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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.

74F05 Thermal effects in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
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[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.
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