Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Elastic stresses in a sphere with an exogenous eccentric spherical inclusion

  • 24 Accesses


We study the axisymmetric elastici problem for a sphere with an exogenous eccentric spherical inclusion. The solution is represented in terms of analytic functions ϕ j(z) andψ j(z)of a complex variable. The coefficients of the generalized Laurent and Taylor expansions of the solutions are found via a certain system of linear algebraic equations. The results of computation are given for the stress concentrations in the case when the inclusion degenerates into a pore and a constant pressure from within is acting, as well as for the case of an inclusion subjected to a preliminary proper strain with various distances between the centers of the spheres.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    A. Ya. Aleksandrov, “On certain methods of numerical solution of the three-dimensional problems of elasticity theory for solids of revolution,” in:Proc. Conf. Num. Meth. Sol. Prob. Elas. and Plast. Th. [in Russian], Novosibirsk (1969), pp. 4–29.

  2. 2.

    L. G. Smirnov, S. V. Priimak, and I. I. Fedik, “The elastic stresses in a half-space with an exogenous spherical inclusion,”Mat. Met. i Fiz.-Mekh. Polya, No. 30, 39–46 (1989).

  3. 3.

    Yu. I. Solov'ev, “On the reduction of three-dimensional axisymmetric problems of the theory of elasticity to boundary-value problems for analytic functions of a complex variable,”Prikl. Mat. Mekh.,35, No. 5, 918–925 (1971).

Download references

Additional information

Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 79–83.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Smirnov, L.G., Fedik, I.I. Elastic stresses in a sphere with an exogenous eccentric spherical inclusion. J Math Sci 64, 966–970 (1993). https://doi.org/10.1007/BF01140327

Download citation


  • Stress Concentration
  • Algebraic Equation
  • Constant Pressure
  • Taylor Expansion
  • Complex Variable