Checkerboard patterns in layout optimization

A. Díaz; O. Sigmund

doi:10.1007/bf01743693

journal article Aug 01, 1995

Checkerboard patterns in layout optimization

A. Díaz O. Sigmund

Structural Optimization Vol. 10 No. 1 pp. 40-45 · Springer Science and Business Media LLC

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References

17

[1]

Avellaneda, M. 1987: Optimal bounds and microgeometries for elastic two-phase composites.SIAM J. Appl. Math. 47, 1216–1228 10.1137/0147082

[2]

Optimal shape design as a material distribution problem

M. P. Bendsøe

Structural Optimization 1989 10.1007/bf01650949

[3]

Bendsøe, M.P. 1994:Methods for the optimization of structural topology, shape and material. Berlin, Heidelberg, New York: Springer (to appear)

[4]

Bendsøe, M.P.; Díaz, A.; Kikuchi, N. 1992: Topology and generalized layout optimization of elastic structures. In: Bendsøe, M.P. and Mota Soares, C.A. (eds.),Topology design of structures, pp. 159–205. Dordrecht: Kluwer

[5]

Generating optimal topologies in structural design using a homogenization method

Martin Philip Bendsøe, Noboru Kikuchi

Computer Methods in Applied Mechanics and Engineer... 1988 10.1016/0045-7825(88)90086-2

[6]

Bensoussan, A.; Lions, J.-L.; Papanicolaou, G. 1978:Asymptotic analysis for periodic structures. Amsterdam: North-Holland

[7]

Berlyand, L.V.; Kozlov, S.M. 1992: Asymptotics of homogenized moduli for the elastic chess-board composite.Arch. Rational Mech. Anal. 118, 95–112 10.1007/bf00375091

[8]

Brezzi, F.; Fortin, M. 1991:Mixed and hybrid finite element methods. Berlin, Heidelberg, New York: Springer 10.1007/978-1-4612-3172-1

[9]

Guedes, J.; Kikuchi, N. 1992: Pre- and postprocessing for materials based on the homogenization method with adaptive finite elements.Comp. Meth. Appl. Mech. & Engng. 83, 143–198 10.1016/0045-7825(90)90148-f

[10]

Jog, C.S.; Haber, R.B. 1994: Stability of finite element models for distributed-parameter optimization and topology design.TAM Report No. 758. Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign

[11]

Jog, C.S.; Haber, R.B.; Bendsøe, M.P. 1992: Topology design using a material with self-optimizing microstructure. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology design of structures, pp. 219–238. Dordrecht: Kluwer

[12]

Lipton, R. 1994: On the relaxation for optimal structural compliance.JOTA 81, 549–568 10.1007/bf02193100

[13]

An engineer's approach to optimal material distribution and shape finding

H.P. Mlejnek, R. Schirrmacher

Computer Methods in Applied Mechanics and Engineer... 1993 10.1016/0045-7825(93)90182-w

[14]

Milton, G. 1990: On characterizing the set of possible effective tensors of composites: the variational method and the translation method.Comm. Pure Appl. Math. 43, 63–125 10.1002/cpa.3160430104

[15]

Milton, G.; Kohn, R.V. 1988: Variational bounds on the effective moduli of anisotropic composites.J. Mech. Phys. Solids 36, 597–629 10.1016/0022-5096(88)90001-4

[16]

Pedersen, P. 1989: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106 10.1007/bf01637666

[17]

Sigmund, O. 1994: Materials with prescribed constitutive parameters: an inverse homogenization problem.Int. J. Solids Struct. 31, 2313–2329 10.1016/0020-7683(94)90154-6

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