Abstract
It is well established that for a compliance constraint, the optimal topology of perforated plates under plane stress tends to that for least-weight trusses (Michell structures) as the “volume fraction” (i.e. the ratio material volume/available volume) approaches zero. It is shown in this note that for two loading conditions the optimal bar orientations for Michell structures are in general non-orthogonal and hence the assumption of orthogonal microstructures in multi-load plate topology optimization must lead to erroneous results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allaire, G.; Kohn, R.V. 1992: Optimal design for minimum weight and compliance in plane stress using extremal microstructures.Preprint
Bendsøe, M.P.; Haber, R.B. 1993: The Michell truss problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study.Struct. Optim. 6 (to be published)
Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. 1993: Optimization methods for-truss geometry and topology design.Struct. Optim. 6 (to be published)
Díaz, A.; Bendsøe, M.P. 1992: Shape optimization of structures for multiple loading conditions using the homogenization method.Struct. Optim. 4, 17–22
Fukushima, J.; Suzuki, K.; Kikuchi, N. 1993: Applications to car bodies: generalized layout design of three-dimensional shells. In: Rozvany, G.I.N. (ed.)Optimization of large structural systems (Proc. NATO ASI, held in Berchtesgaden 1991), pp. 177–191. Dordrecht: Kluwer
Kohn, R.V.; Strang, G. 1986: Optimal design and relaxation of variational problems I, II, III.Pure Appl. Math. 39, 113–137, 139–182, 353–349
Lurie, K.A.; Cherkaev, A.V. 1986: Effective characteristics of composite materials and optimum design of structural members (in Russian)Adv. Mech. 9, 3–81
Pedersen, P. 1989: On optimal orientation of orthotropic materials.Struct. Optim. 1, 101–106
Rozvany, G.I.N. 1989:Structural design via optimality criteria. Dordrecht: Kluwer
Rozvany, G.I.N. 1992: Optimal layout theory: analytical solutions for elastic structures with several deflection constraints and load conditions.Struct. Optim. 4, 247–249
Rozvany, G.I.N.; Olhoff, N.; Bendsøe, M.P.; Ong, T.G.; Szeto, W.T.; Sandler, R. 1987: Least-weight design of perforated elastic plates I.Int. J. Solids Struct. 4, 521–526
Rozvany, G.I.N.; Sigmund, O.; Lewiński, T.; Gerdes, D.; Birker, T. 1993: Exact optimal structural layouts for non-self-adjoint problems.Struct. Optim. 5, 204–206
Rozvany, G.I.N.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization.Struct. Optim. 4, 250–252
Rozvany, G.I.N.; Zhou, M.; Rotthaus, M.; Gollub, W.; Spengemann, F. 1989: Continuum-type optimality criteria methods for large structural systems with a displacement constraint. Part I.Struct. Optim. 1, 47–72
Strang, G.; Kohn, R.V. 1983: Hencky-Prandtl nets and constrained Michell trusses.Comp. Meth. Appl. Mech. Engrg. 36, 207–222
Vigdergauz, S. 1992: Two-dimensional grained composites of extreme rigidity. Paper No. 62,8th. Int. Congr. Theor. Appl. Mech. (held in Haifa)
Zhou, M.; Rozvany, G.I.N. 1993: DCOC: an optimality criteria method for large structural systems. Part I: theory.Struct. Optim. 5, 12–25
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rozvany, G.I.N., Zhou, M. & Birker, T. Why multi-load topology designs based on orthogonal microstructures are in general non-optimal. Structural Optimization 6, 200–204 (1993). https://doi.org/10.1007/BF01743514
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01743514