The Solution of Axisymmetrical and Certain Other Space Problems in the Theory of Elasticity by Means of Analytical Functions

The theory of functions of a complex variable is applied to the solution of problems in the theory of elasticity involving surfaces symmetrical about the axis on the basis of the relation of the axisymmetrical state with the state of a plane surface. The relations between axisymmetrical and plane states are shown and the components for the former are described in functions of a complex variable. A solution for the boundary value problem is given using Cauchy integrals. The results, applying to an isotropic body, are extended to a transverse-isotopic body. Several problems in which the symmetry about the axis does not hold are considered along with their related boundary value problems. (Author) Edited machine trans. of International Symposium of Applications of the Theory of Functions in Continuum Mechanics. Tiflis, 1963. Pirilozheniya Teorii Funktsii v Mekhanike Sploshnoi Sredy. Mekhanika Tverdogo Tela. Trudy Simpoziuma (Applications of the Theory of Functions in Continuum Mechanics v1: Mechanics of Solids), Moscow, 1965 p97-118 (sic) by K. L. Dion.