journal article Dec 01, 1989

Optimal shape design as a material distribution problem

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References
23
[1]
Avellaneda, M. 1987: Optimal bounds and microgeometries for elastic two-phase composites.SIAM J. Appl. Math. 47, 1216–1228 10.1137/0147082
[2]
Bendsøe, M.P. 1983: On obtaining a solution to optimization problems for solid, elastic plates by restriction of the design space.J. Struct. Mech. 11, 501–521 10.1080/03601218308907455
[3]
Bendsøe, M.P. 1986: Generalized plate models and optimal design. In: Eriksen, J.L.; Kinderlehrer, D.; Kohn, R.; Lions, J.-L., (eds.)Homogenization and effective moduli of materials and media, the IMA volumes in mathematics and its applications, pp. 1–26. Berlin, Heidelberg, New York: Springer
[4]
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
[5]
Bendsøe, M.P.; Rodrigues, H.C. 1989: Integrated topology and boundary shape optimization of 2-D solids.MAT-Report No.1989–14, Math. Inst., Techn. Univ. of Denmark, DK-2800 Lyngby
[6]
Bensousson, A.; Lions, J.-L.; Papanicolaou, G. 1978:Asymptotic analysis for periodic structures. Amsterdam: North-Holland
[7]
Bourgat, J.F. 1977: Numerical experiments of the homogenization method for operators with periodic coefficients.Lecture Notes in Mathematics 704, pp. 330–356, Berlin, Heidelberg, New York: Springer
[8]
Cheng, K.T.; Olhoff, N. 1982: Regularized formulation for optimal design of axisymmetric plates.Int. J. Solids Struct. 18, 153–170 10.1016/0020-7683(82)90023-3
[9]
Ding, Y. 1986: Shape optimization of structures: a literature survey.Comp. Struct. 24, 985–1004 10.1016/0045-7949(86)90307-x
[10]
Goodman, J.; Kohn, R.V.; Reyna, L. 1986: Numerical study of a relaxed variational problem from optimal design.Comp. Meth. Appl. Mech. Engrg. 57, 107–127 10.1016/0045-7825(86)90073-3
[11]
Haftka, R.T.; Gandhi, R.V. 1986: Structural shape optimization- a survey.Comp. Meth. Appl. Mech. Engrg. 57, 91–106 10.1016/0045-7825(86)90072-1
[12]
Kohn, R.V.; Strang, G. 1986a: Optimal design and relaxation of variational problems.Comm. Pure Appl. Math. 39, 1–25 (Part I), 139–182 (Part II), and 353–377 (Part III) 10.1002/cpa.3160390102
[13]
Kohn, R.V.; Strang, G. 1986b: Optimal design in elasticity and plasticity.Int. J. Numer. Meth. Eng. 22, 183–188 10.1002/nme.1620220113
[14]
Lurie, K.A.; Fedorov, A.V.; Cherkaev, A.V. 1982: Regularization of optimal design problems for bars and plates. Parts I and II.J. Optim. Theory Appl. 37, 499–521, 523–543 10.1007/bf00934953
[15]
Olhoff, N.; Lurie, K.A.; Cherkaev, A.V.; Fedorov, A.V. 1981: Sliding regimes and anisotropy in optimal design of vibrating axisymmetric plates.Int. J. Solids Struct. 17, 931–948 10.1016/0020-7683(81)90032-9
[16]
Olhoff, N.; Taylor, J.E. 1983: On structural optimization.J. Appl. Mech. 50, 1134–1151 10.1115/1.3167196
[17]
Pedersen, P. 1989a: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106 10.1007/bf01637666
[18]
Pedersen, P. 1989b: Bounds on elastic energy in solids of orthotropic materials.DCAMM Report No.392, Techn. Univ. of Denamrk, DK-2800 Lyngby
[19]
Rossow, M.P.; Taylor, J.E. 1973: A finite element method for the optimal design of variable thickness sheets.AIAA J. 11, 1566–1569 10.2514/3.50631
[20]
Rozvany, G.I.N. 1984: Structural layout theory - the present state of knowledge. In: Atrek, E.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (eds.)Directions in optimum structural design, Chapter 7. Chichester: Wiley & Sons
[21]
Rozvany, G.I.N.; Ong, T.G.; Szeto, W.T.; Olhoff, N.; Bendsøe, M.P. 1987: Least-weight design of perforated plates.Int. J. Solids and Struct. 23, 521–536 (Part I), 537–550 (Part II) 10.1016/0020-7683(87)90015-1
[22]
Rozvany, G.I.N. 1989: Optimality criteria for continuous and segment-wise linear distribution of the cross-sectional parameters. In: Eschenauer, H.A.; Thierauf, G. (eds.)Discretization methods and structural optimization - procedures and applications, pp. 291–298. Berlin, Heidelberg, New York: Springer 10.1007/978-3-642-83707-4_37
[23]
Sanchez-Palencia, E. 1980: Non-homogeneous media and vibration theory.Lecture Notes in Physics 127, Berlin, Heidelberg, New York: Springer
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Published
Dec 01, 1989
Vol/Issue
1(4)
Pages
193-202
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Cite This Article
M. P. Bendsøe (1989). Optimal shape design as a material distribution problem. Structural Optimization, 1(4), 193-202. https://doi.org/10.1007/bf01650949