Abstract
It is shown that Michell's problem of least-weight truss layouts can be obtained by asymptotic expansion of the optimized strain and complementary energies derived for minimum compliance topology of perforated plates in plane stress.
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Achtziger, W.; Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. 1992: Equivalent displacement based formulations for maximum strength truss topology design.IMPACT of Computing in Science and Engineering 4, 315–345
Allaire, G.; Kohn, R.V. 1993a: Topology optimization and optimal shape design using homogenization. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology optimization of structures, pp. 207–218. Dordrecht: Kluwer
Allaire, G.; Kohn, R.V. 1993b: Optimal design for minimum weight and compliance in plane stress using extremal microstructures.European J. Mech. A. (to appear)
Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. 1993: Optimization methods for truss geometry and topology design.DCAMM Report No. S64, The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, Lyngby, Denmark
Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method.Comp. Meth. Appl. Mech. Engrg. 71, 197–224
Hemp, W.S. 1973:Optimum structures. Oxford: Clarendon Press
Jog, C.; Haber, R.; Bendsøe, M.P. 1993a: A displacement-based topology design method with self-adaptive layered materials. In: Bendsøe, M.P.; Mota Soares, C.A. (eds.)Topology optimization of structures, pp. 219–238. Dordrecht: Kluwer
Jog, C.; Haber, R.B.; Bendsøe, M.P. 1993b: Topology design with optimized, self-adaptive materials.DCAMM Report No. 457. AlsoInt. J. Num. Meth. Engng. (to appear)
Lagache, J.-M. 1981: Treillis de volume minimal dans une region donnée.J. de Mécanique 20, 415–448
Lewiński, T.; Zhou, M.; Rozvany, G.I.N. 1993: Exact least-weight truss layouts for rectangular domains with various support conditions. Preprint, FB 10, Universität Essen, Germany
Lipton, R. 1992: On implementation of partial relaxation for optimal structural compliance problems. In: Pedersen, P. (ed.)Optimal design with advanced materials, pp. 457–468. Amsterdam: Elsevier
Michell, A.G.M. 1904: The limits of economy of material in frame structures.Phil. Mag. 8, 589–597
Ong, T.G.; Rozvany, G.I.N.; Szeto, W.T. 1988: Least-weight design of perforated elastic plates for given compliance: non-zero Poisson's ratio.Comp. Meth. Appl. Mech. Eng. 66, 301–322
Pedersen, P. 1989: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106
Prager, W.; Rozvany, G.I.N. 1977: Optimization of structural geometry. In: Bednarek, A.R.; Cesari, L.Dynamical systems, pp. 265–293. New York: Academic Press
Rozvany, G.I.N. 1976:Optimal design of flexural systems. Oxford: Pergamon Press
Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer
Rozvany, G.I.N.; Olhoff, N.; Bendsøe, M.P.; Ong, T.G.; Szeto, W.T. 1987: Least-weight design of perforated elastic plates, I, II.Int. J. Solids Struct. 23, 537–550
Suzuki, K.; Kikuchi, N. 1991: Shape and topology optimization for generalized layout problems using the homogenization method.Comp. Meth. Appl. Mech. Engrg. 93, 291–318
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Bendsøe, M.P., Haber, R.B. The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: An asymptotic study. Structural Optimization 6, 263–267 (1993). https://doi.org/10.1007/BF01743385
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DOI: https://doi.org/10.1007/BF01743385