Exact analytical solutions for some popular benchmark problems in topology optimization

Structural Optimization

Volumn 15, Issue 1, 1998, Pages 42-48

  Rozvany, G I N ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL ANALYSIS; OPTIMIZATION; PROBLEM SOLVING; STRUCTURAL ANALYSIS; TOPOLOGY;

DISCRETIZED TRUSSES;

TRUSSES;

EID: 0031997969     PISSN: 09344373     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01197436     Document Type: Article

References (23)

1. Allaire, G.; Kohn, R.V. 1993: Explicit bounds on the elastic energy of a two-phase composite in two space dimensions. Q. Appl. Math. 51, 675-699
2. Beckers, M.; Fleury, C. 1997: Topology optimization involving discrete variables. In: Mróz, Z., Gutkowski, W. (eds.) Proc. WCSMO-2, pp. 533-538. Warsaw: Inst. Fundam. Techn. Res.
3. Bendsøe, M.P.; Ben-Tal, A.; Zowe, J. 1994: Optimization methods for truss geometry and topology design. Struct. Optim. 7, 141-159
4. Bendsøe, M.P.; Haber, R.B. 1993: The Michell layout problem as a low volume fraction limit of the perforated plate topology optimization problem: an asymptotic study. Struct. Optim. 6, 263-267
5. Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method. Comp. Meth. Appl. Mech. Eng. 71, 197-224
6. Chan, A.S.L. 1960: The design of Michell optimum structures. Cranfield College of Aeronautics Rep. 142
7. Chan, H.S.Y. 1967: Half-plane slip-line fields and Michell structures. Quart. J. Appl. Math. 20, 453-469
8. Diaz, A.R.; Bendsøe, M.P. 1992: Shape optimization of structures for multiple load conditions using a homogenizaton method. Struct. Optim. 4, 17-22
9. Haber, R.B.; Jog, C.S.; Bendsøe, M.P. 1996: A new approach to variable-topology shape design using a constraint on perimeter. Struct. Optim. 11, 1-12
10. Hemp, W.S. 1973: Optimum structures. Oxford: Clarendon
11. Jakobsen, J.B.; Olhoff, N.; Rønholt, E. 1997: Generalized shape optimization of three-dimensional structures using materials with optimum microstructures (to be published)
12. Lev, O.E. 1981: Topology and optimality of certain trusses. J. Struct. Div. ASCE 107, 383-393
13. Lewiński, T.; Zhou, M.; Rozvany, G.I.N. 1994a: Extended exact solutions for least-weight truss layouts - Part I: cantilever with a horizontal axis of symmetry. Int. J. Mech. Sci. 36, 375-398
14. Lewiński, T.; Zhou, M.; Rozvany, G.I.N. 1994b: Extended exact solutions for least-weight truss layouts - Part II: unsymmetric cantilevers. Int. J. Mech. Sci. 36, 399-419
15. Michell, A.G.M. 1904: The limits of economy of material in frame-structures. Phil. Mag. 8, 589-597
16. Nagtegaal, J.C.; Prager, W. 1973: Optimal layout of truss for alternative loads. Int. J. Mech. Sci. 15, 583-592
17. Olhoff, N.; Bendsøe, M.; Rasmussen, J. 1991: On CAD-integrated structural topology and design optimization. Comp. Meth. Appl. Mech. Eng. 89, 259-279
18. Rozvany, G.I.N. 1989: Structural design via optimality criteria. Dordrecht: Kluwer
19. Rozvany, G.I.N. 1996: Some shortcomings in Michell's truss theory. Struct. Optim. 12, 244-250
20. Rozvany, G.I.N.; Birker, T. 1994: On singular topologies in exact layout optimization. Struct. Optim. 8, 228-235
21. Rozvany, G.I.N.; Hill, R.H. 1978: Optimal plastic design: superposition principles and bounds on the minimum cost. Comp. Meth. Appl. Mech. Eng. 13, 151-173
22. Rozvany, G.I.N.; Olhoff, N.; Bendsøe, M.; Ong, T.G.; Sandler, R.; Szeto, W.T. 1985/87: Least-weight design of perforated elastic plates. DCAMM Report No 306. Int. J. Solids Struct. 23, 521-536, 537-550
23. 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 systesm (Proc. NATO ASI held in Berchtesgaden, 23 Sept. - 4 Oct. 1991). Dordrecht: Kluwer