On some sharp bounds for the off-diagonal elements of the homogenized tensor

Dag Lukkassen

Applications of Mathematics (1995)

  • Volume: 40, Issue: 5, page 401-406
  • ISSN: 0862-7940

Abstract

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In this paper we study bounds for the off-diagonal elements of the homogenized tensor for the stationary heat conduction problem. We also state that these bounds are sharp by proving a formula for the homogenized tensor in the case of laminate structures.

How to cite

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Lukkassen, Dag. "On some sharp bounds for the off-diagonal elements of the homogenized tensor." Applications of Mathematics 40.5 (1995): 401-406. <http://eudml.org/doc/32928>.

@article{Lukkassen1995,
abstract = {In this paper we study bounds for the off-diagonal elements of the homogenized tensor for the stationary heat conduction problem. We also state that these bounds are sharp by proving a formula for the homogenized tensor in the case of laminate structures.},
author = {Lukkassen, Dag},
journal = {Applications of Mathematics},
keywords = {stationary heat conduction problem; $Y$-periodicity; homogenized coefficients; bounds; laminate structures; stationary heat equation; laminate structure},
language = {eng},
number = {5},
pages = {401-406},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some sharp bounds for the off-diagonal elements of the homogenized tensor},
url = {http://eudml.org/doc/32928},
volume = {40},
year = {1995},
}

TY - JOUR
AU - Lukkassen, Dag
TI - On some sharp bounds for the off-diagonal elements of the homogenized tensor
JO - Applications of Mathematics
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 40
IS - 5
SP - 401
EP - 406
AB - In this paper we study bounds for the off-diagonal elements of the homogenized tensor for the stationary heat conduction problem. We also state that these bounds are sharp by proving a formula for the homogenized tensor in the case of laminate structures.
LA - eng
KW - stationary heat conduction problem; $Y$-periodicity; homogenized coefficients; bounds; laminate structures; stationary heat equation; laminate structure
UR - http://eudml.org/doc/32928
ER -

References

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  1. Asymptotic analysis for periodic structures, North-Holland, Amsterdam, 1978. (1978) MR0503330
  2. Bounds on effective moduli of composite materials, Lecture notes, School on Homogenization, ICTP, Trieste, 1993. (1993) 
  3. 10.1063/1.1728579, J. Appl. Phys. 33 (1962), 3125–3131. (1962) DOI10.1063/1.1728579
  4. Numerical solution of partial differential equations by the finite element method, Studentlitteratur, Lund, 1987. (1987) Zbl0628.65098MR0911477
  5. Upper and lower bounds for homogenized coefficients, Uspekhi Mat. Nauk 49 (1994), no. 4, 115. (1994) 
  6. On some sharp bounds for the effective conductivity, Proceedings from the first International Conference on Composites Engineering (ICCE/1), New Orleans, 1994, pp. 855–856. (1994) 
  7. On characterizing the set of possible effective tensors of composites: The Variational Method and the Translation Method, Comm. on Pure and Appl. Math. XLIII (1990), 63–125. (1990) Zbl0751.73041MR1024190
  8. The homogenization method: An introduction, Studentlitteratur, Lund, 1993. (1993) MR1250833

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