Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid
Electro-elastic fields around two arbitrarily-shaped holes in a finite electrostrictive solid
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DOI：
10.1016/j.apm.2015.12.001
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发表时间：
2016-04-01
影响因子：
5
通讯作者：
Gao, Cun-Fa
中科院分区：
文献类型：
--
作者：
Dai, Ming;Meng, Li-Cheng;Gao, Cun-Fa
研究了在均匀远场电场作用下，有限电致伸缩固体中两个任意形状孔洞周围的应力和电场集中情况。通过若干保角映射来定义固体的边缘以及孔洞的形状。利用保角映射技术、法贝尔级数和傅里叶展开法，得到了固体的电弹性场以及固体外部和孔洞内部的电场。给出了正方形电致伸缩平面内椭圆、三角形、正方形、卵形和矩形孔洞的大量数值结果。发现固体边缘附近的精确外电场本质上是非均匀的，其最大值似乎远大于均匀远场电场，同时表明当孔洞边界上的最大曲率点接近固体边缘或另一个孔洞时，该点附近的环向应力迅速增大。另一方面，对于单个位于中心的孔洞，如果有限平面的尺寸不小于孔洞尺寸的六倍，则有限电致伸缩平面可近似视为无限平面；而对于两个相互作用的孔洞，当两个孔洞之间的距离大于孔洞尺寸的三倍时，它们之间的相互作用可忽略不计。© 2015爱思唯尔公司。保留所有权利。
Stress and electric field concentration around two arbitrarily-shaped holes in a finite electrostrictive solid subjected to uniform remote electric field are studied. The edge of the solid and the shapes of the holes are defined via several conformal mappings. The electro-elastic field of the solid as well as the electric fields both outside the solid and inside the holes are obtained on using conformal mapping techniques, Faber series and Fourier expansion method. Extensive numerical results are shown for elliptical, triangular, square, oval and rectangular holes in a square electrostrictive plane. The exact external electric field near the edge of the solid is found to be essentially non-uniform and its maximum appears to be much larger than the uniform remote electric field, while it is shown that the hoop stress nearby the point of maximum curvature on the hole's boundary increases rapidly as the point of maximum curvature approaches either the edge of the solid or the other hole. On the other hand, for a single centrally-located hole, the finite electrostrictive plane can be approximately treated as an infinite plane if the size of the finite plane is not less than six times the size of the hole, while for two interacting holes, the interaction between them is negligible when the distance between the two holes is larger than three times the size of the holes. (C) 2015 Elsevier Inc. All rights reserved.