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Three-dimensional extended displacement discontinuity method for vertical cracks in transversely isotropic piezoelectric media

机译:横观各向同性压电介质中垂直裂纹的三维扩展位移不连续性方法

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摘要

The conventional displacement discontinuity method is extended to study a vertical crack under electrically impermeable condition, running parallel to the poling direction and normal to the plane of isotropy in three-dimensional transversely isotropic piezoelectric media. The extended Green's functions specifically for extended point displacement discontinuities are derived based on the Green's functions of extended point forces and the Somigliana identity. The hyper-singular displacement discontinuity boundary integral equations are also derived. The asymptotical behavior near the crack tips along the crack front is studied and the ordinary 1/2 singularity is obtained at the tips. The extended field intensity factors are expressed in terms of the extended displacement discontinuity on crack faces. Numerical results on the extended field intensity factors for a vertical square crack are presented using the proposed extended displacement discontinuity method.
机译:扩展了传统的位移不连续性方法,以研究电渗透条件下的垂直裂纹,该裂纹在三维横向各向同性压电介质中平行于极化方向且垂直于各向同性平面延伸。基于扩展点力的格林函数和Somigliana身份导出了专门用于扩展点位移不连续性的扩展格林函数。还推导了超奇异位移不连续边界积分方程。研究了沿着裂纹前沿的裂纹尖端附近的渐近行为,并在尖端获得了普通的1/2奇点。扩展场强因子用裂纹面上扩展的位移不连续性表示。利用所提出的扩展位移不连续性方法,给出了垂直方形裂纹扩展场强度因子的数值结果。

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