# Transient thermal stress analysis of multilayered hollow cylinder

- Received:
- Revised:

DOI: 10.1007/BF01272526

- Cite this article as:
- Lee, Z.-., Chen, C.K. & Hung, C.-. Acta Mechanica (2001) 151: 75. doi:10.1007/BF01272526

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## Summary

This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.

### Nomenclature

- λ
Lame's constant

- ρ
density

*C*_{v}specific heat

*k*_{r},*k*_{≡}radial and circumferential thermal conductivity

*α*_{r},*α*_{≡}linear radial and circumferential thermal expansion coefficient

*E*_{r},*E*_{≡}radial and circumferential Young's modulus

*v*_{rΘ}Poisson's ratio

- Θ
_{0} reference temperature

- Θ,
*T* dimensional and nondimensional temperature

*r*^{*},*r*dimensional and nondimensional radial coordinate

- τ,
*t* dimensional and nondimensional time

- σ
_{r}^{*},σ_{r} dimensional and nondimensional radial stress

- σ
_{θ}^{*},σ_{θ} dimensional and nondimensional circumferential stress

*U, u*dimensional and nondimensional radial component of displacement