Optimization of conducting structures by using the homogenization method

Structural and Multidisciplinary Optimization

Volumn 24, Issue 2, 2002, Pages 125-140

  Haslinger, J ^a   Hillebrand, A ^b   Karkkainen T ^b   Miettinen, M ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Approximation of the G closure; Homogenization; Optimal material layout

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; NUMERICAL ANALYSIS;

CONDUCTING STRUCTURES; HOMOGENIZATION; LINEAR ELLIPTIC STATE EQUATION;

STRUCTURAL OPTIMIZATION;

EID: 0036747725     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-002-0223-1     Document Type: Article

References (17)

1. Allaire, G.: Aubry, S. 1999: On optimal microstructures for a plane shape optimization problem. Struct. Optim. 17, 86-94
2. Bendsøe, M.P. 1995: Optimization of structural topology, Shape, and Material. Berlin, Heidelberg, New York: Springer
3. Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. 1994: Optimization methods for truss geometry and topology design. Struct. Optim. 7, 141-159
4. Bendsøe, M.P.: Kikuchi, N. 1998: Generating optimal topologies in structural design using a homogenization method. Comp. Meth. Appl. Mech. Engrg. 71, 197-224
5. Burns, T.; Cherkaev, A. 1997: Optimal distribution of multimaterial composites for torsional beams. Struct. Optim. 13, 4-11
6. Dvorák, J.: Haslinger, J.; Miettinen, M. 1999: Homogenization & optimal shape design-based approach in optimal material distribution problems. Part I: The scalar case. Adv. Math. Sci. Appl. 29, 665-694
7. Hillebrand, A. 2002: Optimization of conducting structures using the homogenization method. Ph.Lic. Dissertation in Computer Science, University of Jyväskylä. Department of Mathematical Information Technology, Draft.
8. Kohn, R.V.; Strang, G. 1986: Optimal design and relaxation of variational problems. Comm. Pure Appl. Math. 39, 1-25 (Part I), 139-182 (Part II) and 353-357 (Part III)
9. Lurie, K. A. 1993. Applied optimal control theory of distributed systems. New York: Plenum Press
10. Lurie, K.A.; Cherkaev, A.V. 1984: Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proc. Roy. Soc. Edinburgh 99A, 71-87
11. Maar, B.; Schulz, V. 2000: Interior point multigrid methods for topology optimization. Struct. Multidisc. Optim. 19, 214-224
12. Murat, F.; Tartar, L. 1985: Calcul des variations et homogénéisation. Les Méthodes de l'Homogénéisation, Théorie et Applications en Physique, pp. 319-369. Eyrolles
13. Rozvany, G.I.N.; Zhou, M.: Birker, T. 1993: Why multi-load topology designs based on orthogonal microstructures are in general non-optimal. Struct. Optim. 6, 200-204
14. Schittkowski, K.; Zillober, C.; Zotemantel, R. 1994: Numerical comparison of nonlinear programming algorithms for structural optimization. Struct. Optim. 7, 1-19
15. Sigmund, O.; Petersson, J. 1998: Numerical instabilities in topology optimization. A survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Optim. 16, 68-75
16. Spagnolo, S. 1967: Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore. Ann. Scuóla Norm. Sup. Pisa 21, 637-699
17. Zhikov, V.V.; Kozlov, S.M.; Oleǐnik, O.A. 1994: Homogenization of differential operators and integral functionals. Berlin, Heidelberg, New York: Springer (translated from the Russian by Yosifian, G.A.)