A Basic Problem in Thermoelasticodynamics and its Solution

[+] Author and Article Information
Xiangzhou Zhang

Department of Civil Engineering, Shanghai Tiedao University, Shanghai 200333, P.R.C.

J. Appl. Mech 65(2), 354-361 (Jun 01, 1998) (8 pages) doi:10.1115/1.2789062 History: Received May 05, 1995; Revised July 10, 1997; Online October 25, 2007


Dynamic stresses in a solid sphere, brought about by a sudden temperature rise uniformly distributed over the whole volume of the sphere, is studied as a basic problem in thermoelasticodynamics. Using a simple reduction, the problem is first reduced to an isothermal dynamicresponse one. Exact solution to this dynamic response problem, for a hollow sphere with a fixed inner boundary, is developed with use of a solution in D’Alembertform and a technique of singularity extraction. This hollow sphere solution is further employed in a limit process, in which the inner radius of the sphere tends towards zero, with the objective of thereby creating a solution for the solid sphere. This limit process results in a solid sphere solution, which is exact and explicit, and takes various closed forms for each wave propagation and reflection. Numerical result and discussion regarding this solid sphere solution are given.

Copyright © 1998 by The American Society of Mechanical Engineers
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