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.
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Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 79–83.
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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
- Stress Concentration
- Algebraic Equation
- Constant Pressure
- Taylor Expansion
- Complex Variable