Structural optimization

, Volume 2, Issue 3, pp 133–142 | Cite as

On singular topologies in optimum structural design

  • U. Kirsch


A major obstacle to topological optimization is that the optimal topology might correspond to a singular point in the design space. Despite its crucial importance, the phenomenon of singular optimal topologies is not well understood.

The main objects of this paper are: (a) to clarify some properties of singular optimal topologies; (b) to discuss the effect of various constraints on the optimum; and (c) to present some design considerations related to the particular difficulties involved in topological optimization.

It is shown that singular solutions are obtained mainly due to the nature of stress constraints. Displacement constraints might significantly affect the optimal cross-sections, but not necessarily the optimal topology. The effect of lower bounds on cross-sections is demonstrated and several two-stage solution procedures are discussed.


Civil Engineer Lower Bound Singular Point Optimal Topology Design Space 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Dobbs, M.W.; Felton, L.P. 1969: Optimization of truss geometry.J. Struct. Div. ASCE 95, 2105–2118Google Scholar
  2. Dorn, W.S.; Gomory, R.E.; Greenberg, H.J. 1964: Automatic design of optimal structures.J. de Mécanique 3, 25–52Google Scholar
  3. Hemp, W.S. 1973:Optimum structures. Oxford: Clarendon PressGoogle Scholar
  4. Kirsch, U. 1987: Optimal topologies of flexural systems.Eng. Opt. 11, 141–149Google Scholar
  5. Kirsch, U. 1989a: Optimal topologies of structures.Appl. Mech. Rev. 42, 223–239Google Scholar
  6. Kirsch, U. 1989b Optimal topologies of truss structures.Comp. Meth. Appl. Mech. Eng. 72, 15–28Google Scholar
  7. Kirsch, U. 1989c: On the relationship between optimum structural geometries and topologies. In: Brebbia, C.A.; Hernandez, S. (eds.)Computer aided optimum design of structures. Recent advances, pp. 243–253. Berlin, Heidelberg, New York: SpringerGoogle Scholar
  8. Kirsch, U. 1989d: On some properties of optimum structural topologies.Proc. NATO ASI on Optimization and Decision Support Systems in Civil Engineering (held at Heriot-Watt Univ, Edinburgh)Google Scholar
  9. Kirsch, U. 1989e: Improved optimum structural design by passive control.Eng. Comp. 5, 13–22Google Scholar
  10. Kirsch, U. 1989f: Optimal design of structural control systems.Eng. Opt. (submitted)Google Scholar
  11. Kirsch, U.; Taye, S. 1986: On optimal topologies of grillage structures.Eng. Comp. 1, 229–243Google Scholar
  12. Sved, G.; Ginos, Z. 1968: Structural optimization under multiple loading.Int. J. Mech. Sci. 10, 803–805Google Scholar
  13. Rozvany, G.I.N. 1988: Optimality criteria and layout theory in structural design: recent developments and applications. In: Rozvany, G.I.N.; Karihaloo, B.L. (eds.)Structural optimization. Dordrecht: Kluwer Academic Publ.Google Scholar
  14. Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer Academic Publ.Google Scholar
  15. Topping, B.H.V. 1983: Shape opimization of skeletal structures: a review.J. Struct. Eng, ASCE 109, 1933–1951Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • U. Kirsch
    • 1
  1. 1.Dept. of Civil EngineeringHeriot-Watt University, RiccartonEdinburghUK

Personalised recommendations