Abstract
Some properties of optimal topologies of discrete structures are discussed. Various approximations and simplifications, often assumed in the problem formulation, are first reviewed. Three ground structure formulations are presented and compared: a. the implicit nonlinear programming formulation, where accurate stress and displacement constraints are considered; b. the approximate explicit problem formulation, where the implicit compatibility conditions are neglected; and c. the linear programming formulation, where the compatibility conditions are neglected and only stress constraints are considered. The advantages as well as the limitations of the various formulations are discussed and some properties of the resulting topologies are derived analytically. It is shown that optimal topologies might represent various types of structure and can significantly reduce the weight of the structure. Situations where local optima, singular optima and multiple optimal topologies occur are demonstrated, and the effect of stress and displacement constraints on the optimum is presented.
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References
Bendsoe, M. P., and Kikuchi, N. (1988), ’Generating Optimal Topologies in Structural Design using the Homogenization Method’, Computer Methods in Appl. Mech. and Engrg., 71, 197–224.
Rozvany, G.I.N. (1989), Structural Design via Optimality Criteria, Kluwer, Dordrecht.
Kirsch U. (1989), ’Optimal Topologies of Structures’, Applied Mechanics Review, 42, 223–239
Topping B.H.V. (1983), ’Shape Optimization of Skeletal Structures: A Review’, J. of Structural Engineering, ASCE, 109, 1933–1951.
Dorn, W.S., Gomory, R.E., and Greenberg, H.J. (1964), ’Automatic Design of Optimal Structures’, Journal de Mecanique, 3, 25–52.
Hemp, W.S.(1973), Optimum Structures, Clarendon Press, Oxford, U K.
Reinschmidt, K.F., and Russell, A.D. (1974), ’Applications of Linear Programming in Structural Layout and Optimization’, Comp. and Struct., 4, 855–869.
Kirsch, U. (1989) ’Optimal Topologies of Truss Structures’, Computer Methods in Appl. Mech. and Engrg., 72, 15–28.
Kirsch, U. and Topping, B.H.V. (1992), ’Minimum Weight Design of Structural Topologies’, to be published, ASCE Jour. of Computing in Civil Engineering.
Sheu, C.Y. and Schmit, L.A. (1972), ’Minimum Weight Design of Elastic Redundant Trusses Under Multiple Static Loading Conditions’, AIAA J., 10, 155–162.
Kirsch, U. (1992), Fundamentals and Applications of Structural Optimization, to be published by Springer Verlag, Hidelberg.
Kirsch, U. (1987), ’Optimal Topologies of Flexural Systems’, Engineering Optimization, 11, 141–149.
Sved, G., and Ginos, L. (1968), ’Structural Optimization under Multiple Loading’, Int. J. Mech. Sci., 10, 803–805.
Kirsch, U., and Taye, S. (1986), ’On Optimal Topology of Grillage Structures’, Engineering with computers, 1, 229–243.
Kirsch, U. (1990), ’On singular Topologies in Optimum Structural Design’, Structural Optimization, 2, 133–142.
Kirsch, U. (1990), ’On the Relationship Between Optimum Structural Geometries and Topologies’, Structural Optimization 2, 39–45.
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© 1993 Springer Science+Business Media Dordrecht
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Kirsch, U. (1993). Fundamental Properties of Optimal Topologies. In: Bendsøe, M.P., Soares, C.A.M. (eds) Topology Design of Structures. NATO ASI Series, vol 227. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1804-0_1
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DOI: https://doi.org/10.1007/978-94-011-1804-0_1
Publisher Name: Springer, Dordrecht
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