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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01743385