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Original Articles

Analytical methods for heat conduction in composites

, , &
Pages 67-78 | Received 29 Sep 2007, Published online: 14 Oct 2010

References

  • Allair , G. 2002 . Shape Optimization by the Homogenization Method , New York : Springer Verlag .
  • Bergman , D. J. 1983 . “ Bulk physical properties of composite media. of Collection de la Direction des etudes et recherches d’ Electricite de France, Session qui s'est tenue au Centre du Breau‐sans‐Nappe ” . Paris, France : Eyrolles . du 27 juin au 13 juillet 1985
  • Bergman , D. J. 1978 . The dielectric constants of a composite material‐a problem in classical physics . Phys. Rep. C , 43 : 377 – 407 .
  • Bojarski , B. 1960 . On generalized Hilbert boundary value problem . Soobsch. AN GruzSSR , 25 (4) : 385 – 390 . (in Russian)
  • Cherkaev , A. 2000 . Variational Methods for Structural Optimization , New York : Springer Verlag .
  • Craster , R. V. and Obnosov , Yu. V. 2001 . Four‐phase checkerboard composites . SIAM J. Appl Math. , 61 : 1839 – 1856 .
  • Craster , R. V. , Obnosov , Yu. and A , V. 2004 . three‐phase tessellation: solution and effective properties . Proc. Royal Society London A , 460 : 1017 – 1037 .
  • Gakhov , F. D. 1977 . Boundary Value Problems , 3rd ed. , Nauka . (in Russian); Engl. transl. of 1st ed.: Pergamon Press, 1966
  • Günter , N.M . 1967 . Potential Theory and its Applications to Basic Problems of Mathematical Physics , Ungar Publ. Co. .
  • Jikov , V. V. , Kozlo , S. M. and Olejnik , O. A. 1994 . Homogenization of Differential Operators and Integral Functionals , Springer‐Verlag .
  • Mikhailov , L. G. 1963 . New Class of Singular Integral Equations and its Applications to Differential Equations with Singular Coefficients , AN TadzhSSR . (in Russian); Engl. transl.: Akademie‐Verlag 1970
  • Mikhlin , S. G. 1964 . Integral Equations and their Applications to Certain Problems in Mechanics , 2nd rev. ed. , Macmillan : Mathematical Physics and Technology .
  • Milton , G. W. 2002 . The Theory of Composites , Cambridge : Cambridge University Press .
  • Mityushev , V. 2006 . Representative cell in mechanics of composites and generalized Eisenstein‐Rayleigh sums . Complex Variables , 51 (8–11) : 1033 – 1045 .
  • Mityushev , V. 2007 . Exact solution of the R‐linear problem for a disk in a class of doubly periodic functions . J. Appl. Funct. Anal , 2 (2) : 115 – 127 .
  • Mityushev , V. and Rogosin , S. 1999 . Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions. Theory and Applications , 108 Chapman & Hall / CRC, Monographs and Surveys in Pure and Applied Mathematics .
  • Mityushev Pesetskaya , V. V. , Rogosin , E. V. and Analytica , S. V. 2007 . “ Methods for Heat Conduction in Composites and Porous media ” . Amsterdam : Wiley‐VCH .
  • Wojnar , R. , Bytner , R. and Galka , A. 1999 . “ Effective properties of elastic composites subject to thermal fields ” . In Thermal Stresses V , Edited by: hetnarsk , R. B. 257 – 465 . Lastran Corp.‐Publ. Division Rochester .
  • The work by E.P. is partially supported by the Portuguese Science Foundation (FCT‐Fundação para a Ciência e a Tecnologia) through the grant number SFRH/BPD/34649/2007.

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