We have proposed an approach to the construction of an analytical solution of the three-dimensional elasticity problem for a homogeneous solid isotropic cylinder subjected to normal compressive external forces applied to its end faces. The lateral surface is assumed to be free of force loading. For the determination of the stress-tensor components, a representation via the Dougall harmonic functions is used. Based on the superposition method, we have reduced the problem of determination of the coefficients in the obtained expressions to infinite systems of linear algebraic equations.
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To the blessed memory of my teacher V’yacheslav Volodymyrovych Meleshko
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 55, No. 1, pp. 49–60, January–March, 2012.
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Tokovyy, Y.V. Reduction of a three-dimensional elasticity problem for a finite-length solid cylinder to the solution of systems of linear algebraic equations. J Math Sci 190, 683–696 (2013). https://doi.org/10.1007/s10958-013-1280-2
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DOI: https://doi.org/10.1007/s10958-013-1280-2