Boundary integral equations for anisotropic elasticity of solids containing rigid thread-like inclusions

Abstract

The paper presents a novel approach in derivation and solution of boundary integral equations of anisotropic elasticity of solids containing thin rigid wires (thread-like inclusions). It proposes to model rigid thread-like inclusions as spatial curves, which can rotate as a rigid one and possess certain rigid displacement. Somigliana identity is written for solids containing rigid thread-like inclusions, which are modeled by spatial curves. Based on this identity the hypersingular boundary integral equations are derived, and it is shown that they also include the non-singular terms. The comparison is made between the models and integral equations for 3D rigid thread-like inclusions and 2D rigid line inclusions. A problem for a single rectilinear rigid thread-like inclusion in an infinite elastic medium is considered. Its solution strategy is proposed based on the boundary element approach. Distribution of forces along the inclusion modeling line and the displacement field near its tip are shown.