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A three-dimensional boundary element/Laplace transform solution of uncoupled transient thermo-elasticity in non-homogeneous rock media. (English) Zbl 0999.74112
Summary: We present a boundary element solution of uncoupled transient thermoelasticity for three-dimensional non-homogeneous media. An explicit expression for the thermal integral function is derived, and an efficient Laplace inversion scheme is implemented. The method is illustrated with an example.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
74L10 Soil and rock mechanics
74F05 Thermal effects in solid mechanics
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[1] Biot, General solutions of the equations of elasticity and consolidation for a porous material, Journal of Applied Mechanics 23 (1) pp 91– (1956) · Zbl 0074.19101
[2] Boley, Theory of Thermal Stresses pp 586– (1960)
[3] Rizzo, An advanced boundary integral equation method for three-dimensional thermoelasticity, International Journal for Numerical Methods in Engineering 11 pp 1753– (1977) · Zbl 0387.73007
[4] Deb, Multi-domain two- and three-dimensional thermoelasticity by BEM, International Journal for Numerical Methods in Engineering 32 pp 991– (1991) · Zbl 0825.73904
[5] Mackerle, Thermomechanical analysis with finite and boundary element methods-a bibliography, Finite Elements in Analysis and Design 20 (1) pp 71– (1995) · Zbl 0875.73002
[6] Ochiai, Two-dimensional thermal stress analysis under unsteady state by the improved boundary element method, Journal of Thermal Stresses 19 (2) pp 107– (1996)
[7] Tanaka, Application of boundary element method to 3D problems of coupled thermoelasticity, Engineering Analysis with Boundary Elements 16 (4) pp 297– (1995)
[8] Henry, A new boundary element formulation for two and three dimensional thermoelasticity using particular integrals, International Journal for Numerical Methods in Engineering 26 pp 2061– (1988) · Zbl 0662.73009
[9] Smith, Boundary element analysis of linear thermoelastic consolidation, International Journal for Numerical and Analytical Methods in Geometry 20 pp 457– (1996) · Zbl 0894.73203
[10] Rizzo, A method of solution for certain problems of transient heat conduction, AIAA Journal 8 (11) pp 2004– (1970) · Zbl 0237.65074
[11] Cheng, Boundary integral equation method for linear porous-elasticity with application to soil consolidation, International Journal for Numerical Methods in Engineering 20 pp 279– (1984) · Zbl 0525.73125
[12] Cheng, A direct boundary element method for plane strain poroelasticity, International Journal for Numerical and Analytical Methods in Geometry 12 pp 551– (1988) · Zbl 0662.73056
[13] Sladek, Boundary integral equation method in thermoelasticity, part III: uncoupled thermoelasticity, Applied Mathematical Modelling 8 pp 413– (1984) · Zbl 0578.73013
[14] Smith, Boundary integral analysis of transient thermoelasticity, International Journal for Numerical and Analytical Methods in Geometry 13 pp 283– (1989) · Zbl 0687.73010
[15] Badmus, A Laplace-transform-based three-dimensional BEM for poroelasticity, International Journal for Numerical Methods in Engineering 36 pp 67– (1993) · Zbl 0772.73087
[16] Chen, Boundary element method for dynamic poroelastic and thermoelastic analyses, International Journal of Solids and Structures 32 (15) pp 2257– (1995) · Zbl 0869.73075
[17] Leo, A boundary element method for the analysis of contaminant transport in porous media I: homogeneous porous media, International Journal for Numerical and Analytical Methods in Geometry 23 pp 1681– (1999) · Zbl 0955.76060
[18] Elzein, Groundwater pollution by organic compounds: a three-dimensional analysis of contaminant transport in stratified porous media with multiple sources of non-equilibrium, International Journal for Numerical and Analytical Methods in Geometry 23 pp 1733– (1999) · Zbl 0939.86500
[19] Crump, Numerical inversion of Laplace transforms using a Fourier series approximation, Journal of the Association for Computing Machinery 23 (1) pp 89– (1976) · Zbl 0315.65074
[20] Cruse, Application of the boundary integral equation method to three-dimensional stress analysis, Computer and Structures 3 pp 509– (1974)
[21] Lachat, Effective numerical treatment of boundary integral equations: a formulation for three dimensional elastostatics, International Journal for Numerical Methods in Engineering 10 pp 991– (1976) · Zbl 0332.73022
[22] Kutt HR Quadrature formulae for finite-part integrals 1975
[23] Telles, A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals, International Journal for Numerical Methods in Engineering 24 pp 1– (1987) · Zbl 0622.65014
[24] Davies, Numerical inversion of the Laplace transform: A survey and comparison of methods, Journal of Computational Physics 33 pp 1– (1979) · Zbl 0416.65077
[25] Talbot, The accurate numerical integration of Laplace transforms, Journal of the Institute for Mathematical Applications 23 pp 97– (1979) · Zbl 0406.65054
[26] McDonald, Accelerated convergence divergence, iteration, extrapolation, and curve fitting, Journal of Applied Physics 10 pp 3034– (1964)
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