Boundary element solution of the plane elasticity problem for an anisotropic body with free smooth boundaries

A boundary singular integral equation of the plane problem was constructed using an approach based on the representation of the unknown Lekhnitskii complex potentials in the form of Cauchy type integrals with unknown densities on the boundary of the region occupied by the body. The contours of the holes and cuts and the shape of the outer boundary are exactly or approximately represented in the form of a sequence of straight and curved (in the form of elliptical arcs) boundary elements. The unknown densities on the boundary elements are approximated by a linear combination of some regular functions or complex functions that have a known singularity. In the numerical solution of the integral equation by the collocation method or by the least-squares method and in the subsequent calculations of the stress–strain state, the integrals of all types along the boundary elements are calculated analytically, which significantly increases the accuracy of the results.