-dimensional problem of two arbitrarily shaped holes within an infinite piezoelectric solid subjected to uniform mechanical and electric loads at infinity. Of particular interest are the stress field and electric field around hole with relation to the distance between the two holes. The shape of each hole is characterized by a truncated mapping which can be regarded as that for an elliptical hole with a perturbation. By using the perturbation method and Faber series, both the complex potentials of the piezoelectric solid and the electric fields inside holes are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for oval, elliptical, triangular and square holes. A basic conclusion is that the hoop stress and electric field strength nearby the point of maximum curvature on the hole׳s boundary increase rapidly with decreasing distance between the point of maximum curvature and the other hole. On the other hand, it is shown that the electric field inside non-elliptical hole is always non-uniform regardless of the distance between the two holes, while that inside elliptical hole tends to be uniform with increasing distance between the two holes. Additionally, if the distance between the two holes is more than four times the hole size, the interaction between the two holes is ignorable and the problem of two holes can be divided into two separate problems of only a single hole.
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DOI：
10.1115/1.2791051
发表时间：
1999-06
期刊：
Journal of Applied Mechanics
影响因子：
--
作者：
C. Ru
通讯作者：
C. Ru
DOI：
10.1115/1.2897080
发表时间：
1990-09
期刊：
Journal of Applied Mechanics
影响因子：
--
作者：
C. Hwu
通讯作者：
C. Hwu
影响因子：
3.6
作者：
H. Sosa
通讯作者：
H. Sosa
DOI：
10.1016/j.ijmecsci.2013.07.012
发表时间：
2013-10-01
影响因子：
7.3
作者：
Dai, Ming;Sun, Huiyu
通讯作者：
Sun, Huiyu
影响因子：
2.8
作者：
Q. Qin
通讯作者：
Q. Qin