Axisymmetric static thermoelastic state of a smoothly fixed finite cylinder layered along the axis
- B. V. Protsyuk
- … show all 1 hide
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
By using constructed Green functions of the problems of heat conduction and thermoelasticity, we obtain the solution of the axisymmetric static problem of thermoelasticity for a finite cylinder layered along the axis with a smoothly fixed thermally insulated cylindrical surface under the action of heat sources and in the presence of convective heat exchange from end faces for a wide range of variation in the thickness of the layers. In this case, we use generalized functions, finite Hankel integral transformation, and Green functions of the corresponding problems for one ordinary differential equation or a system of ordinary differential equations. We present results of numerical investigations for a three-layer cylinder.
- A. S. Galitsin and A. N. Zhukovskii, Integral Transforms and Special Functions in Problems of Heat Conduction [in Russian], Naukova Dumka, Kiev (1976).
- Ya. M. Grigorenko, A. T. Vasilenko, and N. D. Pankratova, Problems of the Theory of Elasticity of Inhomogeneous Bodies [in Russian], Naukova Dumka, Kiev (1991).
- V. T. Grinchenko, Equilibrium and Steady-State Vibrations of Elastic Bodies of Finite Sizes [in Russian], Naukova Dumka, Kiev (1978).
- R. M. Kushnir, B. V. Protsyuk, and V. M. Synyuta, “Temperature stresses and displacements in a multilayer plate with nonlinear conditions of heat exchange,” Fiz.-Khim. Mekh. Mater., 38, No. 6, 31–38 (2002); English translation: Mater. Sci., 38, No. 6, 798–808 (2002).
- V. V. Meleshko, Yu. V. Tokovyy, and J. R. Barber, “Axially symmetric temperature stresses in an elastic isotropic cylinder of finite length,” Mat. Met. Fiz.-Mekh. Polya, 53, No. 1, 120–137 (2010); English translation: J. Math. Sci., 176, No. 5, 646–669 (2011).
- B. V. Protsyuk, “Application of the method of Green functions to the determination of the thermoelastic state of layered transversally isotropic spherical bodies,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 3, 95–109 (2004).
- B. V. Protsyuk, “Static and quasistatic axisymmetric problems of thermoelasticity for layered bodies with plane-parallel boundaries,” Mat. Met. Fiz.-Mekh. Polya, 44, No. 4, 103–112 (2001).
- Yu. N. Shevchenko, M. E. Babeshko, V. V. Piskun, and V. G. Savchenko, Space Problems of Thermoelasticity [in Russian], Naukova Dumka, Kiev (1980).
- F. Ashida, S. Sakata, and K. Matsumoto, “Control of thermal stress in a piezo-composite disk,” in: C. K. Chao and C. Y. Lin (editors), Proc. of the 7th Int. Congress on Thermal Stresses (June 4–7, 2007, Taipei, Taiwan), Vol. 1, National Taiwan University of Science and Technology, Taipei (2007), pp. 77–80.
- G. Horvay, I. Giaver, and J. Mirabal, “Thermal stresses in a heat-generating cylinder: The variational solution of boundary layer problem in three-dimensional elasticity,” Arch. Appl. Mech., 27, No. 3, 179–194 (1959).
- J. R. Matthews, “Thermal stress in a finite heat generating cylinder,” Nucl. Eng. Des., 12, 291–296 (1970). CrossRef
- K. T. Sundara Raja Iyengar and K. Chandrashekhara, “Thermal stresses in a finite solid cylinder due to axisymmetric temperature field at the end surface,” Nucl. Eng. Des., 3, 382–393 (1966).
- K. T. Sundara Raja Iyengar and K. Chandrashekhara, “Thermal stresses in a finite solid cylinder due to steady temperature variation along the curved and end surface,” Int. J. Eng. Sci., 5, 393–413 (1967). CrossRef
- T. R. Taucher and F. Ashida, “Application of the potential function method in piezothermoelasticity: solutions for composite circular plates,” J. Therm. Stresses, 22, 387–420 (1999). CrossRef
- R. A. Valentin and J. J. Carey, “Thermal stresses and displacements in finite, heat-generating cylinders,” Nucl. Eng. Des., 12, 277–290 (1970). CrossRef
- Axisymmetric static thermoelastic state of a smoothly fixed finite cylinder layered along the axis
Journal of Mathematical Sciences
Volume 187, Issue 6 , pp 737-757
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Industry Sectors
- B. V. Protsyuk (1)
- Author Affiliations
- 1. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine