CAD-Integrated Structural Topology and Design Optimization

  • N. Olhoff
  • M. P. Bendsøe
  • J. Rasmussen
Part of the International Centre for Mechanical Sciences book series (CISM, volume 325)


Structural optimization [1,2] can be essentially conceived as a rational search for the optimal spatial distribution of material within a prescribed admissible structural domain, assuming the loading and boundary conditions to be given. In the general case, this problem consists in determining both the optimal topology and the optimal design of the structure. Here the label “optimal design” covers the optimal shape or sizing of the design.


Design Variable Topology Optimization Structural Optimization Shape Optimization Master Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    L.A. Schmit, Structural Synthesis — Its Genesis and Development (AIAA Journal 2(1, pp. 992–1000, 1982 )Google Scholar
  2. [2]
    N. Olhoff and J.E. Taylor, On Structural Optimization (J. Appl. Mech. 50 pp. 1134–1151, 1983 )Google Scholar
  3. [3]
    H.A. Eschenauer, P.U. Post and M. Bremicker, Einsatz der Optimierungsprozedur SAPOP zur Auslegung von Bauteilkomponenten (Bauingenieur 2$, pp. 2–12, 1988 )Google Scholar
  4. [4]
    P. Bartholomew and A.J. Morris, STARS: A Software Package for Structural Optimization (in: Proc. Int. Symp. Optimum Structural Design, Univ. of Arizona, USA, 1981 )Google Scholar
  5. [5]
    J. Sobieszanski—Sobieski and J.L. Rogers, A Programming System for Research and Applications in Structural Optimization (in: E. Atrek et. al.: New Directions in Optimum Structural Design, pp.563–585, Wiley, Chichester, 1984 )Google Scholar
  6. [6]
    C. Fleury and V. Braibant, Application of Structural Synthesis Techniques (in: C.A. Mota Soares: Preprints NATO/NASA/NSF/USAF Conf. Computer Aided Optimal Design, Troia, Portugal, 1986, Vol.2, pp.29–53, Techn. Univ. Lisbon, 1986 )Google Scholar
  7. [7]
    B. Esping and D. Holm, Structural Shape Optimization Using OASIS (in: G.I.N. Rozvany and B.L. Karihaloo: Structural Optimization, Proc. IUTAM Symp., Melbourne, Australia, 1988, pp.93–101, Kluwer, Dordrecht, 1988 )Google Scholar
  8. [8]
    R.T. Haftka and B. Prasad, Programs for Analysis and Resizing of Complex Structures (Computers and Structures 1D, pp. 323–330, 1979 )Google Scholar
  9. [9]
    G. Kneppe, W, Hartzheim and G. Zimmermann, Development and Application of an Optimization Procedure for Space and Aircraft Structures (in: H.A. Eschenauer and G. Thierauf: Discretization methods and structural Optimization- Procedures and Applications, Proc. of a GAMM-Seminar, Siegen, FRG, 1988, pp.194–201, Springer-Verlag, Berlin, 1989 )Google Scholar
  10. [10]
    L.X. Qian, Structural Optimization Research in China (in: Proc. Int. Conf. Finite Element Methods, Shanghai, China, pp. 16–24, 1982 )Google Scholar
  11. [11]
    G. Lecina and C. Petiau, Advances in Optimal Design with Composite Materials (in: loc.cit.[6], Vol. 3, pp. 279–2891Google Scholar
  12. [12]
    J.S. Arora, Interactive Design Optimization of Structural Systems (in: loc. cit. [9], pp.10–16)Google Scholar
  13. [13]
    J. Rasmussen, The Structural Optimization System CAOS (Structural Optimization, 2, pp. 109–115, 1990 )CrossRefGoogle Scholar
  14. [14]
    J. Rasmussen, Collection of Examples, CAOS Optimization System, 2nd Edition (Special Report No. lc, Institute of Mechanical Engineering, Aalborg University, Denmark, 1990 )Google Scholar
  15. [15]
    S. Kibsgaard, N. Olhoff and J. Rasmussen, Concept of an Optimization System (in: C.A. Brebbia and S. Hernandez: Computer Aided Optimum Design of Structures: Applications, pp.79–88, Springer-Verlag, Berlin, 1989 )Google Scholar
  16. [16]
    U. Ringertz, A. Branch and Bound Algoritm for Topology Optimization of Truss Structures (Engineering Optimization, 1Q, pp. 111–124, 1986 )Google Scholar
  17. [17]
    M.P. Bendst a and N. Kikuchi, Generating Optimal Topologies in Structural Design Using a Homogenization Method (Comp. Meths. Appl. Mechs. Engrg. 71, pp. 197–224, 1988 )CrossRefGoogle Scholar
  18. [18]
    M.P. Bendst e, Optimal Shape Design as a Material Distribution Problem (Structural Optimization, 1, pp. 193–202, 1989 )Google Scholar
  19. [19]
    M.P. Bendsoe and H.C. Rodrigues, Integrated Topology and Boundary Shape Optimization of 2-D Solids, (Rept. No. 14, 31 pp. Mathematical Institute, Technical Univ. Denmark, 1989 )Google Scholar
  20. [20]
    K. Suzuki and N. Kikuchi, A Homogenization Method for Shape and Topology Optimization (Comp. Meths. Appl. Mechs. Engrg., submitted, 1989 )Google Scholar
  21. [21]
    K. Suzuki and N. Kikuchi, Generalized Layout Optimization of Shape and Topology in Three-Dimensional Shell Structures (Rept. No. 90–05, Dept. Mech. Engrg. and Appl. Mech., Comp. Mech. Lab., University of Michigan, USA, 1990 )Google Scholar
  22. [22]
    N. Kikuchi and K. Suzuki, Mathematical Theory of a Relaxed Design Problem in Structural Optimization (Paper for 3rd Air Force/NASA Symp. Recent Advances in Multidisciplinary Analysis and Optimization, San Francisco, USA, Sept. 1990 )Google Scholar
  23. [23]
    P.Y. Papalambros and M. Chirehdast, An Integrated Environment for Structural Configuration Design (J. Engrg. Design, 1, pp. 73–96, 1990 )CrossRefGoogle Scholar
  24. [24]
    M. Bremicker, M. Chirehdast, N. Kikuchi and P.Y. Papalambros, Integrated Topology and Shape Optimization in Structural Design (Techn. Rept. UMMEAM—DL-90–01, Design Laboratory, College of Engrg., Univ. of Michigan, USA, 1990 )Google Scholar
  25. [25]
    M. Bremicker, Ein Konzept zur Integrierten Topologie — und Gestaltoptimierung von Bauteilen (in: H.H. Müller—Slany: Beiträge zur Maschinentechnik, pp.13–39, Festschrift für Prof. H. Eschenauer, Research Laboratory for Applied Structural Optimization, University of Siegen, FRG, 1990 )Google Scholar
  26. [26]
    J.M. Guedes and N. Kikuchi, Pre and Postprocessings for Materials based on the Homogenization Method with Adaptive Finite Element Methods (Rept., Dept. Mech. Engrg. and Appl. Mech., University of Michigan, USA, 1989 )Google Scholar
  27. [27]
    J.M. Guedes and N. Kikuchi, Computational Aspects of Mechanics of Nonlinear Composite Materials (Rept., Dept. Mech. Engrg. and Appl. Mech., University of Michigan, USA, 1989 )Google Scholar
  28. [28]
    C. Fleury and V. Braibant, Structural Optimization: A New Dual Method Using Mixed Variables (Int. J. Num. Meth. Engrg. 23, pp. 409–428, 1986 )CrossRefMATHMathSciNetGoogle Scholar
  29. [29]
    P. Pedersen, On Optimal Orientation of Orthotropic Materials (Structural Optimization, 1, pp. 101–106, 1989 )Google Scholar
  30. [30]
    P. Pedersen, Bounds on Elastic Energy in Solids of Orthotropic Materials (Structural Optimization, 2, pp. 55–63, 1990 )Google Scholar
  31. [31]
    G.I.N. Rozvany, Structural Layout Theory — the Present State of Knowledge (in: loc.cit. [5], Chapter 7)Google Scholar
  32. [32]
    G.I.N. Rozvany, Structural Design via Optimality Criteria (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989 )Google Scholar
  33. [33]
    G.I.N. Rozvany and M. Zhou, Applications of the COC Algorithm in Layout Optimization (Paper for Proc. Int. Conf. Engineering Optimization in Design Processes, Karlsruhe, FRG, 3–4 September 1990 )Google Scholar
  34. [34]
    P.Pedersen, A Unified Approach to Optimal Design (in: H. Eschenauer and N. Olhoff: Optimization Methods in Structural Design, Proc. Euromech - Colloquium 164, Univ. Siegen, FRG, 1982, pp.182–187, Bibliographishes Institut, Mannheim, FRG, 1983 )Google Scholar
  35. [35]
    V. Braibant and C. Fleury, Shape Optimal Design Using B-splines (Comp. Meths. Appl. Mech. Engrg. 44, pp. 247–267, 1984 )CrossRefMATHGoogle Scholar
  36. [36]
    J.A. Bennett and M.E. Botkin, Structural Shape Optimization with Geometric Description and Adaptive Mesh Refinement (AIAA Journal 23, pp. 458–464, 1985 )Google Scholar
  37. [37]
    R.T. Haftka and R.V. Gandhi, Structural Shape Optimization–A Survey (Comp. Meths. Appl. Mech. Engrg. 5Z, pp. 91–106, 1986 )CrossRefGoogle Scholar
  38. [38]
    Y. Ding, Shape Optimization of Structures: A Literature Survey (Computers and Structures 24, pp. 985–1004, 1986 )MATHGoogle Scholar
  39. [39]
    N. Olhoff, Multicriterion Structural Optimization via Bound Formulation and Mathematical Programming (Structural Optimization 1, pp. 11–17, 1989 )Google Scholar
  40. [40]
    K. Svanberg, The method of Moving Asymptotes–A new Method for Structural Optimization (Int. J. Num. Meth. Engrg. 24, pp. 359–373, 1987 )CrossRefMATHMathSciNetGoogle Scholar
  41. [41]
    E.J. Haug, K.K. Choi and V. Komkov, Design Sensitivity of Structural Systems (Academic Press, New York, 1986 )Google Scholar
  42. [42]
    R.T. Haftka and H.M. Adelmann, Recent Developments in Structural Sensitivity Analysis (Structural Optimization, 1, pp. 137–151, 1989 )Google Scholar
  43. [43]
    G. Cheng and L. Yingwei, A New Computation Scheme for Sensitivity Analysis (Eng. Opt. 12, pp. 219–234, 1987 )Google Scholar
  44. [44]
    P. Pedersen, On the Minimum Mass Layout of Trusses (Advisory Group for Aerospace Research and Development, Conf. Proc. No. 36, Symposium on Structural Optimization, Istanbul, Turkey, AGARD-CP-36–70, 1970 )Google Scholar
  45. [45]
    P. Pedersen, On the Optimal Layout of Multi—Purpose Trusses (Computers and Structures, 2, pp. 695–712, 1972 )Google Scholar
  46. [46]
    P. Pedersen, Optimal Joint Positions for Space Trusses (Journal of The Structural Division, ASCE 99, pp. 2459–2476, 1973 )Google Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • N. Olhoff
    • 1
  • M. P. Bendsøe
    • 2
  • J. Rasmussen
    • 3
  1. 1.University of AalborgAalborgDenmark
  2. 2.Technical University DenmarkLyngbyDenmark
  3. 3.University of AalborgAalborgDenmark

Personalised recommendations