| Title:
|
On some sharp bounds for the off-diagonal elements of the homogenized tensor (English) |
| Author:
|
Lukkassen, Dag |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
40 |
| Issue:
|
5 |
| Year:
|
1995 |
| Pages:
|
401-406 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
stationary heat conduction problem |
| Keyword:
|
$Y$-periodicity |
| Keyword:
|
homogenized coefficients |
| Keyword:
|
bounds |
| Keyword:
|
laminate structures. |
| MSC:
|
35B27 |
| MSC:
|
35Q99 |
| MSC:
|
73B27 |
| MSC:
|
73K20 |
| MSC:
|
74E05 |
| MSC:
|
74E30 |
| idZBL:
|
Zbl 0847.35011 |
| idMR:
|
MR1342369 |
| DOI:
|
10.21136/AM.1995.134303 |
| . |
| Date available:
|
2009-09-22T17:49:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134303 |
| . |
| Reference:
|
[1] A. Bensoussan, J. L. Lions, G. Papanicolaou: Asymptotic analysis for periodic structures.North-Holland, Amsterdam, 1978. MR 0503330 |
| Reference:
|
[2] L. V. Gibiansky: Bounds on effective moduli of composite materials.Lecture notes, School on Homogenization, ICTP, Trieste, 1993. |
| Reference:
|
[3] Z. Hashin, S. Shtrikman: A variational approach to the theory of effective magnetic permeability of multi phase materials..J. Appl. Phys. 33 (1962), 3125–3131. 10.1063/1.1728579 |
| Reference:
|
[4] C. Johnson: Numerical solution of partial differential equations by the finite element method.Studentlitteratur, Lund, 1987. Zbl 0628.65098, MR 0911477 |
| Reference:
|
[5] D. Lukkassen: Upper and lower bounds for homogenized coefficients.Uspekhi Mat. Nauk 49 (1994), no. 4, 115. |
| Reference:
|
[6] D. Lukkassen, L. E. Persson, P. Wall: 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. |
| Reference:
|
[7] G. W. Milton: 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. Zbl 0751.73041, MR 1024190 |
| Reference:
|
[8] L. E. Persson, L. Persson, N. Svanstedt, J. Wyller: The homogenization method: An introduction.Studentlitteratur, Lund, 1993. MR 1250833 |
| . |
