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Solutions of one-dimensional problems of elasticity and thermoelasticity for cylindrical piecewise-homogeneous bodies

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Abstract

We propose a method of direct integration of the equilibrium and continuity equations in stresses for one-dimensional problems of elasticity and thermoelasticity for piecewise-homogeneous cylinders and disks with an arbitrary number of layers. The solutions are reduced to finding the constants of systems of algebraic equations with nearly triangular matrices of coefficients, making it possible to find the unknown constants in a closed form that is functionally dependent on the bulk forces and temperature field.

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Literature cited

  1. V. V. Bolotin and Yu. N. Novichkov,Mechanics of Multilayer Structures [in Russian], Mashinostroenie, Moscow (1980).

    Google Scholar 

  2. V. M. Vigak, “Solutions of problems of the theory of elasticity and thermoelasticity in stresses,”Integr. Peretv. Zastos. Krain. Zad., No. 9, 34–122 (1995).

    Google Scholar 

  3. V. M. Vigak,Control of Thermal Stresses and Displacements [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  4. V. M. Vigak and A. M. Rigin, “Thermal stresses in a multilayer piecewise-homogeneous cylinder,”Mat. Met. Fiz.-Mekh. Polya, No. 15, 63–67 (1982).

    Google Scholar 

  5. Yu. M. Kolyano and B. V. Protsyuk, “Thermoelasticity of a multilayer cylinder,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 8, 718–721 (1976).

    Google Scholar 

  6. V. A. Lomakin,Theory of Elasticity of Inhomogeneous Bodies [in Russian], Moscow University Press (1976).

  7. V. V. Moskvitin,Resistance of Viscoelastic Materials in Application to Charges of Solid-Fuel Reactor Engines[in Russian], Nauka, Moscow (1972).

    Google Scholar 

  8. Ya. S. Podstrigach, V. A. Lomakin, and Yu. M. Kolyano,Thermoelasticity of Bodies of Inhomogeneous Structure [in Russian], Nauka, Moscow (1984).

    Google Scholar 

  9. S. P. Timoshenko, and J. Goodier,Theory of Elasticity, McGraw-Hill, New York (1951).

    Google Scholar 

  10. V. M. Vihak, “Solution of the thermoelastic problem for a cylinder in the case of two-dimensional nonaxisymmetric temperature field,”Z. angew. Mat. Mech.,76, No. 1, 35–43 (1996).

    Google Scholar 

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Authors
  1. V. M. Vigak
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Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 139–148.

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Vigak, V.M. Solutions of one-dimensional problems of elasticity and thermoelasticity for cylindrical piecewise-homogeneous bodies. J Math Sci 96, 3057–3064 (1999). https://doi.org/10.1007/BF02169706

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  • DOI: https://doi.org/10.1007/BF02169706

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