引用本文: 余迎松, 秦太验. 横观各向同性压电材料中裂纹问题的边界元法[J]. 力学与实践, 2005, 27(3).
BOUNDARY ELEMENT METHOD OF MODE-I CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS[J]. MECHANICS IN ENGINEERING, 2005, 27(3).
 Citation: BOUNDARY ELEMENT METHOD OF MODE-I CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS[J]. MECHANICS IN ENGINEERING, 2005, 27(3).

BOUNDARY ELEMENT METHOD OF MODE-I CRACK IN TRANSVERSELY ISOTROPIC PIEZOELECTRIC MATERIALS

• 摘要: 采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程，其中未知函数为裂纹面上的位移间断和电势间断. 在此基础上，使用有限部积分和边界元结合的方法，建立了超奇异积分方程的数值求解方法，并给出了一些典型数值算例的应力强度因子和电位移强度因子的数值结果，结果令人满意.

Abstract: Using Somigiliana's formula, the general solutions andhypersingular integral equations for a three-dimensional impermeable crackproblem in an infinite transversely isotropic piezoelectric solid undermechanicaland electrical loads are given. The unknown functions are thediscontinuities of the elastic displacements and electrical potential of thecrack surface. Then, a numerical technique to solve the hypersingularintegral equations is proposed based on the boundary element method combined withthe finite-part integral method. Finally, a rectangular crack undermechanical tension and electrical fields is analyzed, and the numericalresults of the stress and electric displacement intensity factors arepresented. It is shown that the numerical solutions are satisfactory,which shows that thepresent approach is powerful to solve three-dimensional crack problems ofpiezoelectric materials.

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