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Boundary Element Method, Homogenization and Heat Conduction in Composite Materials

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IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method

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Abstract

The homogenization method for solution of the heat conduction problem is presented below in the context the Boundary Element Method. The approach is introduced for the fiber-reinforced composite with deterministically and randomly defined material properties. Computational implementation of the method can find the application for the composites with random interfaces where application of the Finite Element Method is very complicated. Numerical illustration shows deterministic and probabilistic sensitivity of effective composite heat conductivity with respect to fiber volume ratio and randomness level of composite constituents.

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References

  1. Brebbia, CA., Dominguez, J.: Boundary Elements. An Introductory Course. Comp. Mech. Publ., 1996.

    Google Scholar 

  2. Breitung, K., Casciati, F. and Faravelli, L.: A stochastic boundary element model for soil properties. Proc. of IUTAM/IABEM BEM Symp., pp. 10–11, Cracow 1999.

    Google Scholar 

  3. Burczynski, T.: Boundary Element Method in Structural Mechanics (in Polish). WNT, Warsaw, 1995.

    Google Scholar 

  4. Duddeck F.M.E.: A boundary element method for general media via Parseval’s theorem (in preparation).

    Google Scholar 

  5. Furmanski, P.: Heat conduction in composites: homogenization and macroscopic behaviour, Appl. Mech. Rev. 50(6) (1997), 327–355.

    Article  Google Scholar 

  6. Ghanem, R.G. and Spanos, P.D.: Stochastic Finite Elements: A Spectral Approach. Springer-Verlag, 1991.

    Book  MATH  Google Scholar 

  7. Hassani, B. and Hinton, E.: A review of homogenization and topology optimization: I- homogenization theory for media with periodic structure. Comput. & Struct. 69 (1998), 707–717;

    Article  MATH  Google Scholar 

  8. Hassani, B. and Hinton, E.: A review of homogenization and topology optimization: II — analytical and numerical solution of homogenization equations. Comput. & Struct. 69 (1998), 719–738;

    Article  Google Scholar 

  9. Hassani, B. and Hinton, E.: A review of homogenization and topology optimization: III — topology optimization using optimality criteria. Comput. & Struct. 69 (1998), 739–756.

    Article  Google Scholar 

  10. Haug, E.J., Choi, K.K. and Komkov, V.: Design Sensitivity Analysis of Structural Systems. Series Math. Sci. Engrg., Academic Press, 1986.

    MATH  Google Scholar 

  11. Hurtado, J.E. and Barbat, A.H.: Monte-Carlo techniques in computational stochastic mechanics. Arch. Comput. Meth. Engrg. 5(1) (1998), 3–30.

    Article  MathSciNet  Google Scholar 

  12. Kaminski, M.: Boundary element method homogenization of linear elastic composites. Engrg. Anal. Boundary Elem. 23(10): 815–823, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  13. Kaminski, M.: Homogenized properties of n-components composite materials. Int. J. Engrg. Sci. 38(4): 405–427, 2000.

    Article  MathSciNet  Google Scholar 

  14. Kaminski, M.: Stochastic second-order BEM perturbation formulation. Engrg. Anal. Boundary Elem. 23 (1999), 123–129.

    Article  MATH  Google Scholar 

  15. Kleiber, M. and Hien, T.D.: The Stochastic Finite Element Method. Wiley, 1992.

    MATH  Google Scholar 

  16. Manolis, G.D. and Shaw, R.P.: Boundary integral formulation for 2D and 3D thermal problems exhibiting a linearly varying stochastic conductivity. Comput. Mech. 17(1996), 406–417.

    Article  MATH  Google Scholar 

  17. Panagiotopoulos, P.D., Panagouli, O.K. and Koltsakis, E.K.: The BEM in place bodies with cracks and/or boundaries of fractal geometry. Comput. Mech. 15 (1995), 350–363.

    Article  MathSciNet  MATH  Google Scholar 

  18. Peng, X.Q. et al.: A stochastic finite element method for fatigue reliability analysis of gear teeth subjected to bending. Comput. Mech. 21 (1998), 253–261

    Article  MATH  Google Scholar 

  19. Shaw, R.P. et al.: The 2D free space Green’s function and BEE for a Poisson equation with linearly varying conductivity in two directions. In: Ertekin R.C. et al., eds., Proc. of BETECH 11, pp. 327–332, Comput. Mech. Publ., 1996.

    Google Scholar 

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Author notes

  1. M. Kaminski

    Present address: Division of Mechanics of Materials, Technical University of Lodz, Al. Politechniki 6, 93-590, Lodz, Poland

Authors and Affiliations

  1. Department of Civil Engineering, George Brown School of Engineering, Rice University, Houston, 6100 Main Street, 77005-1892, TX, USA

    M. Kaminski

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  1. M. Kaminski
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Editors and Affiliations

  1. Department for Strength of Materials and Computational Mechanics, Silesian University of Technology, Gliwice, Poland

    Tadeusz Burczynski

  2. Institute of Computer Modelling, Cracow University of Technology, Cracow, Poland

    Tadeusz Burczynski

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© 2001 Springer Science+Business Media Dordrecht

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Kaminski, M. (2001). Boundary Element Method, Homogenization and Heat Conduction in Composite Materials. In: Burczynski, T. (eds) IUTAM/IACM/IABEM Symposium on Advanced Mathematical and Computational Mechanics Aspects of the Boundary Element Method. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9793-7_13

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  • DOI: https://doi.org/10.1007/978-94-015-9793-7_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5737-2

  • Online ISBN: 978-94-015-9793-7

  • eBook Packages: Springer Book Archive

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