Boundary Element Analysis of a Semi-Infinite Anisotropic Plane Containing Inclusions/Holes

Abstract

In this article, the fundamental solutions with Lekhnitskii-like formulations are implemented in the boundary element method (BEM) to calculate the Two-dimensional elastostatic field in a semi-infinite anisotropic plane containing inclusions/holes. In addition to the source point in the semi-infinite plane, four pseudo-sources are superposed to provide traction-free conditions on the plane surface. To avoid mesh modeling at infinity, the fundamental solutions are modified so that the displacements/stresses at the far field automatically vanish. For modeling problems in civil engineering, loading on the plane surface can be specified as part of the boundary condition. When embedded holes are present in the halfplane, loading on the holes can also be applied. Using the sub-region technique, the elastic field in the half-plane containing inclusions can also be investigated. Studies of a few examples indicate that the proposed BEM is a very efficient and versatile methodology to investigate many practical problems, especially in civil engineering.OPEN ACCESS Received: 11/10/2024 Accepted: 10/01/2025 Published: 07/04/2025

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