Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity
ABSTRACT
The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem; using different theories of generalized thermoelasticity; has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.
The present paper deals with thermoelastic problems of finitely long hollow cylinder com-posed of two different materials with axial sym- metry. The medium is traction-free, with neglig-ible body forces and with internal and external heat generations. The governing equations for different theories of the generalized thermoe-lasticity are written in terms of displacement and temperature increment. The exact solution of the problem; using different theories of generalized thermoelasticity; has been deduced. The analytical expressions for displacements, temperature and stresses are found in final forms, and a numerical example has been taken to discuss the effect of the relaxation times. Finally, the results have been illustrated graphi- cally to find the responses of different theories.
Cite this paper
Mashat, D. , Zenkour, A. and Elsibai, K. (2010) Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity. Natural Science, 2, 1171-1179. doi: 10.4236/ns.2010.210145.
Mashat, D. , Zenkour, A. and Elsibai, K. (2010) Transient response of multilayered hollow cylinder using various theories of generalized thermoelasticity. Natural Science, 2, 1171-1179. doi: 10.4236/ns.2010.210145.
References
[1] Biot, M. (1956) Thermoelasticity and irreversible the- rmo-dynamics. Journal of Applied Physics, 27, 240-253. [2] Lord, H.W. and Shulman, Y.A. (1967) A generalized dynamical theory of thermoelasticity. Jornal of Mechanics and Physics of Solids, 15, 299-309. [3] Dhaliwal, R.S. and Sherief, H.H. (1980) Generalized thermoelasticity for anisotropic media. Quarterly of Ap-plied Mathematics, 38, 1-8. [4] Ignaczak, J. (1979) Uniqueness in generalized thermoe-lasticity. Journal of Thermal Stresses, 2, 171-175. [5] Sherief, H.H. and Dhaliwal, R. (1980) A uniqueness theorem and a variational principle for generalized ther-moelasticity. Journal of Thermal Stresses, 3, 223-230. [6] Green, A. and Lindsay, K. (1972) Thermoelasticity. Journal of Elasticity, 2, 1-7. [7] Jane, K.C. and Lee, Z.Y. (1999) Thermoelasticity of mul-tilayered cylinder. Journal of Thermal Stresses, 22, 57-74. [8] Kandil, A. (1975) Investigation of stress analysis in com- pound cylinders under high pressure and temperature. M.Sc. Thesis, CIT Helwan. [9] Sherief, H.H. and Anwar, M.N. (1988) A problem in generalized thermoelasticity for an infinitely long annular cylinder. International Journal of Engineering Science, 26, 301-306. [10] Yan, Y.C. and Chen, C.K. (1986) Thermoelastic transient response of an infinitely long annular cylinder com- posed of two different materials. International Journal of En-gineering Science, 24, 569-581. [11] Lee, Z.-Y. (2006) Generalized coupled transient response of 3-D multilayered hollow cylinder. International Com- munications in Heat and Mass Transfer, 33, 1002-1012. [12] Chen, C.K., Hung, C.I. and Lee, Z.Y. (2001) Transient thermal stresses analysis of multilayered hollow cylinder. Acta Mechanica, 151, 75-88. [13] Chen, C.K., Hung, C.I. and Lee, Z.Y. (2001) Thermoe-lastic transient response of multilayered hollow cylinder with initial interface pressure. Journal of Thermal Str- esses, 24, 987-1006. [14] Allam, M.N., Elsibai, K.A. and Abouelregal, A.E. (2002) Thermal stresses in a harmonic field for an infinite body with a circular cylindrical hole without energy dissipation. Journal of Thermal Stresses, 25, 57-67. [15] Zenkour, A.M., Mashat, D.S. and Elsibai, K.A. (2009) Bending analysis of functionally graded plates in the context of different theories of thermoelasticity. Mathe-matical Problems in Engineering, 2009, Article ID 962351, 1-15.
[1] Biot, M. (1956) Thermoelasticity and irreversible the- rmo-dynamics. Journal of Applied Physics, 27, 240-253. [2] Lord, H.W. and Shulman, Y.A. (1967) A generalized dynamical theory of thermoelasticity. Jornal of Mechanics and Physics of Solids, 15, 299-309. [3] Dhaliwal, R.S. and Sherief, H.H. (1980) Generalized thermoelasticity for anisotropic media. Quarterly of Ap-plied Mathematics, 38, 1-8. [4] Ignaczak, J. (1979) Uniqueness in generalized thermoe-lasticity. Journal of Thermal Stresses, 2, 171-175. [5] Sherief, H.H. and Dhaliwal, R. (1980) A uniqueness theorem and a variational principle for generalized ther-moelasticity. Journal of Thermal Stresses, 3, 223-230. [6] Green, A. and Lindsay, K. (1972) Thermoelasticity. Journal of Elasticity, 2, 1-7. [7] Jane, K.C. and Lee, Z.Y. (1999) Thermoelasticity of mul-tilayered cylinder. Journal of Thermal Stresses, 22, 57-74. [8] Kandil, A. (1975) Investigation of stress analysis in com- pound cylinders under high pressure and temperature. M.Sc. Thesis, CIT Helwan. [9] Sherief, H.H. and Anwar, M.N. (1988) A problem in generalized thermoelasticity for an infinitely long annular cylinder. International Journal of Engineering Science, 26, 301-306. [10] Yan, Y.C. and Chen, C.K. (1986) Thermoelastic transient response of an infinitely long annular cylinder com- posed of two different materials. International Journal of En-gineering Science, 24, 569-581. [11] Lee, Z.-Y. (2006) Generalized coupled transient response of 3-D multilayered hollow cylinder. International Com- munications in Heat and Mass Transfer, 33, 1002-1012. [12] Chen, C.K., Hung, C.I. and Lee, Z.Y. (2001) Transient thermal stresses analysis of multilayered hollow cylinder. Acta Mechanica, 151, 75-88. [13] Chen, C.K., Hung, C.I. and Lee, Z.Y. (2001) Thermoe-lastic transient response of multilayered hollow cylinder with initial interface pressure. Journal of Thermal Str- esses, 24, 987-1006. [14] Allam, M.N., Elsibai, K.A. and Abouelregal, A.E. (2002) Thermal stresses in a harmonic field for an infinite body with a circular cylindrical hole without energy dissipation. Journal of Thermal Stresses, 25, 57-67. [15] Zenkour, A.M., Mashat, D.S. and Elsibai, K.A. (2009) Bending analysis of functionally graded plates in the context of different theories of thermoelasticity. Mathe-matical Problems in Engineering, 2009, Article ID 962351, 1-15.