Skip to main content
SpringerLink
Log in

Note on topology optimization of continuum structures including self-weight

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

This paper proposes to investigate topology optimization with density-dependent body forces and especially self-weight loading. Surprisingly the solution of such problems cannot be based on a direct extension of the solution procedure used for minimum-compliance topology optimization with fixed external loads. At first the particular difficulties arising in the considered topology problems are pointed out: non-monotonous behaviour of the compliance, possible unconstrained character of the optimum and the parasitic effect for low densities when using the power model (SIMP). To get rid of the last problem requires the modification of the power law model for low densities. The other problems require that the solution procedure and the selection of appropriate structural approximations be revisited. Numerical applications compare the efficiency of different approximation schemes of the MMA family. It is shown that important improvements are achieved when the solution is carried out using the gradient-based method of moving asymptotes (GBMMA) approximations. Criteria for selecting the approximations are suggested. In addition, the applications also provide the opportunity to illustrate the strong influence of the ratio between the applied loads and the structural weight on the optimal structural topology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. BENSIG:2003 Bendsøe M, Sigmund O (2003) Topology optimization: theory, methods, and applications. Springer, Berlin Heidelberg New York

  2. BEN:1989 Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193–202

  3. BENKIK:1988 Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224

  4. BRUDUY:2001 Bruyneel M, Duysinx P (2001) Topology optimization with self-weight loading: unexpected problems and solutions. In: Bendsøe M, Olhoff N, Rasmussen J (eds.) Second Max Planck Workshop on Engineering Design Optimization, Nyborg, Denmark, pp124–127

  5. BRUETA:2002 Bruyneel M, Duysinx P, Fleury C (2002) A family of MMA approximations for structural optimization. Struct Multidisc Optim 24:263–276

  6. DUY:1997 Duysinx P (1997) Layout optimization: a mathematical programming approach. Danish Center for Applied Mathematics and Mechanics, DCAMM Report No. 540

  7. DUYBEN:1998 Duysinx P, Bendsøe M (1998) Control of local stresses in topology optimization of continuum structures. Int J Numer Methods Eng 43:1453–1478

  8. DUYETA:1995 Duysinx P, Zhang W, Fleury C, Nguyen V, Haubruge S (1995) A new separable approximation scheme for topological problems and optimization problems characterized by a large number of design variables. In: Rozvany G, Olhoff N (eds.) First World Congress of Structural and Multidisciplinary Optimization. Pergamon, New York, pp1–8

  9. ESCOLH:2001 Eschenauer H, Olhoff N (2001) Topology optimization of continuum structures: a review. ASME Appl Mech Rev 54(4):331–390

  10. FLE:1993a Fleury C (1993) Mathematical programming methods for constrained optimization: dual methods, Vol. 150 of Progress in astronautics and aeronautics, AIAA, Chap. 7, pp123–150

  11. FLEBRA:1986 Fleury C, Braibant V (1986) Structural optimization: A new dual method using mixed variables. Int J Numer Methods Eng 23:409–428

  12. IMA:1998 Imam M (1998) Shape optimization of umbrella-shaped concrete shells subjected to self-weight as the dominant load. Comput Struct 69:513–524

  13. KARKAN:1987 Karihaloo BL, Kanagasundaram S (1987) Optimum design of statically indeterminate beams under multiple loads. Comput Struct 26(3):521–538

  14. KWAETA:1997 Kwak D-Y, Jeong J-H, Cheon J-S, Im Y-T (1997) Optimal design of composite hood with reinforcing ribs through stiffness analysis. Composite Struct 38(1–4):351–359

  15. PARETA:2003 Park K, Chang S, Youn S (2003) Topology optimization of the primary mirror of a multi-spectral camera. Struct Multidisc Optim 25(1):46–53

  16. PEDN:2000 Pedersen N (2000) Maximization of eigenvalues using topology optimization. Struct Multidisc Optim 20:2–11

  17. PEDN:2001 Pedersen N (2001) On topology optimization of plates with prestres. Int J Numer Methods Eng 51:225–239

  18. ROZ:1977 Rozvany G (1977) Optimal plastic design: allowance for selfweight. J Eng Mech Div ASCE 103:1165–1170

  19. ROZ:1989 Rozvany G (1989) Structural design via optimality criteria. Kluwer, Dordrecht

  20. ROZETA:1980 Rozvany G, Nakanamura H, Kuhnell B (1980) Optimal archgrids: allowance for selfweight. Comput Methods Appl Mech Eng 24:287–304

  21. ROZETA:1988 Rozvany G, Yep K, Ong T, Karihaloo B (1988) Optimal design of elastic beams under multiple design constraints. Int J Solids Struct 24(4):331–349

  22. SIG:1997 Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–526

  23. SIG:2001 Sigmund O (2001) Design of multiphysics actuators using topology optimization – Part I: One-material structures – Part II: Two-material structures. Comput Methods Appl Mech Eng 190(49–50):6577–6627

  24. STOSVA:2001 Stolpe M, Svanberg K (2001) An alternative interpolation model for minimum compliance topology optimization. Struct Multidisc Optim 22:116–124

  25. SVA:1987 Svanberg K (1987) The method of moving asymptotes – a new method for structural optimization. Int J Numer Methods Eng 24:359–373

  26. SVA:1995 Svanberg K (1995) A globally convergent version of MMA without linesearch. In: Rozvany G and Olhoff N (eds.), First World Congress of Structural and Multidisciplinary Optimization. Pergamon, New York, pp9–16

  27. TURWAS:1999 Turteltaub S, Washabaugh P (1999) Optimal distribution of material properties for an elastic continuum with structure-dependent body force. Int J Solids Struct 36:4587–4608

  28. WANROZ:1983 Wang C, Rozvany G (1983) On plane Prager – structure – non-parallel external loads and allowance for selfweight. Int J Mech Sci 25:529–541

  29. ZHOROZ:1991 Zhou M, Rozvany G (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336

Download references

Author information

Authors and Affiliations

  1. SAMTECH S.A., Belgium

    M. Bruyneel

  2. Ground Vehicle Engineering Laboratory, University of Liège, Chemin des Chevreuils, 1, Building B52, B-4000, Liège, Belgium

    P. Duysinx

Authors
  1. M. Bruyneel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Duysinx
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Duysinx.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruyneel, M., Duysinx, P. Note on topology optimization of continuum structures including self-weight. Struct Multidisc Optim 29, 245–256 (2005). https://doi.org/10.1007/s00158-004-0484-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-004-0484-y

Keywords

Search

Navigation