Separation of the elasticity theory equations with radial inhomogeneity : PMM vol. 38, n 6, 1974, pp. 1139–1144

The separation of a system of three elasticity theory equations in the static case to a system of two equations and one independent equation for a space with a radial inhomogeneity is presented in a spherical coordinate system. These equations are solved by separation of variables for specific kinds of radial inhomogeneity. In particular, solutions are found for the Lamé coefficients μ = const, λ (ifr) is an arbitrary function, μ = μ_or^β, λ = λ_or^β.While methods of solving problems associated with the equilibrium of an elastic homogeneous sphere have been studied sufficiently 1], problems with spherical symmetry of the boundary conditions have mainly been solved for an inhomogeneous sphere 2, 3],For a particular kind of inhomogeneity dependent on one Cartesian coordinate, the equations have been separated completely in 4], A system of three equations with a radial inhomogeneity in a spherical coordinate system is separated below by a method analogous to 4].