Plane problem of elasticity theory for anisotropic bodies with thin elastic inclusions

Abstract

Based on the coupling principle for continua of different dimensions, we constructed integral equations for determining the plane stress of an anisotropic elastic body with thin inhomogeneities of the material’s structure. For the numerical solution of these equations, we used the boundary element method and proposed new basic functions for the description of the near-end area of an inhomogeneity. The interpolation quadratures and the polynomial transformations are adopted for the efficient numerical evaluation of the corresponding singular and hypersingular integrals. Numerical examples show a high efficiency of the approach developed for the determination of the stressed state of anisotropic bodies that contain cracks and thin elastic and rigid inclusions.