GREEN''''S FUNCTIONS FOR A 2D ANISOTROPIC MEDIUM WITH A HYPERBOLIC BOUNDARY

By using Stroh's formalism and the conformal mapping technique, this paper derives simple explicit Green's functions of a piezoelectric anisotropic body with a free or fixed hyperbolic boundary. The corresponding elastic fields in the medium are obtained, too. In particular, degenerated solutions of an external crack from those of a hyperbolic problem are analysed in detail. Then the singular stress fields and the fracture mechanics parameters are found. The solutions obtained are valid not only for plane and antiplane problems but also for the coupled ones between inplane and outplane deformations.     

条带域内二维各向异性压电介质的Green函数

以压电各向异性弹性介质广义平面变形的Stroh一般解为基础,采用复变函数方法(即保角变换技术),研究了条带域介质内物理场的封闭形式解,求得了介质内某一点同时存在广义线位错和广义线力作用时的简单明确解,它就是边界元法中的Green函数.还分析了极化介质表面的电荷分布情况,并进而讨论了线电荷q与边界分布电荷间的库仑力问题.文中结果不仅适用于平面或反平面变形问题,而且也适用于两者耦合的二维变形问题.     

Green's functions for a piezoelectric semi-infinite body with a fixed conductor surface

By using Stroh's formalism, simple explicit compact expressions of Green's functions for a piezoelectric semi-infinite body, with a fixed conductor surface electrode, subject to a singularity (i.e., a generalized line dislocation and a generalized line force at a point z°) are presented. Coulomb forces acted on the free line charge at z° due to the boundary polarization charges of the medium and the induction charges of the conductor together with the electromechanical coupling effects inside the region are analyzed in detail. The obtained results are valid not only for plane and antiplane problems but also for the coupled problems between inplane and outplane deformations.     

GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline material with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given.Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.