Boundary element analysis of transversely isotropic bi-material halfspaces with inclined planes of isotropy and interfaces

Abstract

In this paper, a single‐region boundary element method (BEM) is presented for the analysis of transversely isotropic bi‐material halfspaces with arbitrarily inclined planes of isotropy and material interfaces. The proposed BEM uses the fundamental solution of a transversely isotropic bi‐material fullspace and five boundary element techniques. Infinite boundary elements are introduced to consider the far‐fields of a transversely isotropic bi‐material halfspace. The effective integration methods are proposed for dealing with various integrals in the discretized boundary integral equation. The stresses at internal points are obtained using the coordinate transformation of kernel functions, and the stresses on the boundary surface are calculated using an improved traction recovered method. Numerical verifications of displacements and stresses for a benchmark problem are conducted, and excellent agreement with previously published results is obtained. Numerical examples are presented to illustrate the influence of non‐horizontal or horizontal planes of isotropy in bi‐material halfspaces on the displacements and stresses induced by the tractions on the horizontal boundary surface. Results reveal that the elastic fields vary clearly with the dip angle of the isotropic plane and the stresses across the bimaterial interface are closely related to the ratios of the elastic parameters of the bi‐material.