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On the relationship between optimum structural topologies and geometries

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Abstract

The relationship between two optimal design problems is investigated: (a) The fixed geometry problem, where the topology is optimized for a predetermined geometry. (b) The fixed topology problem, where the geometry is optimized for a given topology. Assuming approximate linear programming formulations, conditions of optimality are derived and geometries of multiple optimal topologies are studied. Some considerations related to a general design procedure for optimization of topology, geometry and cross-sections are discussed.

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References

  • Dorn, W.S.; Gomory, R.E.; Greenberg, H.J. 1964: Automatic design of optimal structures.J. de Mech. 3, 25–52

    Google Scholar 

  • Hansen, S.R.; Vanderplaats, G.N. 1988: An approximation method for configuration optimization of trusses.Proc. AIAA/ASME/ASCE/AHS 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, Virginia), pp. 1667–1676

  • Kirsch, U. 1982: Synthesis of structural geometry using approximation concepts.Comp. Struct. 15, 305–314

    Google Scholar 

  • Kirsch, U.; Taye, S. 1986: On optimal topology of grillage structures.Eng. Comp 1, 229–243

    Google Scholar 

  • Kirsch, U. 1987: Optimal topologies of flexural systems.Eng. Opt. 11, 141–149

    Google Scholar 

  • Kirsch, U. 1989a: Optimal topologies of truss structures.Comp. Meth. Appl. Mech. Eng. 72, 15–28

    Google Scholar 

  • Kirsch, U. 1989b: Optimal topologies of structures.Appl. Mech. Rev. 42, 223–239

    Google Scholar 

  • Lipson, S.L.; Gwin, L.B. 1977: The complex method applied to optimal truss configuration.Comp. Struct. 7, 461–468

    Google Scholar 

  • Topping, B.H.V. 1983: Shape optimization of skeletal structures. A review.J. Struct. Eng. ASCE 109, 1933–1951

    Google Scholar 

  • Vanderplaats, G.N.; Moses, F. 1972: Automated design of trusses for optimum geometry.J. Struct. Div. ASCE 98, 671–690

    Google Scholar 

  • Vanderplaats, G.N. 1984: Numerical methods for shape optimization. An assessment of the state of the art. In: Atrek, E.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (eds.)New directions in optimum structural design. Chichester: John Wiley and Sons

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Heriot-Watt University, EH14 4AS, Riccarton, Edinburgh, United Kingdom

    U. Kirsch (Visiting Professor and Carnegie Research Fellow)

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  1. U. Kirsch
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On leave from Technion-Israel Institute of Technology

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Kirsch, U. On the relationship between optimum structural topologies and geometries. Structural Optimization 2, 39–45 (1990). https://doi.org/10.1007/BF01743519

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  • DOI: https://doi.org/10.1007/BF01743519

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