A model with length scales for composites with periodic structure. Steady state heat conduction problem

✍ Scribed by T. Lewiński; St. Kucharski

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 986 KB
• Volume: 9
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00370034

✦ Synopsis

A new high-order model for analysing distribution of temperature in periodic composites is proposed. The original scalar elliptic problem with e Y-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 0 and the vector field r 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: O~(x) = O(x) + eh'(x/e)O,(x) analogous with the first terms of the two-scale asymptotic expansion known from the homogenization theory. The functions h" are defined as approximations of the solutions to the basic cell problems. In contrast to the two-scale expansion the expression for 0 ~ satisfies the boundary condition.