Acta Mechanica Solida Sinica

, Volume 23, Issue 2, pp 156–166 | Cite as

Transient Thermal Response in Thick Orthotropic Hollow Cylinders with Finite Length: High Order Shell Theory

Article

Abstract

The transient thermal response of a thick orthotropic hollow cylinder with finite length is studied by a high order shell theory. The radial and axial displacements are assumed to have quadratic and cubic variations through the thickness, respectively. It is important that the radial stress is approximated by a cubic expansion satisfying the boundary conditions at the inner and outer surfaces, and the corresponding strain should be least-squares compatible with the strain derived from the strain-displacement relation. The equations of motion are derived from the integration of the equilibrium equations of stresses, which are solved by precise integration method (PIM). Numerical results are obtained, and compared with FE simulations and dynamic thermo-elasticity solutions, which indicates that the high order shell theory is capable of predicting the transient thermal response of an orthotropic (or isotropic) thick hollow cylinder efficiently, and for the detonation tube of actual pulse detonation engines (PDE) heated continuously, the thermal stresses will become too large to be neglected, which are not like those in the one time experiments with very short time.

Key words

dynamic thermo-elasticity thermal response high order shell theory thick hollow cylinder 

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References

  1. [1]
    Kardomateas, G.A., The initial phase of transient thermal stresses due to general boundary thermal loads in orthotropic hollow cylinders. Journal of Applied Mechanics, 1990, 57(3): 719–724.CrossRefGoogle Scholar
  2. [2]
    Cho, H. and Kardomateas, G.A., Thermal shock stresses due to heat convection at a bounding surface in a thick orthotropic cylindrical shell. International Journal of Solids and Structures, 2001, 38(16): 2769–2788.CrossRefGoogle Scholar
  3. [3]
    Ding, H.J., Wang, H.M. and Chen, W.Q., Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems. Acta Mechanica Sinica, 2004, 20(5): 477–483.CrossRefGoogle Scholar
  4. [4]
    Radu, V., Taylor, N. and Paffumi, E., Development of new analytical solutions for elastic thermal stress components in a hollow cylinder under sinusoidal transient thermal loading. International Journal of Pressure Vessels and Piping, 2008, 85(12): 885–893.CrossRefGoogle Scholar
  5. [5]
    Noda, N., Hetnarski, R.B. and Tanigawa, Y., Thermal Stresses, 2nd ed. New York: Taylor & Francis, 2003.Google Scholar
  6. [6]
    Cook, G.M. and Tessler, A., A {3, 2}-order bending theory for laminated composite and sandwich beams. Composites Part B: Engineering, 1998, 29(5): 565–576.CrossRefGoogle Scholar
  7. [7]
    Zhong, W.X., On precise integration method. Journal of Computational and Applied Mathematics, 2004, 163(1): 59–78.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, 2nd ed. Oxford: Clarendon Press, 1959.MATHGoogle Scholar
  9. [9]
    Cho, H., Kardomateas, G.A. and Valle, C.S., Elastodynamic solution for the thermal shock stresses in an orthotropic thick cylindrical shell. Journal of Applied Mechanics, 1998, 65(1): 184–193.CrossRefGoogle Scholar
  10. [10]
    Beltman, W.M. and Shepherd, J.E., Linear elastic response of tubes to internal detonation loading. Journal of Sound and Vibration, 2002, 252(4): 617–655.CrossRefGoogle Scholar
  11. [11]
    Shepherd,J.E., Structural response of piping to internal gas detonation. Proceeding of PVP2006-ICPVT-11, Vancouver BC, Canada, 2006.Google Scholar
  12. [12]
    Zhou, J.X., Deng, Z.C. and Hou, X.H., Critical velocity of sandwich cylindrical shell under moving internal pressure. Applied Mathematics and Mechanics, 2008, 29(2): 1569–1578.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.Department of Engineering MechanicsNorthwestern Polytechnical UniversityXi’anChina
  2. 2.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina

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