Structural Engineering and Mechanics

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A boundary element method based on time-stepping approximation for transient heat conduction in anisotropic solids

  • Tanaka, Masa (Department of Mechanical Engineering, Faculty of Engineering, Shinshu University) ;
  • Matsumoto, T. (Department of Mechanical Engineering, Faculty of Engineering, Shinshu University) ;
  • Yang, Q.F. (Graduate School of Shinshu University)
  • Published : 1996.01.25
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Abstract

The time-stepping boundary element method has been so far applied by the authors to transient heat conduction in isotropic solids as well as in orthotropic solids. In this paper, attempt is made to extend the method to 2-D transient heat conduction in arbitrarily anisotropic solids. The resulting boundary integral equation is discretized by means of the boundary element with quadratic interpolation. The final system of equations thus obtained is solved by advancing the time step from the given initial state to the final state. Through numerical compuation of a few examples the potential usefulness of the proposed method is demonstrated.

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References

  1. Brebbia, C.A. Telles, J.C.F. and Wrobel, L.C. (1984), Boundary Element Techniques-Theory and Applications in Engineering, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 141-176
  2. Carslaw, H.S. and Jaeger, J.C. (1978), Conduction of Heat in Solids, 2nd ed., clarendon Press, Oxford.
  3. Curran, D., Cross, M. and Lewis, B.A. (1980), "Solution of parabolic differential equations using discretization in time", Appl. Math. modelling, 4, 389-400. https://doi.org/10.1016/0307-904X(80)90166-3
  4. Ingber, M.S. (1978), "An efficient boundary element method for a class of parabolic differential equations using discretization in time", Numerical Methods in Partial Differential Equations, 3, 187-197.
  5. Ingber, M.S. and Phan-Thien, N. (1992), "A boundary element approach for parabolic differential equations using a classs of particular solutions", Appl. Math. Modelling, 16, 124-132. https://doi.org/10.1016/0307-904X(92)90063-9
  6. Liggett, J.A. and Liu, P.L.F. (1979), "Unsteady flow in confined aquifers: A comparison of two boundary integral methods", Water Resour. Res., 15, 861-866. https://doi.org/10.1029/WR015i004p00861
  7. Matsumoto, T., Tanaka, M. and Fujii, H. (1990), "Transient analysis of scalar wave equation using the boundary element method based kon a time-stepping scheme", Advances in BEM in Japan and USA., Computational Mechanics Publications, Southampton-Boston, 203-218.
  8. Matsumoto, T. and Tanaka, M. (1993), "Boundary stress calculation using regularized boundary integral equation for displacement gradients", Int. J. Numerical Methods in Engineering, 36, 783-797. https://doi.org/10.1002/nme.1620360505
  9. Matsumoto, T., Tamaka, M. and Hondoh, K. (1993), "Some nonsingular direct formulations of boundary integral equations for thin elastic plate bending", Appl. Math. Modelling, 17, 586-594. https://doi.org/10.1016/0307-904X(93)90066-P
  10. Pina, H.L.G. and Fernandes, J. L. M. (1984), "Applications in transient heat conduction", Topics in Boundary Element Research, 1, ed. by C.A. Brebbia, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 41-58.
  11. Rizzo, F.J. and Shippy, D.J. (1970), "A method of solution for certain problems of transient heat conduction", AIAA J., 8, 2004-2009. https://doi.org/10.2514/3.6038
  12. Roures, V. and Alarcon, E. (1983), "Transient heat conduction problems using B.I.E.M.", Computers and Structures, 16(6), 717-730. https://doi.org/10.1016/0045-7949(83)90063-9
  13. Sladek, V., Sladek, J. and Tanaka, M. (1993), "Regularization of hypersingular and nearly singular integrals in the potential theory and elasticity", Int. J. Numerical Methods in Engineering, 36, 1609-1628. https://doi.org/10.1002/nme.1620361002
  14. Taigbenu, A.E. and Liggett, J.A. (1985), "Boundary element calculations for the diffusion equation", J. Eng. Mech., 111(3), 311-328. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:3(311)
  15. Tanaka, M. and Matsumoto, T. (1990), "Transient elastodynamic boundary element formulations based on the time-stepping scheme", Int. J. Pressure Vessels & Piping, 42, 371-332.
  16. Tanaka, M., Matsumoto, T. and Yang, Q.F. (1993), "A time-stepping boundary element method for transient heat conduction in orthotropic bodies", Eng. Anal. with Boundary Elements, 12, 85-91. https://doi.org/10.1016/0955-7997(93)90002-3
  17. Tanaka, M., Matsumoto, T. and Yang, Q.F. (1994), "Time-stepping boundary element method applied to 2-D transient heat conduction problems", Appl. Math. Modelling, 18, 569-576. https://doi.org/10.1016/0307-904X(94)90142-2
  18. Wrobel, L.C. and Brebbia, C.A. (1979), "The boundary element method for steady-state and transient heat conduction", Numerical Methods in Thermal Problems, 1, ed. by R.W. Lewis and K. Morgan, Pineridge Press, Swansea. 58-73.