Optimal material layout for 3D elastic structures

Structural Optimization

Volumn 13, Issue 1, 1997, Pages 60-64

  Diaz A ^a   Lipton, R ^b  

^a Michigan State University   (United States)

^b Worcester Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; ELASTICITY; MATHEMATICAL MODELS; OPTIMIZATION; PROBLEM SOLVING; STRUCTURAL DESIGN; THREE DIMENSIONAL;

OPTIMAL ORTHOTROPY;

LAMINATED COMPOSITES;

EID: 0031077415     PISSN: 09344373     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf01198376     Document Type: Article

References (23)

1. Allaire, G.; Bonnetier, E.; Francfort, G.; Jouve, F. 1995: Shape optimization by the homogenization method. Preprint
2. Allaire, G.; Kohn, R.V. 1993: Optimal design for minimum weight and compliance in plane stress using extremal microstructure. Europ. J. Mech. 12, 839-878
3. Avellaneda, M. 1987: Optimal bounds and microgeometries for elastic composites. SIAM J. Appl. Math. 47, 1218
4. Bendsøe, M.; Díaz, A.; Kikuchi, N. 1993: Topology and generalized layout optimization of elastic structures. In: Mota Soares C.A.; Bendsøe, M.P. (eds.) Topology design of structures, pp. 159-205. Dordrecht: Kluwer
5. Cherkaev, A.; Palais, R. 1995: Optimal design of three-dimensional axisymmetric structures. In: Olhoff, N.; Rozvany, G.I.N. (eds.) First World Congress of Structural and Multidiciplinary Optimization, pp. 201-206. Oxford: Pergamon
6. Díaz, A.; Lipton, R.; Soto, C. 1995: A new formulation of the problem of optimum reinforcement of Reissner-Mindlin plates. Comp. Meth. Appl. Mech. Eng. 123, 121-139
7. Francfort, G.; Murat, F. 1986: Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94, 307-334
8. 2 and applications. Arch. Rat. Mech. Anal 131, 305
9. Gibianski, L.; Cherkaev, A. 1984: Design of composite plates of extremal rigidity. Ioffe Physicotechnical Institute (preprint). English translation to appear in: Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
10. Gibianski, L.; Cherkaev, A. 1984: Design of composite plates of extremal rigidity. Ioffe Physicotechnical Institute (preprint). English translation to appear in: Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
11. Kohn, R.V.; Lipton, R. 1988: Optimal bounds for the effective energy of a mixture of isotropic, incompressible elastic materials. Arch. Rat. Mech. Anal. 102, 331-350
12. Lipton, R. 1986: An optimal lower bound on the energy dissipation rate for homogenized Stokes flow. Ph.D. Thesis, New York University
13. Lipton, R. 1994a: Optimal bounds on effective elastic tensors for orthotropic composites. Proc. Royal. Soc. Lond. A 443, 399-410
14. Lipton, R. 1994b: Composites with symmetry and their extremal properties. Int. J. Solids Struct. 31, 3407-3417
15. Lipton, R. 1994c: A saddle-point theorem with application to structural optimization. J. Optimiz. Theory Appl. 81, 549-567
16. Lurie, K.A.; Cherkaev, A.V. 1984: Exact estimates of conductivity of composites formed of two isotropically conducting media taken in prescribed proportion. Proc. Roy. Soc. Edin. 99A, 71
17. Lurie, K.A.; Cherkaev, A.V. 1986: Effective characteristics of composite materials and the optimal design of structural elements. Uspekhi Mekaniki, Advances in Mechanics 9. English translation to appear in Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
18. Lurie, K.A.; Cherkaev, A.V. 1986: Effective characteristics of composite materials and the optimal design of structural elements. Uspekhi Mekaniki, Advances in Mechanics 9. English translation to appear in Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
19. Milton, G.W.; Kohn, R.V. 1988: Variational bounds on the effective moduli of anisotropic composites. J. Mech. Phys. Solids 36, 597-629
20. Murat, F.; Tartar, L. 1985: Calcul des variations et homogenei-sation. In: Les methodes de l'homogeneisation: theorie et applications en physique, Coll de la Dir des Etudes et Recherches de Electricite de France, Eyrolles, Paris, pp 319-369. English translation to appear in Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
21. Murat, F.; Tartar, L. 1985: Calcul des variations et homogenei-sation. In: Les methodes de l'homogeneisation: theorie et applications en physique, Coll de la Dir des Etudes et Recherches de Electricite de France, Eyrolles, Paris, pp 319-369. English translation to appear in Kohn, R.V. (ed.) Topics in the mathematical modeling of composite materials. Boston: Birkhauser
22. Suzuki, K.; Kikuchi, N. 1991: Generalized layout optimization of shape and topology in three-dimensional shell structures. In: Komkov, V. (ed.) Geometric aspects of industrial design. Philadelphia: SIAM
23. Tartar, L. 1985: Estimations fines de cofficients homogeneises. In: Kree, P. (ed.) Ennio De Georgi colloquium, Research Notes in Mathematics, 125, pp. 168-187. Boston: Pitman