SOLUTION OF AN ELLIPTICAL HOLE IN A FINITE ELECTROSTRICTIVE SOLID
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摘要: 基于电致伸缩材料的基本方程, 该文采用Faber级数方法研究了含有椭圆型孔洞的有限大电致伸缩材料板在受到电载荷作用下的二维问题。采用各向同性体平面理论中的复势方法, 以Faber级数、保角映射及最小二乘边界配置技术为工具, 提出了含有单个椭圆孔的有限大电致伸缩材料板在电载荷作用下的级数解, 详细讨论了板的尺寸、孔洞的尺寸、孔洞的分布以及洞内的电场对于孔边应力的影响规律。最后通过几组数值算例, 讨论了各种参数的变化对孔周应力集中的影响, 并就特殊情况与文献中的一些结果进行了比较, 结果表明最小二乘边界配置法具有精度高、收敛速度快等优点。Abstract: Based on the complex potential method in the plane theory of isotropic elasticity, a series solution for the stress field of a finite plate containing an elliptical hole subjected to electrical loads is studied by means of the Faber series expansion. The key point is that the technique of least squares boundary collocation is employed twice. According to this method mentioned above, electric field and stress field can be obtained, respectively. The effects of plate size, hole size, hole distribution and electric field inside the elliptical hole on the stress field around the elliptical hole are studied in detail. Several conclusions valuable to practices are drawn. Finally, the effects of the parameters on the hole stress concentration and the stress intensity factors are studied through several numerical examples. It is shown from the obtained results for special examples that the least squares boundary collocation technique presented has many advantages such as high accuracy and good convergence.
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