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Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 110))

Abstract

Shape optimal design is the synthesis of structural analysis and mathematical programming combined with computer aided geometric design (CAGD) concepts and behavior sensitivity analysis. This generally accepted idea is realized by CARAT. The underlying models are formulated with special regard to a general overall model of structural optimization which is efficient as well as flexible enough to be applied to shape optimal design of arbitrary shells in three dimensional space. Special emphasis is given to potential optimization algorithms (e.g. an extension of the method of moving asymptotes), practical design capabilities, clearly formulated interactions like variable linking, and modular computer codes. Shape optimizations of an initially axisymmetric shell, a fly-wheel and a bell demonstrate the capabilities of the presented approach.

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References

  • Atrek E., Gallagher R. H., Ragsdell K. M. and Zienkiewicz O. C. (1984, eds.), New Directions in Optimum structural Design. Wiley, Chichester, New York.

    Google Scholar 

  • Bendsøe M. P. and Kikuchi N. (1988), Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, vol.71, 197–224.

    Article  Google Scholar 

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

    Google Scholar 

  • Bletzinger K.-U. (1990), Formoptimierung von Flächentragwerken. Ph. D. Dissertation, Institut für Baustatik, Universität Stuttgart.

    Google Scholar 

  • Bletzinger K.-U., Kimmich S. and Ramm E. (1992a), Efficient modeling in shape optimal design. Computing Systems in Engineering, vol. 2, 483–495.

    Article  Google Scholar 

  • Bletzinger K.-U. and Ramm E. (1992b), Form finding of shells by structural optimization. To appear in Engineering with Computers.

    Google Scholar 

  • Bletzinger K.-U. (1992c), Extended method of moving asymptotes based on second order informations. Accepted for publication in Structural Optimization.

    Google Scholar 

  • Böhm W., Farm G. and Kahmann J. (1984), A survey of curve and surface methods in CAGD. Computer Aided Geometric Design, vol. 1, 1–60.

    Article  Google Scholar 

  • Braibant V. and Fleury, C. (1986), Shape optimal design and CAD oriented formulation. Engineering with Computers, vol. 1, 193–204.

    Article  Google Scholar 

  • Eschenauer H. A. and Thierauf G. (1989a, eds.), Discretization Methods and Structural Optimization — Procedures and Applications. Proceedings of the GAMM-Seminar of the same name, Oct. 5–7, 1988, Siegen, Lecture Notes in Engineering, Springer, Heidelberg, Berlin.

    Google Scholar 

  • Eschenauer H., Post U. and Bremicker M. (1989b), Einsatz der Optimierungsprozedur SA-POP zur Auslegung von Bauteilkomponenten. Bauingenieur, vol. 63, 515–526.

    Google Scholar 

  • Faux I. D. and Pratt M. J. (1979), Computational Geometry for Design and Manufacture. Ellis Horwood Publishers, Chichester.

    Google Scholar 

  • Fleury C. (1986), Structural optimization — a new dual method using mixed variables. International Journal for Numerical Methods in Engineering, vol. 23, 409–428.

    Article  Google Scholar 

  • Gallagher R.H. (1973), Fully stressed design. In: Optimum Structural Design — Theory and Applications (edited by R. H. Gallagher and O. C. Zienkiewicz), J. Wiley, London, New York, 1973.

    Google Scholar 

  • Haftka R. T. and Grandhi R. V. (1986), Structural shape optimization — a survey. Computer Methods in Applied Mechanics and Engineering, vol. 57, 91–106.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Haftka R. T., Gürdal Z. and Kamat M. R (1990), Elements of Structural Optimization. 2nd edition, Kluwer Academic Publishers, Dordrecht.

    Google Scholar 

  • Kimmich S. (1990), Strukturoptimierung und Sensibilitätsanalyse mit finiten Elementen. Ph.D. Dissertation, Institut für Baustatik, Universität Stuttgart.

    Google Scholar 

  • Kimmich S., Reitinger R. and Ramm E. (1992), Integration of different numerical techniques in shape optimization. To appear in Structural Optimization, vol. 4, 1992.

    Google Scholar 

  • Mota Soares C. A. (1987, ed.), Computer Aided Optimal Design — Structural and Mechanical Systems. NATO-ASI Series F: Computer and System Sciences, vol. 27, Springer, Berlin, Heidelberg.

    Google Scholar 

  • Philippi U. and Nachtigall W. (1991), Constructional morphology of sea urchin tests. In: proceedings of the 2nd International Symposium on Natural Structures — Principles, Strategies, and Models in Architecture and Nature, Stuttgart, Oct. 1 to 4 1991, Mitteilungen des SFB 230, Heft 6, Sonderforschungsbereich 230, Stuttgart, 183–191.

    Google Scholar 

  • Prasad B. (1983), Explicit constraint approximation forms in structural optimization, part 1: analyses and projections. Computer Methods in Applied Mechanics and Engineering, vol. 40, 1–26.

    Article  Google Scholar 

  • Ramm E., Bletzinger K.-U. and Kimmich, S. (1991a), Strategies in shape optimization of free form shells, in: Nonlinear Computational Mechanics — State of the Art (edited by P. Wriggers, W. Wagner),, Springer, Heidelberg, Berlin, 163–192.

    Google Scholar 

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

    Article  Google Scholar 

  • Ramm E. and Reitinger R. (1992), Force follows form in shell design. Presented at: IASS-CSCE International Congress on “Innovative Large Span Structures”, 13–17 July 1992, Toronto, Canada.

    Google Scholar 

  • Rozvany G. (1991, ed.), Optimization of large structural systems. Proceedings of the NATO/DFG conference of the same name, vol. 1 to 3, Berchtesgaden, 23. Sept.–4. Oct. 1991.

    Google Scholar 

  • Schittkowski K. (1981), The nonlinear programming method of Wilson, Han and Powell with an augmented Lagrangian type line search function. Numerische Mathematik, vol. 38, 83–114.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Schoofs B., van Asperen F., Maas P. and Lehr A. (1985), Experimental design theory and structural optimization design for a major-third church bell. CAMP’ 85, C 4.2.

    Google Scholar 

  • Schwefel H. P. (1981), Numerical Optimization of Computer Models. J. Wiley & sons, Chichester.

    Google Scholar 

  • Starnes J. H. and Haftka R. T. (1979), Preliminary design of composite wings for buckling, strength, and displacements constraints. Journal of Aircraft, vol. 16, 564–570.

    Article  Google Scholar 

  • Svanberg K. (1987), The method of moving asymptotes — a new method for structural optimization. International Journal for Numerical Methods in Engineering, vol. 24, 359–373.

    Article  Google Scholar 

  • Vanderplaats G. N. (1982), Structural optimization — past, present and future. AIAA-Journal, vol. 20, 992–1000.

    Article  Google Scholar 

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

    Google Scholar 

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© 1993 Birkhäuser Verlag Basel

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Bletzinger, KU., Reitinger, R., Kimmich, S., Ramm, E. (1993). Shape Optimization with Program CARAT. In: Hörnlein, H.R.E.M., Schittkowski, K. (eds) Software Systems for Structural Optimization. International Series of Numerical Mathematics, vol 110. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8553-9_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8553-9_6

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-7643-2836-8

  • Online ISBN: 978-3-0348-8553-9

  • eBook Packages: Springer Book Archive

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