Skip to main content
SpringerLink
Log in
Book cover

Nonlinear Analysis of Shells by Finite Elements pp 257–268Cite as

Basics of Shape Optimal Design

  • Chapter

  • 350 Accesses

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 328))

Abstract

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].

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Braibant, V. and Fleury, C.: Shape optimal design and CAD oriented formulation, Engng. with Comp., 1 (1986), 193–204.

    Article  Google Scholar 

  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. Eschenauer, H.; Post, U. and Bremicker, M.: Einsatz der Optimierungsprozedur SAPOP zur Auslegung von Bauteilkomponenten, Bauingenieur, 63 (1989), 515–526.

    Google Scholar 

  4. Kimmich, S. and Ramm, E.: Structural optimization and analysis with program system CARAT, in: [12] 1989, 186–193.

    Google Scholar 

  5. Rasmussen, J.: The structural optimization system CAOS, Structural Optimization, 2 (1990), 109–115.

    Article  Google Scholar 

  6. Chargin, M. K.; Raasch, I.; Bruns, R. and Deuermeyer, D.: General shape optimization capability, Finite Elements Anal. Des., 7 (1991), 343–354.

    MATH  Google Scholar 

  7. Schmit, L. A.: Structural synthesis–its genesis and development, AIAA Journal, 19 (1981), 1249–1263.

    Article  Google Scholar 

  8. Vanderplaats, G. N.: Structural optimization–past, present and future, AIM-Journal, 20 (1982), 992–1000.

    MathSciNet  MATH  Google Scholar 

  9. Haftka, R. T. and Grandhi, R. V.: Structural shape optimization–a survey, Comp. Meth. Appl. Mech. Engng., 57 (1986), 91–106.

    Article  MathSciNet  MATH  Google Scholar 

  10. Bennett, J. A. and Botkin, M. E. (eds.): The Optimum Shape - Automated Structural Design, Plenum Press, New York, London, 1986.

    Google Scholar 

  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. 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. Vanderplaats, G. N.: Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, New York, 1984.

    MATH  Google Scholar 

  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. Haftka, R. T.; Gürdal, Z. and Kamat, M. P.: Elements of Structural Optimization, 2nd edition, Kluwer Academic Publishers, Dordrecht, 1990.

    Book  MATH  Google Scholar 

  16. Petiau, C.: Structural optimization of aircraft, Thin Walled Struct., 11 (1991), 43–64.

    Article  Google Scholar 

  17. Bletzinger, K.-U.: Formoptimierung von Flächentragwerken, Ph. D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.

    Google Scholar 

  18. Kimmich, S.: Strukturoptimierung und Sensibilitätsanalyse mit finiten Elementen, Ph.D. Dissertation, Institut für Baustatik, Universität Stuttgart, 1990.

    Google Scholar 

  19. Ramm, E. and Mehlhorn, G.: On shape finding methods and ultimate load analyses of reinforced concrete shells, Engineering Structures, 13 (1991), 178–198.

    Article  Google Scholar 

  20. Bletzinger, K.-U. and Ramm, E. Form finding of shells by structural optimization, to appear in Engng. with Comp., 1992.

    Google Scholar 

  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. Böhm, W.; Farin, G. and Kahmann, J.: A survey of curve and surface methods in CAGD, Comp. Aided Geom. Des., 1 (1984), 1–60.

    MATH  Google Scholar 

  23. Faux, I. D. and Pratt, M. J.: Computational Geometry for Design and Manufacture, Ellis Norwood Publishers, Chichester, 1979.

    MATH  Google Scholar 

  24. Andelfinger, U: Untersuchungen zur Zuverlässigkeit hybrid -gemischterfiniter Elemente für Flächentragwerke, Ph.D.-Dissertation, Institut für Baustatik, Universität Stuttgart, 1991.

    Google Scholar 

  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. Haftka, R. T. and Adelman, H. M.: Recent developments in structural sensitivity analysis, Structural Optimization, 1 (1989), 137–151.

    Article  Google Scholar 

  27. Dems, K. and Haftka, R. T.: Two approaches to sensitivity analysis for shape variation of structures, Mech. Struct. & Mach., 16 (1988), 501–522.

    Article  MathSciNet  Google Scholar 

  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.

    MATH  Google Scholar 

  29. Luenberger, D. G.: Linear and Nonlinear Programming, Addison-Wesley, Reading, 1984.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  31. Fleury, C.: Structural optimization–a new dual method using mixed variables, Int. J. Num. Meth. Engng., 23 (1986), 409–428.

    Article  MathSciNet  MATH  Google Scholar 

  32. Svanberg, K.: The method of moving asymptotes–a new method for structural optimization, Int. J. Num. Meth. Engng., 24 (1987), 359–373.

    Article  MathSciNet  MATH  Google Scholar 

  33. Fleury, C.: Sructural weight optimization by dual methods of convex programming, Int. J. Num. Meth. Engng., 14 (1979), 1761–1783.

    Article  MATH  Google Scholar 

  34. Berke, L. and Khot, N. S.: Structural optimization using optimality criteria, in: [11] 1987, 271–311.

    Google Scholar 

  35. Ding, Y.: Shape optimization of structures: a literature survey, Comp. & Struct., 24 (1986), 985–1004.

    Article  MATH  Google Scholar 

  36. Esping, B. J. D.: A CAD approach to the minimum weight design problem, Int. J. Num. Meth. Engng., 21 (1985), 1049–1066.

    Article  MATH  Google Scholar 

  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. Lootsma, F. A. and Ragsdell, K. M.: State of the art in parallel nonlinear optimization, Parallel Computing, 6 (1988), 133–155.

    Article  MathSciNet  MATH  Google Scholar 

  39. Prasad, B.: Explicit constraint approximation forms in structural optimization, part 1: analyses and projections, Comp. Meth. Appl. Mech. Engng., 40 (1983), 1–26.

    Article  MATH  Google Scholar 

  40. Ramm, E. and Schunck, E.: Heinz Isler - Schalen, Krämer, Stuttgart, 1986.

    Google Scholar 

  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.

    Article  Google Scholar 

  42. Schwefel, H. P.: Numerical Optimization of Computer Models, J. Wiley & sons, Chichester, 1981.

    Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  45. Adelman, H. M. and Haftka, R. T.: Sensitivity Analysis of discrete structural systems, AIM-Journal, 24 (1988), 823–832.

    Google Scholar 

  46. Adeli, H. and Balasubramanyam, K. V.: A synergetic man-machine approach to shape optimization of structures, Comp. & Struct., 30 (1988), 553–561.

    Article  Google Scholar 

  47. Arora, J. S. and Haug, E. J.: Methods of design sensitivity analysis in structural optimization, AIM-Journal, 17 (1979), 970–974.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Stuttgart, Stuttgart, Germany

    K.-U. Bletzinger & E. Ramm

Authors
  1. K.-U. Bletzinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Ramm
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Vienna University of Technology, Austria

    F. G. Rammerstorfer

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Wien

About this chapter

Cite this chapter

Bletzinger, KU., Ramm, E. (1992). Basics of Shape Optimal Design. In: Rammerstorfer, F.G. (eds) Nonlinear Analysis of Shells by Finite Elements. International Centre for Mechanical Sciences, vol 328. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2604-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-2604-2_8

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82416-0

  • Online ISBN: 978-3-7091-2604-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation