Application of fractional order theory of thermoelasticity to a 1D problem for a cylindrical cavity

• Autorzy: Raslan W. E.
• Języki publikacji: EN

Abstrakty

EN

In this work, we apply the fractional order theory of thermoelasticity to a 1D problem of an infinitely long cylindrical cavity. Laplace transform techniques are used to solve the problem. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.

Słowa kluczowe

EN

fractional calculus; cylindrical cavity; thermoelasticity

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2014
• Tom: Vol. 66, nr 4
• Strony: 257--267
• Opis fizyczny: Bibliogr. 27 poz., tab., wykr.

Twórcy

autor

Raslan W. E.

• Department of Mathematics and Engineering Physics Mansoura University Mansoura, Egypt

Bibliografia

• 1. M. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys., 27, 240–253, 1956.
• 2. H. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, J. Mech. Phys., Solid, 15, 299–309, 1967.
• 3. H. Sherief, N. El-Maghraby, An internal penny-shaped crack in an infinite thermoelastic solid, J. Thermal Stresses, 26, 333–352, 2003.
• 4. H. Sherief, N. El-Maghraby, A mode-I crack problem for an infinite space in generalized thermoelasticity, J. Thermal Stresses, 28, 465–484, 2005.
• 5. H. Sherief, F. Hamza, Generalized two-dimensional thermoelastic problems in spherical regions under axisymmetric distributions, J. Thermal Stresses, 19, 55–76, 1994.
• 6. H. Sherief, F. Hamza, Generalized thermoelastic problem of a thick plate under axisymmetric temperature distribution, J. Thermal Stresses, 17, 435–452, 1994.
• 7. H. Sherief, M. Ezzat, Solution of the generalized problem of thermoelasticity in the form of series of functions, J. Thermal Stresses, 17, 75–95, 1994.
• 8. H. Sherief, F. Hamza, A. El-Sayed, Theory of generalized micropolar thermoelasticity and an axisymmetric half-space problem, J. Thermal Stresses, 28, 409–437, 2005.
• 9. H. Sherief, M. Allam, M. El-Hagary, Generalized theory of thermoviscoelasticity and a half-space problem, Int. J. Thermophys., 32, 1271–1295, 2011.
• 10. H. Sherief, E. Hussein, A mathematical model for short-time filtration in poroelastic media with thermal relaxation and two temperatures, Transp. Porous Med., 91, 199–223, 2012.
• 11. J. Tenreiro Machado, M. Alexandra, J. Trujillo, Science metrics on fractional calculus development since 1966, Fractional Calculus and Applied Analysis, 16, 479–500, 2013.
• 12. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific Publishing, Singapore, 2000.
• 13. H. Sherief, A.M.A. El-Sayed, S.H. Behiry, W.E. Raslan, Using fractional derivatives to generalize the Hodgkin–Huxley model, Fractional Dynamics and Control, Springer, 2012, pp. 275–282.
• 14. M. Caputo, F. Mainardi, A new dissipation model based on memory mechanism, Pure Appl. Geophys., 91, 134–147, 1971.
• 15. M. Caputo, F. Mainardi, Linear model of dissipation in anelastic solids, Rivista Del Nuovo Cimento, 1, 161–198, 1971.
• 16. M. Caputo, Vibrations on an infinite viscoelastic layer with a dissipative memory, J. Accoust. Soc. Am., 56, 897–904, 1974.
• 17. K. Adolfsson, M. Enelund, P. Olsson, On the fractional order model of viscoelasticity, Mechanics of Time Dependent Materials, 9, 15–34, 2005.
• 18. Y.Z. Povstenko, Thermoelasticity that uses fractional heat conduction equation, J. Math. Sci., 162, 296–305, 2009.
• 19. Y.Z. Povstenko, Fractional heat conduction and associated thermal stress, J. Thermal Stresses, 28, 83–102, 2005.
• 20. Y.Z. Povstenko, Fractional Cattaneo-type equations and generalized thermoelasticity, J. Thermal Stresses, 34, 97–114, 2011.
• 21. Y.Z. Povstenko, Fractional radial heat conduction in an infinite medium with a cylindrical cavity and associated thermal stresses, Mechanics Research Communications, 37, 436–440, 2010.
• 22. Y.Z. Povstenko, The Neumann boundary problem for axisymmetric fractional heat conduction equation in a solid with cylindrical hole and associated thermal stress, Meccanica, 47, 23–29, 2012.
• 23. H. Sherief, A.M.A. El-Sayad, A.M. Abd El-Latief, Fractional order theory of thermoelasticity, Int. J. Solids Structures, 47, 269–275, 2010.
• 24. H. Sherief, A.M. Abd El-Latief, Application of fractional order theory of thermoelasticity to a 1D Problem for a half-space, ZAMM – Journal of Applied Mathematics and Mechanics, 2013, doi: 10.1002/zamm.201200173.
• 25. H. Sherief, A.M. Abd El-Latief, Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity, Int. J. Mech. Sci., 74, 185–189, 2013.
• 26. W.W. Bell, Special Functions for Scientist and Engineering, Van Nostrand Company LTD, London, 1968.
• 27. G. Honig, U. Hirdes, A method for the numerical inversion of the Laplace transform, J. Comp. Appl. Math., 10, 113–132, 1984.