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Transient thermoelastic analysis for a multilayered hollow cylinder with piecewise power law nonhomogeneity due to asymmetric surface heating

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Abstract

This paper is concerned with the theoretical treatment of transient thermoelastic problems involving a multilayered hollow cylinder with piecewise power law nonhomogeneity due to the asymmetrical heating of its surfaces. The thermal and thermoelastic constants of each layer are expressed as power functions of the radial coordinate, and their values continue on the interfaces. The exact solution for the two-dimensional temperature change in a transient state is obtained using the Laplace transformation and separation-of-variables method. The exact solution for the thermoelastic response of a multilayered hollow cylinder under the state of generalized plane strain, where the strain is not bound, is obtained herein. Some numerical results for the temperature change and the stress distributions are presented in figures. The influence of the functional grading on the thermal stresses is investigated. Furthermore, the influence on the axial stress of the restraint condition in the axial direction is investigated.

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References

  1. Miyamoto Y., Kaysser W.A., Rabin B.H., Kawasaki A., Ford R.G.: Functionally Graded Materials: Design, Processing and Applications. Kluwer, Dordrecht (1999)

    Book  Google Scholar 

  2. Ishikawa K.: Functionally Graded Materials in the 21st Century. Kluwer, Dordrecht (2001)

    Book  Google Scholar 

  3. Müller E., Drasar C., Schliz J., Kaysser W.A.: Functionally Graded Materials for sensor and energy applications. Mater. Sci. Eng. A 362, 17–39 (2003)

    Article  Google Scholar 

  4. Yang Q., Gao C.F.: Non-axisymmetric thermal stress around a circular hole in a functionally graded infinite plate. J. Therm. Stress. 33, 318–334 (2010)

    Article  MathSciNet  Google Scholar 

  5. Yang Q., Gao C.F.: Non-axisymmetric thermal stress of a functionally graded coated circular inclusion in an infinite matrix. Mech. Res. Commun. 50, 27–32 (2013)

    Article  MathSciNet  Google Scholar 

  6. Tanigawa Y., Fukuda T., Ootao Y., Tanimura S.: Transient thermal stress analysis of a multilayered composite laminated cylinder with a uniformly distributed heat supply and [its analytical development to nonhomogeneous materials]. Trans. Jpn. Soc. Mech. Eng. 55A, 1133–1138 (1989)

    Article  Google Scholar 

  7. Ootao Y., Fukuda T., Tanigawa Y.: Transient thermal stress analysis of a multi-layered composite hollow cylinder due to asymmetric heating and its application to nonhomogeneous materials. Theor. Appl. Mech. 38, 177–188 (1989)

    MATH  Google Scholar 

  8. Ootao Y., Tanigawa Y.: Three-dimensional transient thermal stress analysis of nonhomogeneous hollow sphere with respect to rotating heat source. Trans. Jpn. Soc. Mech. Eng. 60A, 2273–2279 (1994)

    Article  Google Scholar 

  9. Sugano Y., Sato K., Kimura N., Sumi N.: Three-dimensional analysis of transient thermal stresses in a nonhomogeneous plate. Trans. Jpn. Soc. Mech. Eng. 62A, 728–736 (1996)

    Article  Google Scholar 

  10. Ootao Y., Tanigawa Y.: Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating. J Therm. Stress. 22, 35–55 (1999)

    Article  Google Scholar 

  11. Sugano Y.: An expression for transient thermal stress in a nonhomogeneous plate with temperature variation through thickness. Ing. Arch. 57, 147–156 (1987)

    Article  MATH  Google Scholar 

  12. Vel S.S., Batra C.: Three-dimensional analysis of transient thermal stresses in functionally graded plates. Int. J. Solids Struct. 40, 7181–7196 (2003)

    Article  MATH  Google Scholar 

  13. Ootao Y., Tanigawa Y.: Three-dimensional solution for transient thermal stresses of functionally graded rectangular plate due to nonuniform heat supply. Int. J. Mech. Sci. 47, 1769–1788 (2005)

    Article  MATH  Google Scholar 

  14. Obata Y., Noda N.: Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material. J. Therm. Stress. 17, 471–487 (1994)

    Article  Google Scholar 

  15. Zimmerman R.W., Lutz M.P.: Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stress. 22, 177–188 (1999)

    Article  Google Scholar 

  16. Ye G.R., Chen W.Q., Cai J.B.: A uniformly heated functionally graded cylindrical shell with transverse isotropy. Mech. Res. Commun. 28, 535–542 (2001)

    Article  MATH  Google Scholar 

  17. Jabbari M., Sohrabpour S., Eslami M.R.: General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads. Trans. ASME J. Appl. Mech. 70, 111–118 (2003)

    Article  MATH  Google Scholar 

  18. Poultangari R., Jabbari M., Eslami M.R.: Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads. Int. J. Press. Vessel Pip. 85, 295–305 (2008)

    Article  Google Scholar 

  19. Jabbari M., Mohazzab A.H., Bahtui A.M., Eslami R.: Analytical solution for three-dimensional stresses in a short length FGM hollow cylinder. ZAMM 87, 413–429 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. You L.H., Ou H., Li J.: Stress analysis of functionally graded thick-walled cylindrical Vessels. AIAA 45, 2790–2798 (2007)

    Article  Google Scholar 

  21. Peng X., Li X.: Thermoelastic analysis of functionally graded annulus with arbitrary gradient. Appl. Math. Mech. 30, 1211–1220 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Vel S.S.: Exact thermoelastic analysis of functionally graded anisotropic hollow cylinders with arbitrary materials gradient. Mech. Adv. Mater. Struct. 18, 14–31 (2011)

    Article  Google Scholar 

  23. Ootao Y., Tanigawa Y.: Transient thermoelastic analysis for a functionally graded hollow cylinder. J. Therm. Stress. 29, 1031–1046 (2006)

    Article  Google Scholar 

  24. Ootao Y., Tanigawa Y.: Transient thermoelastic problem of a functionally graded hollow cylinder due to asymmetrical surface heating. J. Therm. Stress. 32, 1217–1234 (2009)

    Article  Google Scholar 

  25. Zhao J., Ai X., Li Y., Zhou Y.: Thermal shock resistance of functionally gradient solid cylinders. Mater. Sci. Eng. A 418, 99–110 (2006)

    Article  Google Scholar 

  26. Shao Z.S., Wang T.J., Ang K.K.: Transient thermo-mechanical analysis of functionally graded hollow circular cylinders. J. Therm. Stress. 30, 81–104 (2007)

    Article  Google Scholar 

  27. Guo L.C., Noda N.: Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model. Int. J. Solids Struct. 44, 6768–6790 (2007)

    Article  MATH  Google Scholar 

  28. Ootao Y.: Transient thermoelastic analysis for a multilayered hollow cylinder with piecewise power law nonhomogeneity. J. Solid Mech. Mater. Eng. 4, 1167–1177 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Graduate School of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, 599-8531, Japan

    Yoshihiro Ootao & Masayuki Ishihara

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  1. Yoshihiro Ootao
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  2. Masayuki Ishihara
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Correspondence to Yoshihiro Ootao.

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Ootao, Y., Ishihara, M. Transient thermoelastic analysis for a multilayered hollow cylinder with piecewise power law nonhomogeneity due to asymmetric surface heating. Acta Mech 225, 2903–2922 (2014). https://doi.org/10.1007/s00707-014-1204-3

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  • DOI: https://doi.org/10.1007/s00707-014-1204-3

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