Basics of Shape Optimal Design

  • K.-U. Bletzinger
  • E. Ramm
Part of the International Centre for Mechanical Sciences book series (CISM, volume 328)


At present optimum structural design is understood as a synthesis of several disciplines which individually are to a large extend developed [1]: (i) design modeling, (ii) structural analysis, (iii) behavior sensitivity analysis, (iv) mathematical programming, and (v) interactive computer graphics. Their interactions reflect the typical loop of each design process (Fig. 1). The art of structural optimization is to join the interdisciplinary dependencies in a clear, integrated overall model and to convert it into an efficient and practical computer code [2]. Today, all the leading software packages offer optimization modules, although of different quality and still mainly restricted to sizing.

A lot of special software and procedures have been developed and presented in the literature which deal with shape optimal design [3–6]. The related process is reviewed and accompanied by a number of excellent papers [7–9], proceedings [10–12], and books [13–15] which clearly show the evolution from the first beginnings with sizing of structures to the latest developments in shape optimal design. Fields of applications are steadily increasing. Especially in automotive [6] and aircraft industries [16] the methods found wide-spread recognition as instruments of numerical simulation to improve structural quality. Civil engineering is yet behind to use structural optimization as a regular tool. But also here the methods can be used as an extra design aid; e.g. for the shape design of free formed shells [17–20]. It is the intention of this contribution to give some insight into the basic ideas of the methods and the underlying modeling; the application to general shells is described in [21].


Structural Optimization Design Sensitivity Analysis Design Node Shape Optimal Design Continuity Patch 
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.


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  1. 1.
    Braibant, V. and Fleury, C.: Shape optimal design and CAD oriented formulation, Engng. with Comp., 1 (1986), 193–204.CrossRefGoogle Scholar
  2. 2.
    Bletzinger, K.-U.; Kimmich, S. and Ramm, E.: Efficient modeling in shape optimal design, to appear in Computing Systems in Engineering, 1992.Google Scholar
  3. 3.
    Eschenauer, H.; Post, U. and Bremicker, M.: Einsatz der Optimierungsprozedur SAPOP zur Auslegung von Bauteilkomponenten, Bauingenieur, 63 (1989), 515–526.Google Scholar
  4. 4.
    Kimmich, S. and Ramm, E.: Structural optimization and analysis with program system CARAT, in: [12] 1989, 186–193.Google Scholar
  5. 5.
    Rasmussen, J.: The structural optimization system CAOS, Structural Optimization, 2 (1990), 109–115.CrossRefGoogle Scholar
  6. 6.
    Chargin, M. K.; Raasch, I.; Bruns, R. and Deuermeyer, D.: General shape optimization capability, Finite Elements Anal. Des., 7 (1991), 343–354.zbMATHGoogle Scholar
  7. 7.
    Schmit, L. A.: Structural synthesis–its genesis and development, AIAA Journal, 19 (1981), 1249–1263.CrossRefGoogle Scholar
  8. 8.
    Vanderplaats, G. N.: Structural optimization–past, present and future, AIM-Journal, 20 (1982), 992–1000.MathSciNetzbMATHGoogle Scholar
  9. 9.
    Haftka, R. T. and Grandhi, R. V.: Structural shape optimization–a survey, Comp. Meth. Appl. Mech. Engng., 57 (1986), 91–106.MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bennett, J. A. and Botkin, M. E. (eds.): The Optimum Shape - Automated Structural Design, Plenum Press, New York, London, 1986.Google Scholar
  11. 11.
    Mota Soares, C. A. (ed.): Computer Aided Optimal Design - Structural and Mechanical Systems, NATO-ASI Series F: Computer and System Sciences, vol. 27, Springer, Berlin, Heidelberg, 1987.Google Scholar
  12. 12.
    Eschenauer, H. A. and Thierauf, G. (eds.): Discretization Methods and Structural Optimization - Procedures and Applications, Proc. GAMM-Seminar, Oct. 5–7, 1988, Siegen, Lecture Notes in Engineering, Springer, 1989.Google Scholar
  13. 13.
    Vanderplaats, G. N.: Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, New York, 1984.zbMATHGoogle Scholar
  14. 14.
    Atrek, E.; Gallagher, R. H.;Ragsdell, K. M. and Zienkiewicz, O. C. (eds.): New Directions in Optimum structural Design, Wiley, Chichester, New York, 1984.Google Scholar
  15. 15.
    Haftka, R. T.; Gürdal, Z. and Kamat, M. P.: Elements of Structural Optimization, 2nd edition, Kluwer Academic Publishers, Dordrecht, 1990.CrossRefzbMATHGoogle Scholar
  16. 16.
    Petiau, C.: Structural optimization of aircraft, Thin Walled Struct., 11 (1991), 43–64.CrossRefGoogle Scholar
  17. 17.
    Bletzinger, K.-U.: Formoptimierung von Flächentragwerken, Ph. D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.Google Scholar
  18. 18.
    Kimmich, S.: Strukturoptimierung und Sensibilitätsanalyse mit finiten Elementen, Ph.D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.Google Scholar
  19. 19.
    Ramm, E. and Mehlhorn, G.: On shape finding methods and ultimate load analyses of reinforced concrete shells, Engineering Structures, 13 (1991), 178–198.CrossRefGoogle Scholar
  20. 20.
    Bletzinger, K.-U. and Ramm, E. Form finding of shells by structural optimization, to appear in Engng. with Comp., 1992.Google Scholar
  21. 21.
    Ramm, E.: Shape finding methods of shells, lecture notes CISM course NonlinearAnalysis of Shells by Finite Elements, Udine, June 24–28, 1991.Google Scholar
  22. 22.
    Böhm, W.; Farin, G. and Kahmann, J.: A survey of curve and surface methods in CAGD, Comp. Aided Geom. Des., 1 (1984), 1–60.zbMATHGoogle Scholar
  23. 23.
    Faux, I. D. and Pratt, M. J.: Computational Geometry for Design and Manufacture, Ellis Norwood Publishers, Chichester, 1979.zbMATHGoogle Scholar
  24. 24.
    Andelfinger, U: Untersuchungen zur Zuverlässigkeit hybrid -gemischterfiniter Elemente für Flächentragwerke, Ph.D.-Dissertation, Institut für Baustatik, Universität Stuttgart, 1991.Google Scholar
  25. 25.
    Büchter, N. and Ramm, E.: Shell theory versus degeneration - a comparison in large rotation finite element analysis, submitted to Int. J. Num. Meth. Engng., 1990.Google Scholar
  26. 26.
    Haftka, R. T. and Adelman, H. M.: Recent developments in structural sensitivity analysis, Structural Optimization, 1 (1989), 137–151.CrossRefGoogle Scholar
  27. 27.
    Dems, K. and Haftka, R. T.: Two approaches to sensitivity analysis for shape variation of structures, Mech. Struct. & Mach., 16 (1988), 501–522.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Barthelemy, B.; Chon, C. T. and Haftka, R. T.: Accuracy problems associated with semi-analytical derivatives of static response, Finite Elements Anal. Des., 4 (1988), 249–265.zbMATHGoogle Scholar
  29. 29.
    Luenberger, D. G.: Linear and Nonlinear Programming, Addison-Wesley, Reading, 1984.zbMATHGoogle Scholar
  30. 30.
    Schittkowski., K.: The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function, Numerische Mathematik, 38 (1981), 83–114.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Fleury, C.: Structural optimization–a new dual method using mixed variables, Int. J. Num. Meth. Engng., 23 (1986), 409–428.MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Svanberg, K.: The method of moving asymptotes–a new method for structural optimization, Int. J. Num. Meth. Engng., 24 (1987), 359–373.MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Fleury, C.: Sructural weight optimization by dual methods of convex programming, Int. J. Num. Meth. Engng., 14 (1979), 1761–1783.CrossRefzbMATHGoogle Scholar
  34. 34.
    Berke, L. and Khot, N. S.: Structural optimization using optimality criteria, in: [11] 1987, 271–311.Google Scholar
  35. 35.
    Ding, Y.: Shape optimization of structures: a literature survey, Comp. & Struct., 24 (1986), 985–1004.CrossRefzbMATHGoogle Scholar
  36. 36.
    Esping, B. J. D.: A CAD approach to the minimum weight design problem, Int. J. Num. Meth. Engng., 21 (1985), 1049–1066.CrossRefzbMATHGoogle Scholar
  37. 37.
    Gallagher, R.H.: Fully stressed design, in: Optimum Structural Design - Theory and Applications (Eds. R. H. Gallagher and O. C. Zienkiewicz ), J. Wiley, London, New York, 1973.Google Scholar
  38. 38.
    Lootsma, F. A. and Ragsdell, K. M.: State of the art in parallel nonlinear optimization, Parallel Computing, 6 (1988), 133–155.MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Prasad, B.: Explicit constraint approximation forms in structural optimization, part 1: analyses and projections, Comp. Meth. Appl. Mech. Engng., 40 (1983), 1–26.CrossRefzbMATHGoogle Scholar
  40. 40.
    Ramm, E. and Schunck, E.: Heinz Isler - Schalen, Krämer, Stuttgart, 1986.Google Scholar
  41. 41.
    Santos, J. L. T.; Godse, M. M. and Chang, K.-H.: An interactive post-processor for structural design sensitivity analysis and optimization: sensitivity display and what-if study, Comp. & Struct., 35 (1990), 1–13.CrossRefGoogle Scholar
  42. 42.
    Schwefel, H. P.: Numerical Optimization of Computer Models, J. Wiley & sons, Chichester, 1981.Google Scholar
  43. 43.
    Starnes J. H. and Haftka, R. T.: Preliminary design of composite wings for buckling, strength, and displacements constraints, J. Aircraft, 16 (1979), 564–570.CrossRefGoogle Scholar
  44. 44.
    Thanedar, P B.; Arora, J. S.; Tseng, C. H. et al.: Performance of some SQP algorithms on structural optimization problems, J. Num. Meth. Engng., 23 (1986), 2187–2203.MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Adelman, H. M. and Haftka, R. T.: Sensitivity Analysis of discrete structural systems, AIM-Journal, 24 (1988), 823–832.Google Scholar
  46. 46.
    Adeli, H. and Balasubramanyam, K. V.: A synergetic man-machine approach to shape optimization of structures, Comp. & Struct., 30 (1988), 553–561.CrossRefGoogle Scholar
  47. 47.
    Arora, J. S. and Haug, E. J.: Methods of design sensitivity analysis in structural optimization, AIM-Journal, 17 (1979), 970–974.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Wien 1992

Authors and Affiliations

  • K.-U. Bletzinger
    • 1
  • E. Ramm
    • 1
  1. 1.University of StuttgartStuttgartGermany

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