The Application of Complex Potentials to the Problems of Plane Stress State for an Inhomogeneous Material

Abstract

Problems of elasticity theory of inhomogeneous bodies (such as a plate) about the of plane stress state are considered in spatial formulation. It is assumed that the material is inhomogeneous by thickness and its properties change symmetrically with respect to its median plane. A method of solving such types of problems using complex potentials is elaborated. The basic correlations of the method are obtained. The exact analytical solutions of two problems are presented: about the inhomogeneous radial stretching of the contour of a circular disk and about the inhomogeneous radial stretching of the bypass of a circular aperture in an infinite plate.