Solution of the axisymmetric problem of the theory of elasticity for transversely isotropic bodies with the aid of generalized analytic functions

Abstract

Abstract The solution of the axisymmetric problem for transversely isotropic bodies, expressed in terms of generalized analytic functions, is constructed. We obtain formulas for the displacements and stresses, similar to the corresponding formulas of the plane problem. The representation of the generalized analytic functions by analytic ones, are indicated, and the analogue of the Cauchy-type integral which gives the possibility of reducing the boundary value problems to integral equations, is presented. As an example, we consider the action of forces which are distributed along a circumference in the interior of a transversely isotropic space. The plane problems of the theory of elasticity for transversely isotropic bodies are solved effectively with the aid of analytic functions of a complex variable [1], In [2, 3] the solution of axisymmetric and nonaxisymmetric problems for bodies of revolution with the aid of analytic functions and contour integrals,was considered. In the case of an isotropic elastic medium, the solution of axisym-metric problems with the aid of a class of generalized analytic functions [4] was proposed.