Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical me
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Thermal shock analysis and thermo-elastic stress waves in functionally graded thick hollow cylinders using analytical method Ali Safari-Kahnaki • Seyed Mahmoud Hosseini Masoud Tahani
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Received: 9 November 2010 / Accepted: 22 June 2011 / Published online: 10 July 2011 Ó Springer Science+Business Media, B.V. 2011
Abstract Transient stress field and thermo-elastic stress wave propagation are studied in functionally graded thick hollow cylinder under arbitrary thermomechanical shock loading, in this article. Thermomechanical properties of functionally graded (FG) cylinder are assumed to be temperature independent and vary continuously and smoothly in the radial direction. The governing dynamic equations are analytically solved in temperature and elastic fields. To solve the problem, Laplace transform is used respect to time in all constitutive equations and boundary conditions. At first, temperature field equation analytically solved using Laplace transform and series method. The dynamic behaviors of thermo-elastic stresses are illustrated and discussed for various grading patterns of thermo-mechanical properties in several points across the thickness of FG cylinder. Time history of temperature field and thermal stresses are obtained
A. Safari-Kahnaki M. Tahani Mechanical Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, PO Box 91775-1111, Mashhad, Iran e-mail: [email protected] M. Tahani e-mail: [email protected] S. M. Hosseini (&) Industrial Engineering Department, Faculty of Engineering, Ferdowsi University of Mashhad, PO Box 91775-1111, Mashhad, Iran e-mail: [email protected]; [email protected]
using the residual theorem and the fast Laplace inverse transform method (FLIT), respectively. Also, the effects of the cylinder thickness and convection heat transfer coefficient on dynamic response of FG cylinder are revealed and discussed. The presented analytical method provides a ground to study the time histories of radial and hoop stresses in FG cylinders with different thickness and various volume fraction exponents. The advantage of this method is its mathematical ability to support simple and complicated mathematical function for the thermo-mechanical boundary conditions. A reasonable agreement can be seen in comparison of obtained results based on the presented analytical method with published data. Keywords Analytical solution Functionally graded materials Thick hollow cylinder Thermal stresses Shock loading
1 Introduction One of the most important structures in various industries (such as aerospace, chemical and petroleum industries) is thick hollow cylinder that is used as pressure vessels and cylindrical shells. Consequently, the dynamic characteristics of cylinder are obviously important for engineering purposes and optimum design. In modern industries using new materials such as composites and functionally graded materials (FGMs) in cylindrical shells are increasing
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because of their capability to control stresses caused by thermal and
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