Review of Methods of Mechanical Digital Design Based on Topology Optimization

Article Preview

Abstract:

The basic mathematical model of topology optimization of continuum structures is introduced at first. Then the authors focus on reviewing the development of PDE methods and optimization algorithms. This paper details the development and applications of Finite Element Method, Boundary Element Method and Finite Volume Method. This paper also illustrates several typical applications and achievements of optimization algorithms, such as Optimality Criteria method, mathematical programming method and intelligent algorithm. Based on our research, this paper finally summarizes the process of the structural topology optimization and describes the directions of the topology optimization in the field of mechanical digital design.

You might also be interested in these eBooks

Info:

Periodical:

Pages:

193-201

Citation:

Online since:

February 2013

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2013 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] T.D. H.A. Eschenauer and N. Olhoff: Appl Mech Rev, Vol. 54 (2001) No. 4, p.331.

Google Scholar

[2] M.A. MP. Bendsøe and 0. Sigmund. Topology Optimization: Theory, Methods and Applieations (Springer-Verlag, Berlin Heidelberg New York 2003).

Google Scholar

[3] T.D. G. Cheng and N. Olhoff: Int. J. Solids Struct, Vol. 17(1981),P. 305.

Google Scholar

[4] T.D. MP. Bendsøe and N. Kikuchi: Computer Methods in Applied Mechanics and Engineering, Vol. 71 (1988), p.197.

Google Scholar

[5] T.D. W. Prager and GIN. Rozvany: International Joumal of Mechanieal Sciences, Vol. 17 (1985) No. 10, p.627.

Google Scholar

[6] T.D. W. Prager and JE. Taylor: Problems of optimal structural desigu.J. Applied Meehs, Vol. 35 (1968), p.102.

Google Scholar

[7] M.A. GIN. Rozvany: Optimal design of flexural systems (Pergamon Press, Oxford 1976).

Google Scholar

[8] M.A. GIN. Rozvany: Struetural design via optimality criteria (Kluwer Academic Publishers Group, Dordrecht. Boston. London, 1989).

Google Scholar

[9] T.D. T. Buhl, CBW. Peterson and O. Sigmund: Struetural and MultidiseiPlinaly Optimization, Vol. 19 (2000), p.93.

Google Scholar

[10] T.D. HC. Gea and J. Luo: Computers and Structures, Vol. 79(2001), p. (1977).

Google Scholar

[11] T.D. CBW. Peterson, T. Buhl and O. Sigmund: International Joumal for Numerieal Methods in Engineering, Vol. 50 (2001), p.2683.

Google Scholar

[12] T.D. O. Siglnund: Computer Methods in Applied Mechanics and Engineering, Vol. 190 (2001), p.6577.

Google Scholar

[13] T.D. O. Sigmund: Computer Methods in Applied Mechanics and Engineering, Vol. 190 (2001), p.6605.

Google Scholar

[14] T.D. K. Yuge and N. Kikuehi: Structural Optimization, Vol. 10 (1995), p.197.

Google Scholar

[15] T.D. D. Jung and HC. Gea: Finite Elements in Analysis and Design, Vol. 40 (2004), p.1417.

Google Scholar

[16] T.D. T. Borrvall and J. Petersson: Comput Methods Appl Meeh Eng, Vol. 190 (2001) No. 46-47, p.6201.

Google Scholar

[17] T.D. S. Wang, E. Sturler and GH. Paulino: Int J Numer Methods Eng, Vol. 69 (2007) No. 12, p.2441.

Google Scholar

[18] T.D. O. Amir, MP. Bendsøe and O. Siglnund: Int J Numer Methods Eng, Vol. 78 (2009) No. 12, p.1474.

Google Scholar

[19] T.D. R. Stainko: Commun Numer Methods Eng, Vol. 22 (2006) No. 2, p.109.

Google Scholar

[20] T.D. Z. Liu and JG Korvink: Engineering Optimization, Vol. 40 (2008) No. 6, p.529.

Google Scholar

[21] T.D. A. Gersborg-Hansen, MP Bendsøe and O. Sigmund: Structural and Multidisciplinary Optimization, Vol. 31 (2006) No. 4, p.251.

Google Scholar

[22] T.D. E. Kita and H. Tanie: Struct Optim, Vol. 17 (1999) No. 23, p.130.

Google Scholar

[23] T.D. Y. Lin and K. Grosh: Proc SPIE, Vol. 3984 (2000), p.387.

Google Scholar

[24] T.D. K. Tai and RT. Fenne: Int. J. Solids Struet, Vol. 36 (1999) No. 14, p. (2021).

Google Scholar

[25] T.D. S. Cho and H. Jung: Comput Methods AppI Meeh Engrg, Vol. 192 (2003), p.2539.

Google Scholar

[26] T.D. S. Cho and J. Kwak : Comput Methods Appl Mech Engrg, Vol. 195 (2006), p.5909.

Google Scholar

[27] T.D. G. Pingen, A. Evgrafov and K. Mante: Structural and MultidisciPlinary Optimization, Vol. 34 (2007) No. 6, p.507.

Google Scholar

[28] M.A. R Kanaglekar: Development and Implementation of Discontinuous Galerkin(DG) Finite Element Methods for Topology Optimization (University of Cincinnati, 2005).

Google Scholar

[29] T.D. AGM. Michell: Philosophical Magazine, Vol. 8 (1904) No. 6, p.589.

Google Scholar

[30] T.D. M. Zhou and GIN. Rozvany: Computer Methods in Applied Mechanics and Engineering, Vol. 89 (1991), p.197.

Google Scholar

[31] T.D. M. Zhou and GIN. Rozvany: PartΙ: Theory Structural Optimization, Vol. 5 (1995), p.12.

Google Scholar

[32] T.D. M. Zhou and GIN. Rozvany: DCOC:, PartII: Algorithm. Structural Optimization, Vol. 6 (1993), p.250.

Google Scholar

[33] T.D. M. Zhou and GIN. Rozvany: Computer Methods in Applied Mechanics and Engineering, Vol. 128 (1995), p.387.

Google Scholar

[34] T.D. Z.D. Ma Z, N. Kikuchi and H.C. Cheng: Computational Methods in Applied Mechanics and Engineering, Vol. 121 (1995), p.259.

Google Scholar

[35] T.D. S. Nishiwaki, M.I. Frecker, S. Min and N. Kikichi: International Journal for Numerical Methods in Engineering, Vol. 42 (1998), p.535.

Google Scholar

[36] T.D. L.A. Schmit and B. Farshi: AIAAJ, Vol 12 (1974), p.692.

Google Scholar

[37] M.A. J.M. Sun: Optimization of Mechanical Design (China Machine Press, 2004). (In Chinese).

Google Scholar

[38] T.D. L.G. Khachiyan: Soviet Math. Dokl, Vol. 20 (1979), p.191.

Google Scholar

[39] T.D. N. Karmarka: Combinatorica, Vol. 4 (1984), P. 373.

Google Scholar

[40] T.D. C. Fleury and V. Braibant: International Journal for Numerical Methods in Engineering, Vol 24 (1986), p.359.

Google Scholar

[41] T.D. K. Svanberg: International Journal for Numerical Methods in Engineering, Vol 24 (1987), p.359.

Google Scholar

[42] G. K. Svanberg: two primal-dual interior-point methods for the MMA subproblems. Technical Report TRITA-MAT-1998-OS12, Dept. of mathematics (KTH, Stockholm, 1998).

Google Scholar

[43] G. K. Svanberg: The MMA for modeling and solving optimization problems. WCSMO-3 (Buffalo, NY, 1999).

Google Scholar

[44] G. W. H Zhang and C. Fleury: Structural shape optimization and convex programming methods. Lecture at Symp. on Optimization of Mechanical Systems (IUTAM) (Stuttgart, Germany).

Google Scholar

[45] G. K. Svanberg: A new globally convergent version of MMA. Technical Report TRITA-MAT-1999-OS2, Dept. of Mathematics (KTH, Stockholm, Sweden, 1999).

Google Scholar

[46] T.D. K. Svanberg: SIAM Journal on Optimization, Vol. 12 (2002), p.555.

Google Scholar

[47] T.D. W.H. Zhang, C. Fleury and Duysinx: Structural Optimization, Vol. 12 (1996), p.143.

Google Scholar

[48] T.D. M. Bruyneel, P. Duysinx and C. Fleury: Structural and Multidiscipline Optimization, Vol. 24 (2002), p.263.

Google Scholar

[49] T.D. C. Fleury and M. Geradin: Computers & Structures, Vol. 8 (1978) No. 1, p.7.

Google Scholar

[50] M.A. C. Fleury and L. A Schmit: Dual methods and approximation concepts in structural synthesis(National Aeronautics and Space Administration, United States 1980).

Google Scholar

[51] T.D. Manohar P. Kamat: Structural Optimization-status and Promise, (Progress in Astronautics and aeronautics, American 1993).

Google Scholar

[52] T.D. M. Beckers: Structural Optimization, Vol. 17 (1999), p.14.

Google Scholar

[53] T.D. W.H. Zhang and P. Duysinx: Computers and Structures, Vol. 81 (2003), p.2173.

Google Scholar

[54] M.A. J.H. Holland: Adaptive in natural and artificial systems (University of Michigan Press, Ann Arbor, MI 1975).

Google Scholar

[55] T.D. C.D. Chapman, K. Saitou and M.J. Jakiela: Journal of Mechanical Design, Vol. 116 (1994), p.1005.

Google Scholar

[56] T.D. Yasuhiko Nakanishi: Computer Methods in Applied Mechanics and Engineering, Vol. 19 (2001)No. 9, p.3849.

Google Scholar

[57] T.D. S. Kirpatrick, C.D. Gelatl and MP. Vecchi: J. Science, Vol. 220 (1983), p.671.

Google Scholar

[58] T.D. A.R. Yildiz, N. Őztürk, N. Kaya and F. Őztürk: Structural and Multidiscipline Optimization, Vol. 25 (2003), p.251.

Google Scholar

[59] T.D. T.Y. Chen and C.C. Shieh: Computers and Structures, Vol. 78 (2000), p.459.

Google Scholar

[60] T.D. J.L. Deng: The Journal of Grey System, Vol. 1 (1989), p.1.

Google Scholar

[61] T.D. B.Y. Chen, J.C. Yao and Y.F. zhong: Journal of Mechanical Engineering, Vol. 39 (2003) No. 1, pp.101-106. (In Chinese).

Google Scholar