Solution of Problems of Elasticity Theory for Multiply Connected Half-Planes and Strips

Abstract

A general solution of problems of elasticity theory for anisotropic half-planes and strips with arbitrary holes and cracks is presented, which uses the complex potentials of the plane problem of the theory of elasticity of an anisotropic body, conformal mappings, representations of holomorphic functions by Laurent series, and satisfaction of boundary conditions by the generalized least squares method. The problems are reduced to overdetermined systems of linear algebraic equations solved by the singular value decomposition. The results of numerical studies are described for a strip with a circular hole under its tension or under the action of a uniform pressure along a segment of a rectilinear boundary, as well as for the tension of a strip with a circular hole and a crack in the bridge, including those extending to the border of the strip or to the contour of the hole. An isotropic half-plane and a strip with holes and cracks are considered as special cases of the general problem. The influence of the geometric characteristics of holes and cracks, the physical and mechanical properties of the strip on the values and distribution of stresses material was studied.