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Axisymmetric thermal stresses in a half-space in the framework of fractional thermoelasticity

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EN
Abstrakty
EN
A theory of thermal stresses based on the time-fractional heat conduction equation is considered. The Caputo fractional derivative is used. The fundamental solution to the axisymmetric heat conduction equation in a half-space under the Dirichlet boundary condition and the associated thermal stresses are investigated.
Twórcy
autor
  • Jan Długosz University in Częstochowa, Institute of Mathematics and Computer Science, al. Armii Krajowej 13/15, 42-200, Częstochowa, Poland
Bibliografia
  • [1] A. Carpinteri, P. Cornetti, A fractional calculus approach to the description of stress and strain localization, Chaos, Solitons Fractals 13 (2002), 85-94.
  • [2] R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, In: A. Carpinetti, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, pp. 223-276. Springer, Wien, 1997.
  • [3] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  • [4] F. Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics. In: A. Carpinteri and F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mecanics, pp. 291-348. Springer, Wien, 1997.
  • [5] F. Mainardi, Applications of fractional calculus in mechanics, In: P. Rusev, I. Dimovski, V. Kiryakova (Eds.), Transform Methods and Special Functions, pp. 309-334. Bulgarian Academy of Sciences, Sofia, 1998.
  • [6] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press, London, 2010.
  • [7] N. Noda, R. B. Hetnarski, Y. Tanigawa, Thermal Stresses, 2nd edn. Taylor and Francis, New York, 2003.
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  • [11] Y. Povstenko, Fractional heat conduction equation and associated thermal stresses, J. Thermal Stresses 28 (2005), 83–102.
  • [12] Y. Povstenko, Thermoelasticity which uses fractional heat conduction equation, J. Math. Sci. 162 (2009), 296-305.
  • [13] Y. Povstenko, Theory of thermoelasticity based on the space-time-fractional heat conduction equation, Phys. Scr. T 136 (2009), 014017, 6 pp.
  • [14] Y. Povstenko, Signaling problem for time-fractional diffusion-wave equation in a halfplane in the case of angular symmetry, Nonlinear Dyn. 59 (2010), 593-605.
  • [15] Y. Povstenko, Fractional Cattaneo-type equations and generalized thermoelasticity, J. Thermal Stresses 34 (2011), 97-114.
  • [16] Y. Povstenko, Theories of thermal stresses based on space-time-fractional telegraph equations, Comp. Math. Appl. 64 (2012), 3321-3328.
  • [17] Y. Povstenko, Fractional Thermoelasticity, In: R.B. Hetnarski (Ed.), Encyclopedia of Thermal Stresses, vol. 4, pp. 1778-1787, Springer, New York, 2013.
  • [18] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integrals and Series. Elementary Functions, Nauka, Moscow, 1981. (In Russian).
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  • [27] G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, New York, 2005.
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Bibliografia
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bwmeta1.element.baztech-abfa4584-3ccb-415b-8006-24d7e5318ba2
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