Abstract
The causes of singular structural topologies, which prevent most iterative computational algorithms from reaching the global optimal solution, are explained in the light of the theory of exact optimal layouts. This theory is also used for deriving eight fundamental characteristics of singular topologies. The above findings are illustrated with case studies of exact optimal layouts for a single load and for two load conditions with stress constraints.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barta, J. 1957: On the minimum weight of certain redundant structures.Acta Techn. Acad. Sci. Hung. 18, 67–76
Birker, T.; Lewiński, T.; Rozvany, G.I.N. 1994: A well-posed non-selfadjoint layout problem: least-weight plane truss for one load condition and two displacement constraints.Struct. Optim. 8, 195–205
Cheng, G.; Jiang, Z. 1992: Study on topology optimization with stress constraints.Eng. Optimiz. 20, 129–148
Dorn, W.S.; Gomory, R.E.; Greenberg, H.J. 1964: Automatic design of optimal structures.J. de Mécanique 3, 25–52
Kirsch, U. 1990: On singular topologies in optimum structural design.Struct. Optim. 2, 133–142
Kirsch, U. 1994: Singular and local optima in structural optimization.Proc. AIAA/NASA/USAF/ISSMO Symp. on Multidisciplinary Analysis and Optimization (held in Panama City, FL, Sept. 1994), pp. 150–160. Washington D.C.: AIAA
Lewiński, T.; Zhou, M.; Rozvany, G.I.N. 1994: Extended exact solutions for least-weight truss layouts. Parts I, II.Int. J. Mech. Sci. 36, 375–398, 399–419
Michell, A.G.M. 1904: The limits of economy of material in framestructures.Phil. Mag. 8, 589–597
Prager, W. 1978: Optimal layout of trusses with a finite number of joints.J. Mech. Phys. Solids 26, 241–250
Prager, W.; Shield, R.T. 1967: A general theory of optimal plastic design.J. Appl. Mech. ASME 34, 184–186
Rozvany, G.I.N. 1974/1975: Analytical treatment of some extended problems in structural optimization, Part II.J. Struct. Mech. 3, 387–402
Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer
Rozvany, G.I.N.; Birker, T.; Lewiński, T. 1994: Some unexpected properties of exact least-weight plane truss layouts with displacement constraints for several alternate loads.Struct. Optim. 7, 76–86
Rozvany, G.I.N.; Prager, W. 1976: Optimal design of partially discretized grillages.J. Mech. Phys. Solids 24, 125–136
Rozvany, G.I.N.; Zhou, M.; Birker, T. 1993: Why multi-load topology designs based on orthogonal microstructures are in general non-optimal.Struct. Optim. 6, 200–204
Rozvany, G.I.N.; Zhou, M.; Gollub, W. 1993: Layout optimization by COC methods: analytical solutions. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems (Proc. NATO/DFG ASI, held in Berchtesgaden 1991), pp. 77–102. Dordrecht: Kluwer
Schmit, L.A: 1960: Structural design by systematic synthesis.Proc. 2nd Nat. Conf. on Elec. Comp. ASCE (held in Pittsburgh, PA, Sept. 1960), pp. 105–132
Sved, G. 1954: The minimum weight of certain redundant structures.Austral. J. Appl. Sci. 5, 1–8
Sved, G.; Ginos, Z. 1968: Structural optimization under multiple loading.Int. J. Mech. Sci. 10, 803–805
Zhou, M.; Rozvany, G.I.N. 1992/1993: DCOC — an optimality criteria method for large systems. Part I: theory, Part II: algorithm.Struct. Optim. 5, 12–25;6, 250–262
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rozvany, G.I.N., Birker, T. On singular topologies in exact layout optimization. Structural Optimization 8, 228–235 (1994). https://doi.org/10.1007/BF01742707
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01742707