Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

doi:10.1088/1674-1056/21/1/014601

中国物理B ›› 2012, Vol. 21 ›› Issue (1): 14601-014601.doi: 10.1088/1674-1056/21/1/014601

Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

Ibrahim A. Abbas¹, Mohamed I. A. Othman²

(1)Department of Mathematics, Faculty of Science and Arts - Khulais, King AbdulAziz University, Jeddah, Saudi Arabia; Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt; (2)Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

收稿日期:2011-03-28 修回日期:2011-07-21 出版日期:2012-01-15 发布日期:2012-01-20

Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

Ibrahim A. Abbas^a)b) and Mohamed I. A. Othman^c)^†

^a Department of Mathematics, Faculty of Science and Arts - Khulais, King AbdulAziz University, Jeddah, Saudi Arabia; ^b Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt; ^c Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt

Received:2011-03-28 Revised:2011-07-21 Online:2012-01-15 Published:2012-01-20

摘要/Abstract

摘要： In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

关键词: generalized thermoelsticity, thermal shock, temperature dependent elastic moduli, finite element method

Abstract: In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.

Key words: generalized thermoelsticity, thermal shock, temperature dependent elastic moduli, finite element method

中图分类号: (Thermoelasticity and electromagnetic elasticity (electroelasticity, magnetoelasticity))

46.25.Hf

Ibrahim A. Abbas, Mohamed I. A. Othman. Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli[J]. 中国物理B, 2012, 21(1): 14601-014601.

Ibrahim A. Abbas and Mohamed I. A. Othman . Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli[J]. Chin. Phys. B, 2012, 21(1): 14601-014601.

参考文献 20

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[15]	Abbas I A 2007 Forschung im Ingenieurwesen 71 215
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[17]	Abbas I A and Abd-allah A N 2008 Arch. Appl. Mech. 78 283
[18]	Abbas I A and Othman M I A 2009 Int. J. Industrial Mathematics 1 121
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Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

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