Abstract
A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with εY-periodic coefficients (Y is a cube) is replaced with a vectorial elliptic problem of constant coefficients. The unknown fields are: the averaged distribution of temperature θ and the vector field φ which stands for perturbation of the temperature within the cells of periodicity. The recovery of temperature in the original composite is given by the approximation: 0ε(x)=0(x) +h a (x/ε)ϕ a (x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h α are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for θε satisfies the boundary condition.
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Communicated by M. Kleiber, September 6, 1991
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Lewiński, T., Kucharski, S. A model with length scales for composites with periodic structure. Steady state heat conduction problem. Computational Mechanics 9, 249–265 (1992). https://doi.org/10.1007/BF00370034
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DOI: https://doi.org/10.1007/BF00370034