×

zbMATH — the first resource for mathematics

Boundary integral analysis of transient thermoelasticity. (English) Zbl 0687.73010
Summary: A simple and efficient method for the solution of uncoupled transient thermoelastic problems using boundary integral techniques is presented. The method employs a Laplace transformation to remove temporarily the time dependence of the governing equations. Numerical analysis is then carried out in the transform space, and results in the time-position space are found by numerical inversion of the Laplace transform. The method has the advantage that it avoids time-stepping and the costly evaluation of domain integrals. Boundary element and analytic solutions are compared, and the effect of cooling on the stresses around a deep underground opening is examined.

MSC:
74F05 Thermal effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] and , ’An application of boundary element method to thermoelastic problems’, in Proc. 5th Int. Conf. on Boundary Elements (C. A. Brebbia, T. Futagami and M. Tanaka, Eds.), 1983, pp. 417-426.
[2] and , ’A boundary element investigation of 3-D thermoelastic problems in transient heat conduction states’, in Proc. 7th Int. Conf. on Boundary Elements ( C. A. Brebbia and G. Maier, Eds.), 1985, pp. 3-3-3-16.
[3] Chaudouet, Int. j. numer. methods eng. 24 pp 25– (1987)
[4] Sladek, Appl. Math. Modelling 8 pp 413– (1984)
[5] Sharp, J. Appl. Mech. 53 pp 298– (1986)
[6] Banerjee, Int. j. numer. anal. methods geomech. 5 pp 15– (1981)
[7] Talbot, J. Inst. Math. Applic. 23 pp 97– (1979)
[8] Rizzo, AIAAJ. 8 pp 2004– (1970)
[9] Rizzo, Int. j. numer. methods eng. 11 pp 1753– (1977)
[10] and , Conduction of Heat in Solids, Clarendon Press, Oxford, 1957.
[11] and , Theory of Thermal Stresses, Wiley, New York, 1960. · Zbl 0095.18407
[12] Thermoelasticity, Pergamon Press, London, 1962.
[13] (Ed), Encyclopedia of Physics, Mechanics of Solids, Vol. VI, p. 73. Springer-Verlag, Berlin, 1965.
[14] and , Boundary Element Methods in Solid Mechanics, Allen & Unwin, London, 1983.
[15] McPherson, Int. J. Mining Geol. Eng. 4 pp 165– (1985)
[16] Mouset-Jones, Int. J. Mining Geol. Eng. 4 pp 197– (1986)
[17] (Eds.), Handbook of Mathematical Functions, National Bureau of Standards Applied Mathematics, Series 55, U. S. Government Printing Offices, Washington, DC, 1964.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.