This paper presents an axisymmetric boundary element analysis of one-layered transversely isotropic material of halfspace extent with either ellipsoidal or spherical cavity. This analysis uses the fundamental solution of a transversely isotropic bi-material fullspace subject to the body force uniformly concentrated at a circular ring. The finite and infinite boundary elements are, respectively, used to discretize the finite and semi-infinite regions of the external boundary and the finite boundary elements are used to discretize the internal boundary. Different types of the integrals in the discretized boundary integral equations are efficiently calculated. An improved traction recovered method is applied to calculate the stresses on the boundary. Using one set of BEM mesh, a total of 12 case studies are calculated for the elastic fields of the one-layered transversely isotropic solid by uniform traction on the external horizontal boundary. The solid has either an ellipsoidal, a spherical, or none cavity in the upper layer. Four combinations of two transversely isotropic metals are adopted for the one-layered solid. One metal is the stiff zinc and the other is the soft magnesium. The displacements for the cases with magnesium as the upper layer are larger than those with zinc as the upper layer. Besides, the effects of the lower solid materials to the displacements are limited. The BEM results also reveal the variations of the displacements and stresses within the halfspace with or without cavities for different cases.

本文介绍了半空间范围内具有椭圆形或球形空腔的单层横向各向同性材料的轴对称边界元分析。该分析使用横向各向同性双材料全空间的基本解，该全空间受制于均匀地集中在圆环上的体力。有限和无限边界元素分别用于离散化外部边界的有限和半无限区域，有限边界元素用于离散化内部边界。有效地计算了离散边界积分方程中不同类型的积分。一种改进的牵引恢复方法被应用于计算边界上的应力。使用一组BEM网格，通过在外部水平边界上的均匀牵引，总共计算了12个案例研究，用于单层横向各向同性固体的弹性场。固体在上层具有椭圆形，球形或无腔。一层固体采用两种横向各向同性金属的四种组合。一种金属是硬质锌，另一种是软质镁。以镁为上层的情况下的位移比以锌为上层的情况大。此外，较低的固体材料对位移的影响是有限的。BEM结果还揭示了在不同情况下有或没有空腔的情况下半空间内位移和应力的变化。固体在上层具有椭圆形，球形或无腔。一层固体采用两种横向各向同性金属的四种组合。一种金属是硬质锌，另一种是软质镁。以镁为上层的情况下的位移比以锌为上层的情况大。此外，较低的固体材料对位移的影响是有限的。BEM结果还揭示了在不同情况下有或没有空腔的情况下半空间内位移和应力的变化。固体在上层具有椭圆形，球形或无腔。一层固体采用两种横向各向同性金属的四种组合。一种金属是硬质锌，另一种是软质镁。以镁为上层的情况下的位移比以锌为上层的情况大。此外，较低的固体材料对位移的影响是有限的。BEM结果还揭示了在不同情况下有或没有空腔的情况下半空间内位移和应力的变化。以镁为上层的情况下的位移比以锌为上层的情况大。此外，较低的固体材料对位移的影响是有限的。BEM结果还揭示了在不同情况下有或没有空腔的情况下半空间内位移和应力的变化。以镁为上层的情况下的位移比以锌为上层的情况大。此外，较低的固体材料对位移的影响是有限的。BEM结果还揭示了在不同情况下有或没有空腔的情况下半空间内位移和应力的变化。