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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, 23(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417
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, 23(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417
Bojing Zhu, Taiyan Qin. 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, 23(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417
Citation: Bojing Zhu, Taiyan Qin. 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, 23(4): 510-516. DOI: 10.6052/0459-1879-2007-4-2006-417

垂直磁压电材料界面三维裂纹的超奇异积分法

Application of hypersingular integral equation method to a three-dimensional crack perpendicular to the interface in electromagnetoelastic bimaterials

  • 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.

     

    Abstract: This paper proposes a hypersingular integral equation method toanalyze the three-dimensional mixed-mode crack perpendicular to theinterface in anisotropic electromagnetoelastic (EME) bimaterials underextended electro-magneto-elastic coupled loads through theoreticalanalysis and numerical simulations. Using the Green's functions, the generalextended displacement solutions of three-dimensional mixed-mode crackmeeting the interface in anisotropic EME bimaterials under extended loads isanalyzed by the boundary element method. Then this crack problem is reduced tosolve a set of hypersingular integral equations coupled with boundaryintegral equations. The exact analytical solution of the extended singularstresses and extended stress intensity factors near the crack front areobtained. At last, a numerical method for the hypersingular integral equationfor a three-dimensional mixed-mode rectangular crack subjected to extendedloads by the body force method is proposed. Numerical solutions of theextended stress intensity factors of some examples are obtained.

     

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