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Thermal Stresses in Bodies with Random Initial Temperature Distribution

¹ Department of Mechanical System Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa 9928510, Japan
² Department of Mechanical Engineering, Iwate University, 4-3-5 Ueda, Morioka 0208551, Japan

^* To whom correspondence should be addressed.

	Abstract

This paper describes a stochastic analysis in the one-dimensional uncoupled linear thermoelasticity. The autocorrelation functions of transient temperature and thermal stresses are analytically obtained in seven simple geometries: infinite plate, infinite strip, hollow sphere, infinite body with a spherical cavity, infinite hollow cylinder, annular disk and infinite body with a cylindrical hole, which have a random initial temperature distribution. Numerical calculations are performed for some geometries under the condition that the randomness in the initial temperature is given as a homogeneous white noise. The transient behavior of the mean square temperature and thermal stresses is illustrated and it is observed in objects confined to a finite region that whereas the maximum value of the mean square thermal stresses occurs within the objects shortly after the heat flow begins, it appears at a lateral surface after a length of time has elapsed.

Key Words: Thermoelasticity, random field, thermal stress, heat conduction, random initial temperature

First published on March 11, 2009
Mathematics and Mechanics of Solids 2009, doi:10.1177/1081286508100497


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