Abstract
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.
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References
Dobbs, M.W.; Felton, L.P. 1969: Optimization of truss geometry.J. Struct. Div. ASCE 95, 2105–2118
Dorn, W.S.; Gomory, R.E.; Greenberg, H.J. 1964: Automatic design of optimal structures.J. de Mécanique 3, 25–52
Hemp, W.S. 1973:Optimum structures. Oxford: Clarendon Press
Kirsch, U. 1987: Optimal topologies of flexural systems.Eng. Opt. 11, 141–149
Kirsch, U. 1989a: Optimal topologies of structures.Appl. Mech. Rev. 42, 223–239
Kirsch, U. 1989b Optimal topologies of truss structures.Comp. Meth. Appl. Mech. Eng. 72, 15–28
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: Springer
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)
Kirsch, U. 1989e: Improved optimum structural design by passive control.Eng. Comp. 5, 13–22
Kirsch, U. 1989f: Optimal design of structural control systems.Eng. Opt. (submitted)
Kirsch, U.; Taye, S. 1986: On optimal topologies of grillage structures.Eng. Comp. 1, 229–243
Sved, G.; Ginos, Z. 1968: Structural optimization under multiple loading.Int. J. Mech. Sci. 10, 803–805
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.
Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer Academic Publ.
Topping, B.H.V. 1983: Shape opimization of skeletal structures: a review.J. Struct. Eng, ASCE 109, 1933–1951
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on leave from Technion-Israel Institute of Technology
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Kirsch, U. On singular topologies in optimum structural design. Structural Optimization 2, 133–142 (1990). https://doi.org/10.1007/BF01836562
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DOI: https://doi.org/10.1007/BF01836562