Abstract
Prager (1974) demonstrated through an example that the optimal layout of least-weight trusses for a stress constraint — termed also Michell trusses—can be nonunique. The strain field for the above example, however, seems to violate Michell's optimality criteria. It is shown in this note that the above example of nonuniqueness is completely correct if we restrict the truss members to a smaller subset of the plane.
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References
Hemp, W. 1973:Optimum structures. Oxford: Clarendon
Michell, A.G.M. 1904: The limits of economy of material infframestructures.Phil. Mag. 8, 589–597
Morley, C.T. 1966: The minimum reinforcement of concrete slabs.Int. J. Mech. Sci. 8, 305–319
Prager, W. 1974:Introduction to structural optimization. Vienna: Springer
Rozvany, G.I.N. 1966: A rational approach to plate design.J. Amer. Conc. Inst. 63, 1077–1094.
Rozvany, G.I.N. 1972: Grillages of maximum strength and maximum stiffness.Int. J. Mech. Sci. 14, 651–666.
Sigmund, O.; Zhou, M.; Rozvany, G.I.N. 1993: Layout optimization of large FE-systems by new optimality criteria methods: applications to beam systems. In: Haug, E.J. (ed)Proc. NATO ASI Concurrent Engineering Tools and Technologies for Mechanical System Design (held in Iowa City, 1992). Berlin, Heidelberg, New York: Springer
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Rozvany, G.I.N. On the validity of Prager's example of nonunique Michell structures. Structural Optimization 13, 191–194 (1997). https://doi.org/10.1007/BF01199239
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DOI: https://doi.org/10.1007/BF01199239