Optimal design of micro-mechanisms by the homogenization method

Revue Europeenne des Elements

Volumn 11, Issue 2-4, 2002, Pages 405-416

  Allaire, Grégoire ^a   Jouve, François ^a  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Homogenization; Micro mechanisms; Shape optimization

Indexed keywords

HOMOGENIZATION METHOD;

MICROMECHANISMS; MICROTOOLS; OBJECTIVE FUNCTIONS; OPTIMAL DESIGN; OPTIMIZATION METHOD; SHAPE OPTIMIZATION PROBLEM;

SHAPE OPTIMIZATION;

EID: 0842332649     PISSN: 12506559     EISSN: None     Source Type: Journal    
DOI: 10.3166/reef.11.405-416     Document Type: Article

References (19)

1. ALLAIRE G., Shape optimization by the homogenization method, Springer Verlag, New York 2001.
2. ALLAIRE G., AUBRY S., JOUVE F., "Shape optimization with general objective functions using partial relaxation,", Topology optimization of structures and composite continua, G.I.N. Rozvany and N. Olhoff eds., p. 239-249, Kluwer Academic Publishers, 2000.
3. ALLAIRE G., AUBRY S., JOUVE F., "Eigenfrequency optimization in optimal design,", Comput. Methods Appl. Mech. Engrg., Vol. 190, 2000, p. 3565-3579.
4. ALLAIRE G., BONNETIER E., FRANCFORT G., JOUVE F., "Shape optimization by the homogenization method,", Nümerische Mathematik, Vol. 76, 1997, p. 27-68.
5. ALLAIRE G., BELHACHMI Z., JOUVE F., "The homogenization method for topology and shape optimization. Single and multiple loads case,", Revue Européenne des Éléments Finis, Vol. 5, 1996, p. 649-672.
6. ALLAIRE G., KOHN R.V., "Optimal design for minimum weight and compliance in plane stress using extremal microstructures,", Europ. J. Mech. A/Solids, Vol. 12, num. 6, 1993, p. 839-878.
7. BENDSOE M., Methods for optimization of structural topology, shape and material, Springer Verlag, New York, 1995.
8. BENDSOE M., KIKUCHI N., "Generating Optimal Topologies in Structural Design Using a Homogenization Method,", Comp. Meth. Appl. Mech. Eng., Vol. 71, 1988, p. 197-224.
9. CHERKAEV A., KOHN R.V., Editors, "Topics in the mathematical modeling of composite materials,", Progress in Nonlinear Differential Equations and their Applications, Vol. 31, Birkhaüser, Boston, 1997.
10. DIAZ A., BENDSOE M., "Shape optimization of structures for multiple loading conditions using a homogenization method,", Struct. Optim., Vol. 4, 1992, p. 17-22.
11. DIAZ A., KIKUCHI N., "Solutions to shape and topology eigenvalue optimization problems using a homogenization method,", Int. J. Num. Meth. Engng., Vol. 35, 1992, p. 1487-1502.
12. JONSMANN J., SIGMUND O., BOUWSTRA S., "Compliant thermal microactuators,", Sensors and actuators, Vol. 76, 1999, p. 463-469.
13. KOHN R.V., STRANG G., "Optimal Design and Relaxation of Variational Problems I-II-III,", Comm. Pure Appl. Math., Vol. 39, 1986, p. 113-137, 139-182, 353-377.
14. LURIE K., CHERKAEV A., "Effective characteristics of composite materials and the optimal design of structural elements,", Uspekhi Mekhaniki, Vol. 9, 1986, p. 3-81. English translation in [CHE 97].
15. MINOTTI P., BOURBON G., LANGLET P., MASUZAWA T., "Arrayed electrostatic scratch drive actuators: towards visible effects up to the human scale,", J. of Intelligent Material Systems and Structures, Vol. 9, 1998, p. 837-846.
16. MURAT F., TARTAR L., "Calcul des Variations et Homogé néisation,", in D. Bergman et. al. (eds.), Les Méthodes de l'Homogénéisation Théorie et Applications en Physique, Coll. Dir. Etudes et Recherches EDF, Vol. 57, 1985, Eyrolles, Paris, p. 319-369. English translation in [CHE 97].
17. ROZVANY G., BENDSOE M., KIRSCH U., "Layout optimization of structures,", Appl. Mech. Reviews, Vol. 48, 1995, p. 41-118.
18. SIGMUND O., "On the design of compliant mechanisms using topology optimization,", Mech. Struct. Mach., Vol. 25, 1997, p. 493-524.
19. SIGMUND O., "Design of multiphysics actuators using topology optimization, part I: one-material structures,", DCAMM Report 632, Technical University of Denmark, 2000