Advertisement

Disks, Cylinders, and Spheres

  • Richard B. HetnarskiEmail author
  • M. Reza Eslami
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 158)

Abstract

Thick cylinders, spheres, and disks are components of many structural systems. Due to their capacity to withstand high pressures, radial loads, and radial temperature gradients, the problem of thermal stress calculations is an important design issue. This chapter presents the method to calculate thermal stresses in such structural members which are made either of homogeneous/isotropic materials or of functionally graded materials. The latter ones, classified as new materials, are mainly designed to withstand high temperatures and high temperature gradients, and they may be designed in such a way that the applied loads, mechanical or thermal, produce a uniform stress distribution across their radial direction. Functionally graded materials exhibit the unique design features, where by selection of proper grading profiles, stress distribution within the element may be optimized.

References

  1. 1.
    Noda N (2014) Axisymmetric thermal stresses in solid cylinders. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 1. Springer, Dordrecht, pp 317–326CrossRefGoogle Scholar
  2. 2.
    Noda N (2014) Three-dimensional thermal stresses cylinders. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 11. Springer, Dordrecht, pp 6132–6139CrossRefGoogle Scholar
  3. 3.
    Ishihara M, Noda N (2014) Axisymmetric thermal stresses cylinders. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 7. Springer, Dordrecht, pp 3452–3464CrossRefGoogle Scholar
  4. 4.
    Nappa L (2014) Thermal stresses in elastic cylinders and circular shells. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 10. Springer, Dordrecht, pp 5333–5344Google Scholar
  5. 5.
    Hetnarski RB, Ignaczak J (2011) The mathematical theory of elasticity, 2nd edn. CRC Press, Boca RatonzbMATHGoogle Scholar
  6. 6.
    Noda N, Hetnarski RB, Tanigawa Y (2003) Thermal stresses, 2nd edn. Taylor and Francis, New YorkGoogle Scholar
  7. 7.
    Noda N (2014) Axisymmetric thermal stresses in disks. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 1. Springer, Dordrecht, pp 307–317CrossRefGoogle Scholar
  8. 8.
    Tanigawa Y, Noda N (2014) Axisymmetric thermal stresses spheres. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 1. Springer, Dordrecht, pp 326–336CrossRefGoogle Scholar
  9. 9.
    Hata T (2014) One-dimensional thermal stresses in spheres. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 7. Springer, Dordrecht, pp 3464–3469CrossRefGoogle Scholar
  10. 10.
    Taler J, Ocłoń P (2014) Transient heat conduction in sphere. In: Hetnarski RB (ed) Encyclopedia of thermal stresses, vol 11. Springer, Dordrecht, pp 6186–6198CrossRefGoogle Scholar
  11. 11.
    Gatewood BE (1957) Thermal stresses. McGraw-Hill, New YorkzbMATHGoogle Scholar
  12. 12.
    Gatewood BE (1941) Thermal stresses in long cylindrical bodies. Phil Mag Ser 7(32):282–301MathSciNetCrossRefGoogle Scholar
  13. 13.
    Nowacki W (1986) Thermoelasticity, 2nd edn. PWN-Polish Scientific Publishers, Pergamon Press, Warsaw, OxfordzbMATHGoogle Scholar
  14. 14.
    Boley BA, Weiner JH (1962) Theory of thermal stresses. Wiley, New YorkzbMATHGoogle Scholar
  15. 15.
    Sabbaghian M, Eslami MR (1974) Creep relaxation of non axisymmetric thermal stresses in thick walled cylinders. AIAA J 12(12):1652–1658CrossRefGoogle Scholar
  16. 16.
    Muskhelishvili NI (1953) Some basic problems of the mathematical theory of elasticity. Noordhoff, Groningen, HollandzbMATHGoogle Scholar
  17. 17.
    Wang CT (1953) Applied elasticity. McGraw-Hill, New YorkzbMATHGoogle Scholar
  18. 18.
    Zimmerman RW, Lutz MP (1999) Thermal stress and thermal expansion in a uniformly heated functionally graded cylinder. J Therm Stress 22:177–188CrossRefGoogle Scholar
  19. 19.
    Han X, Liu GR, Lam KY (2000) A quadratic layer element for analyzing stress waves in FGMs and its applications in material characterization. J Sound Vib 236(2):307–321CrossRefGoogle Scholar
  20. 20.
    Obata Y, Noda N (1995) Transient thermal stresses in a hollow sphere of functionally gradient material. In: Proceedings of thermal stresses symposium, Shizuoka University, Hamamatsu, pp 335–338Google Scholar
  21. 21.
    Obata Y, Noda N (1997) Two-dimensional unsteady thermal stresses in a partially heated plate made of functionally graded material. In: Proceedings of thermal stresses symposium, Rochester Institute of Technology, Rochester, pp 735–738Google Scholar
  22. 22.
    Obata Y, Kanayama K, Ohji T, Noda N (1999) Two-dimensional unsteady thermal stresses in a partially heated circular cylinder made of functionally graded material. In: Proceedings of the third congress on thermal stresses, Kraków University of Technology, Kraków, Poland, pp 595–598Google Scholar
  23. 23.
    Jabbari M, Sohrabpour S, Eslami MR (2002) Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. Int J Pres Ves Pip 79:493–497CrossRefGoogle Scholar
  24. 24.
    Jabbari M, Sohrabpour S, Eslami MR (2003) General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads. J Appl Mech 70:111–118CrossRefGoogle Scholar
  25. 25.
    Katsuo M, Sawa T, Kawaguchi K, Kawamura H (1996) Axisymmetrical thermal stress analysis of laminated composite finite hollow cylinders restricted at both ends in steady state. In: Proceedings of the 1996 ASME international mechanical engineering congress and exposition, pp 17–22Google Scholar
  26. 26.
    Okumura IA, Noda N (1991) Thermoelastic potential functions in transversely isotropic solids and their applications. J Therm Stress 14(3):309–331MathSciNetCrossRefGoogle Scholar
  27. 27.
    Misra JC, Achari RM (1980) On axisymmetric thermal stresses in an anisotropic hollow cylinder. J Therm Stress 3(4):509–520CrossRefGoogle Scholar
  28. 28.
    Chen PYP (1980) Axisymmetric thermal stresses in an anisotropic finite hollow cylinder. J Therm Stress 6(2–4):197–205Google Scholar
  29. 29.
    Lu Y, Xiao J, Zhang K (1997) Steady-state temperature distribution and thermal stress of functionally gradient material cylinder. Wuhan Jiaotong Keji Daxue Xuebao/J Wuhan Transp Univ 21(2):158–163 (in Chinese)Google Scholar
  30. 30.
    Horgan CO, Chan AM (1999) The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. J Elast 55:4359MathSciNetzbMATHGoogle Scholar
  31. 31.
    Tutuncu N, Ozturk M (2001) The exact solution for stresses in functionally graded pressure vessels. Composites, Part B 32:683–686CrossRefGoogle Scholar
  32. 32.
    Liew KM, Kitipornchai S, Zhang XZ, Lim CW (2003) Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders. Int J Solids Struct 40:2355–2380CrossRefGoogle Scholar
  33. 33.
    Zhang XD, Liu DQ, Ge C (1994) Thermal stress analysis of axial symmetry functionally gradient materials under steady temperature field. J Funct Grad Mater 25:452–455Google Scholar
  34. 34.
    Obata Y, Noda N (1994) Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material. J Therm Stress 17(3):471–487CrossRefGoogle Scholar
  35. 35.
    Jabbari M, Bahtui A, Eslami MR (2006) Axisymmetric mechanical and thermal stresses in thick long FGM cylinders. J Therm Stress 29(7):643–663CrossRefGoogle Scholar
  36. 36.
    Bahtui A, Jabbari M, Eslami MR, Mechanical stresses in thick FGM pressure vessels. In: Proceedingsof the international congress and exhibition on pressure vessel and piping, OPE 2006, Chennai, India, 7–9 February 2006Google Scholar
  37. 37.
    Jabbari M, Mohazzab AH, Bahtui A, Eslami MR (2007) Analytical solution for three-dimensional stresses in a short length FGM hollow cylinder. ZAMM 87(6):413–429MathSciNetCrossRefGoogle Scholar
  38. 38.
    Rice RG, Do DD (1995) Applied mathematics and modeling for chemical engineering. Wiley, New York, pp 131–132Google Scholar
  39. 39.
    Cheung JB, Chen TS, Thirumalai K (1974) Transient thermal stresses in a sphere by local heating. ASME J Appl Mech 41(4):930–934CrossRefGoogle Scholar
  40. 40.
    Takeuti Y, Tanigawa Y (1982) Transient thermal stresses of a hollow sphere due to rotating heat source. J Therm Stress 5(3–4):283–298CrossRefGoogle Scholar
  41. 41.
    Sternberg E, Eubanks EA, Sadowsky MA (1952) On the axisymmetric problem of elasticity theory for a region bounded by two concentric spheres. In: Proceedings of first US National congress of applied mechanics, ASME, New York, pp 209–215Google Scholar
  42. 42.
    Lutz MP, Zimmerman RW (1996) Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere. J Therm Stress 19:39–54CrossRefGoogle Scholar
  43. 43.
    Obata Y, Noda N (1994) Steady thermal stress in a hollow circular cylinder and a hollow sphere of a functionaly gradient material. J Therm Stress 14:471–487CrossRefGoogle Scholar
  44. 44.
    Noda N (1986) Thermal stresses in materials with temperature-dependent properties. In: Hetnarski RB (ed) Thermal stresses I. Elsevier Science, AmsterdamGoogle Scholar
  45. 45.
    Eslami MR, Babaei MH, Poultangari R (2005) Thermal and mechanical stresses in a functionally graded thick sphere. Int J Pres Ves Pip 82:522–527CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations