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垂直磁压电材料界面三维裂纹的超奇异积分法
引用本文:朱伯靖,秦太验. 垂直磁压电材料界面三维裂纹的超奇异积分法[J]. 力学学报, 2007, 39(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417
作者姓名:朱伯靖  秦太验
作者单位:中国农业大学理学院,北京,100083;中国农业大学理学院,北京,100083
摘    要:应用有限部积分概念和广义位移基本解,垂直于磁压电双材料界面三维复合型裂纹问题被转化为求解一组以裂纹表面广义位移间断为未知函数的超奇异积分方程问题. 进而,通过主部分析法精确地求得裂纹尖端光滑点附近的奇性应力场解析表达式. 然后,通过将裂纹表面位移间断未知函数表达为位移间断基本密度函数与多项式之积,使用有限部积分法对超奇异积分方程组建立了数值方法. 最后,通过典型算例计算,讨论了广义应力强度因子的变化规律.

关 键 词:磁压电双材料  超奇异积分  裂纹  复合型  应力强度因子
文章编号:0459-1879(2007)04-0510-07
收稿时间:2006-09-05
修稿时间:2006-09-052007-04-04

APPLICATION OF HYPERSINGULAR INTEGRAL EQUATION METHOD TO A THREE-DIMENSIONAL CRACK PERPENDICULAR TO THE INTERFACE IN ELECTROMAGNETOELASTIC BIMATERIALS
Zhu Bojing,Qin Taiyan. APPLICATION OF HYPERSINGULAR INTEGRAL EQUATION METHOD TO A THREE-DIMENSIONAL CRACK PERPENDICULAR TO THE INTERFACE IN ELECTROMAGNETOELASTIC BIMATERIALS[J]. chinese journal of theoretical and applied mechanics, 2007, 39(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417
Authors:Zhu Bojing  Qin Taiyan
Affiliation:College of Science, China Agricultural University, Beijing 100083, China
Abstract:This paper proposes a hypersingular integral equation method to analyze the three-dimensional mixed-mode crack perpendicular to the interface in anisotropic electromagnetoelastic(EME)bimaterials under extended electro-magneto-elastic coupled loads through theoretical analysis and numerical simulations.Using the Green's functions,the general extended displacement solutions of three-dimensional mixed-mode crack meeting the interface in anisotropic EME bimaterials under extended loads is analyzed by the boundary element method.Then this crack problem is reduced to solve a set of hypersingular integral equations coupled with boundary integral equations.The exact analytical solution of the extended singular stresses and extended stress intensity factors near the crack front are obtained.At last,a numerical method for the hypersingular integral equation for a three-dimensional mixed-mode rectangular crack subjected to extended loads by the body force method is proposed.Numerical solutions of the extended stress intensity factors of some examples are obtained.
Keywords:electromagnetoelastic bimaterials   hypersingular integral equation   crack   mixed-mode   stress intensity factors
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