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Shape Optimization as a Discrete Optimization Problem — Solution Procedures Using Continuous Approximations

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Discretization Methods and Structural Optimization — Procedures and Applications

Part of the book series: Lecture Notes in Engineering ((LNENG,volume 42))

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Abstract

Shape optimization in a general setting requires the determination of the spatial material distribution and for every point in space we have material or no material. Various ways of attacking this general problem by use of layered materials and porous, periodic media are presented and it is illustrated that the method allows a determination of the topology of a mechanical element.

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References

  1. R.T. Haftka and R.V. Gandhi: Structural shape optimization - a survey. Comp. Meth. Appl. Mech. Engng.. Vol. 57 (1986), pp. 91–106.

    Article  MATH  Google Scholar 

  2. R.V. Kohn and G. Strang: Optimal Design and Relazation of Variational Problems. Comm. Pure Appl. Math.. Vol. 39 (1986), pp. 1–25 (Part I), pp. 139-182 (Part II) and pp. 353-377 (Part III).

    Article  MathSciNet  Google Scholar 

  3. E. Sanchez-Palencia: Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics. Vol. 127, Springer Verlag 1980.

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  4. M.P. Bendsøe and N. Kikuchi: Generating Optimal Topologies in Structural Design Using a Homogenization Method. Comput. Meth. Appl. Mech. Engng. 1988 (to appear).

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  5. R.V. Kohn-: Recent Progress in the Mathematical Modeling of Composite Materials Preprint. Courant Institute, NYU.

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  6. M. Avellaneda: Optimal Bounds and Microgeometrics for Elastic Two-Phase Compos-ites. SIAM J. Appl. Math. Vol. 47 (1987), pp. 1216–1228.

    Article  MATH  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematical Institute, The Technical University of Denmark, Building 303, DK-2800, Lyngby, Denmark

    Martin Philip Bendsøe

Authors
  1. Martin Philip Bendsøe
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Editor information

Editors and Affiliations

  1. Institute of Mechanics and Control Engineering, University of Siegen, 5900, Siegen, Germany

    Hans A. Eschenauer

  2. Dept. of Civil Engineering, University of Essen, 4300, Essen, Germany

    Georg Thierauf

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© 1989 Springer-Verlag Berlin, Heidelberg

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Bendsøe, M.P. (1989). Shape Optimization as a Discrete Optimization Problem — Solution Procedures Using Continuous Approximations. In: Eschenauer, H.A., Thierauf, G. (eds) Discretization Methods and Structural Optimization — Procedures and Applications. Lecture Notes in Engineering, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83707-4_6

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  • DOI: https://doi.org/10.1007/978-3-642-83707-4_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50784-0

  • Online ISBN: 978-3-642-83707-4

  • eBook Packages: Springer Book Archive

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