双压电材料三维界面端部力电耦合场奇异性

计算物理 ›› 2016, Vol. 33 ›› Issue (1): 57-65.

双压电材料三维界面端部力电耦合场奇异性

王静平¹, 葛仁余¹, 韩有民¹, 张金轮¹, 程长征²

1. 安徽工程大学汽车新技术安徽省工程技术研究中心, 安徽芜湖 241000;
2. 合肥工业大学土木与水利工程学院, 安徽合肥 230009

收稿日期:2014-12-16 修回日期:2015-04-10 出版日期:2016-01-25 发布日期:2016-01-25
通讯作者: 葛仁余(1969-),男,博士,副教授,E-mail:gerenyu@sina.com
作者简介:王静平(1970-),男,硕士,讲师,研究方向:复合材料力学
基金资助:
国家自然科学基金（11372094）及安徽省教育厅（TSKJ2014B16和TSKJ2014B13）资助项目

Electromechanical Fields at Three-Dimensional Interface Edge Between Two Bounded Piezoelectric Materials

WANG Jingping¹, GE Renyu¹, HAN Youmin¹, ZHANG Jinlun¹, CHENG Changzheng²

1. Anhui Engineering Technology Research Center of Automobile New Technology, Anhui Polytechnic University, Wuhu 241000, China;
2. School of Civil Engineering, Hefei University of Technology, Hefei 230009, China

Received:2014-12-16 Revised:2015-04-10 Online:2016-01-25 Published:2016-01-25

摘要/Abstract

摘要： 基于切口根部物理场的幂级数渐近展开假设，从三维应力平衡方程和麦克斯韦方程组出发，导出关于双压电材料楔形界面切口端部奇性指数的特征微分方程组，并将切口的力电学边界条件表达为奇性指数和特征角函数的组合，从而将双压电材料楔形界面切口端部奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解，运用插值矩阵法求解界面端部若干阶应力奇性指数和相应特征函数.计算结果与已有结果对比表明本文方法的有效性和具有较高的计算精度.

关键词: 奇异性, 压电材料, 渐近展开, 特征函数, 插值矩阵法

Abstract: With asymptotic assumption for physical field near notch tip, characteristic differential equations for electroelastic singularities of wedges that contain bounded piezo/piezo materials are built from three-dimensional equilibrium equations and Maxell equations. Mechanical and electric boundary conditions are expressed by combination of singularity orders and characteristic angle functions. Thus, evaluation of singularity orders is transformed into solving ordinary differential equations (ODEs) under designated boundary conditions. Interpolating matrix method is introduced to solve derivative ODEs. More electroelastic singularity orders and associated eigenfunctions in wedges that comprise two bounded transverse isotropic piezoelectrics materials are obtained. It shows that the method is efficient and has high accuracy compared with existent solutions.

Key words: singularity, piezoelectric material, asymptotic expansion, characteristic angle functions, interpolating matrix method

中图分类号:

O343.4

王静平, 葛仁余, 韩有民, 张金轮, 程长征. 双压电材料三维界面端部力电耦合场奇异性[J]. 计算物理, 2016, 33(1): 57-65.

WANG Jingping, GE Renyu, HAN Youmin, ZHANG Jinlun, CHENG Changzheng. Electromechanical Fields at Three-Dimensional Interface Edge Between Two Bounded Piezoelectric Materials[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(1): 57-65.

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