Approximate Solutions in Linear, Coupled Thermoelasticity

[+] Author and Article Information
R. E. Nickell

Rohm and Haas Company, Huntsville, Ala.

J. L. Sackman

Division of Civil Engineering, University of California, Berkeley, Calif.

J. Appl. Mech 35(2), 255-266 (Jun 01, 1968) (12 pages) doi:10.1115/1.3601189 History: Received June 18, 1967; Revised September 06, 1967; Online September 14, 2011


A method for obtaining approximate solutions to initial-boundary-value problems in the linear theory of coupled thermoelasticity is developed. This procedure is a direct variational method representing an extension of the Ritz method. As an illustration of the procedure, it is applied to a class of one-dimensional, transient problems involving weak thermal shocks. The problems considered are: (a) Rapid heating of a half space through a thermally conducting boundary layer, and (b) gradual heating of the boundary surface of a half space. The solutions generated by the extended Ritz method are compared, for accuracy, to solutions obtained from a numerical inversion scheme for the Laplace transform based on Gaussian quadrature. These comparisons indicate that the variational procedure developed here can yield accurate results.

Copyright © 1968 by ASME
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