On One Method of Solution in Displacements Axisymmetric Problem Theory of Elasticity in Spherical Coordinates for Radially Inhomogeneous Body

Abstract

Various physical fields (temperature, radiation, humidity ets.) lead to continuous inhomogeneity of solids. If you have a point source, or source distributed on a spherical surface such fields have central symmetry. In elastic bodies, it leads to functional dependencies of the radius the mechanical characteristics of the material – E(r) and n(r) . Replacement of the elastic constants on functions for solving elasticity problem leads to differential equations with variable coefficients. The paper deals with the numerical-analytical method of solving axisymmetric problem in spherical coordinates for radially inhomogeneous bodies. The method consists in reducing the system of equations in partial derivatives to an infinite system of ordinary differential equations of second order. The obtained system of ordinary differential equations is solved numerically.