Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading A.R. Shahani a, * , S.M. Nabavi a,b a Faculty of Mechanical Engineering, K.N.T. University of Technology, P.O. Box 16765-3381, Tehran, Iran b Applied Science and Research Association (ASRA), Tehran, Iran Received 1 January 2006; accepted 13 June 2006 Available online 9 August 2006 Abstract Thermoelasticity problem in a thick-walled cylinder is solved analytically using the finite Hankel transform. Time- dependent thermal boundary conditions are assumed to act on the inner surface of the cylinder. For the mechanical bound- ary conditions two different cases are assumed: Traction–displacement problem (traction is prescribed on the inner surface and the fixed displacement boundary condition on the outer one) and Traction–Traction problem (tractions are prescribed on both the inner and outer surfaces of the hollow cylinder). The quasi-static solution of the thermoelasticity problem is derived analytically, i.e., the transient thermal response of the cylinder is derived and then, quasi-static structural problem is solved and closed form relations are extracted for the thermal stresses in the two problems. The results show to be in accordance with that cited in the literature in the special cases. Ó 2006 Elsevier Inc. All rights reserved. Keywords: Thermoelasticity; Quasi-static; Thick-walled cylinder; Hankel transform 1. Introduction In typical problems of dynamic thermoelasticity the heating rates are sufficiently slow and the strain and temperature rates of change are of comparable magnitudes, both of the inertia and thermomechanical cou- pling terms in the governing equations can be dropped and dropping them greatly simplifies the equations and render them amenable to analytical solution. This assumption forms the basis of conventional transient thermal stress analysis and time enters only as a parameter from the transient temperature distribution in the body. A detail discussion on the effects of these terms can be found in Refs. [1,2]. Wang [3] presents a method for the analysis of the dynamic thermoelasticity problem in a hollow cylinder. The main disadvantage of his work is that the heat conduction equation is not solved for the problem and in 0307-904X/$ - see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2006.06.008 * Corresponding author. Tel.: +98 217 343 300; fax: +98 217 334 338. E-mail address: [email protected] (A.R. Shahani). Applied Mathematical Modelling 31 (2007) 1807–1818 www.elsevier.com/locate/apm brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Elsevier - Publisher Connector
Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading
Jun 24, 2023
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