Some basic issues of topology optimization

Solid Mechanics and its Applications

Volumn 137, Issue , 2006, Pages 77-86

  Rozvany, George I N ^a   Pomezanski, Vanda ^a   Querin, Osvaldo M ^b   Gaspar, Zsolt ^a   Logo, Janos ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

^b UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Analytical solutions; Checkerboard control; Hyper optimality; Non gradient methods; SIMP; Topology benchmarks; Topology optimization

Indexed keywords

GRADIENT METHODS; SHAPE OPTIMIZATION; TOPOLOGY;

CHECKERBOARD CONTROL; NON-GRADIENT METHODS; OPTIMALITY; SIMP; TOPOLOGY BENCHMARKS;

STRUCTURAL OPTIMIZATION;

EID: 56449113327     PISSN: 18753507     EISSN: None     Source Type: Book Series    
DOI: 10.1007/1-4020-4752-5_8     Document Type: Conference Paper

References (26)

1. Bendsøe, M.P. and Sigmund, O. (2003) Topology Optimization, Springer, Berlin.
2. Bendsøe, M.P., Diaz, A. and Kikuchi, N. (1993) Topology and generalized layout optimization of elastic structures, in Topology Design of Structures, Proc. NATO ARW held in Sesimbra, 1992, M.P. Bendsøe and C.A. Mota Soares (eds), Kluwer Academic Publishers, Dordrecht.
3. Buhl, T. (2000) Simultaneous topology optimization of structure and supports, Struct.Multidisc. Optim., 23, 257-261.
4. Gaspar, G., Logo, J. and Rozvany, G.I.N. (2002) Addenda and corrigenda to a paper (Rozvany, G.I.N. (2001) Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics, Struct. Multidisc. Optim., 21, 90-108) (Pubitemid 32535045)
5. Struct. Multidisc. Optim., 24, 338-342.
6. Haber, R.B. and Bendsøe, M.P. (1996) A new approach to variable-topology shape design using constraint on the perimeter, Struct. Optim., 11, 1-12. (Pubitemid 126651006)
7. Lewinski, T. (2006) Variational proof of optimality criteria for Michell structures with preexisting members, Struct. Multidisc. Optim., accepted.
8. Lewinski, T., Zhou, M. and Rozvany, G.I.N. (1994) Extended exact solutions for least-weight truss layouts. Part I. Cantilever with a horizontal axis of symmetry. Part II. Unsymmetric cantilevers, Int. J. Mech. Sci., 36, 375-419.
9. Michell, A.G.M. (1904) The limits of economy of material in frame structures, Phil. Mag., 8, 589-597.
10. Pomezanski, V., Querin, O.M. and Rozvany, G.I.N. (2005) CO-SIMP: Extended SIMP algorithm with direct COrner COntact COntrol, Struct. Multidisc. Optim., 30, 164-168. (Pubitemid 41009795)
11. Poulsen, T.A. (2002) A simple scheme to prevent checkerboard patterns and one node connected hinges in topology optimization, Struct. Multidisc. Optim., 24, 396-399.
12. Prager, W. and Rozvany, G.I.N. (1977) Optimization of structural geometry (invited lecture), in Dynamical Systems, Proc. Univ. Florida Int. Symposium, Gainesville, March 1976, A.R. Bednarek and L. Cesari (eds), Academic Press, New York, pp. 265-294.
13. Prager, W. and Shield, R.T. (1967) A general theory of optimal plastic design, J. Appl. Mech., 34, 184-186.
14. Rozvany, G.I.N. (1976) Optimal Design of Flexural Systems, Pergamon, Oxford.
15. Rozvany, G.I.N. (1989) Structural Design via Optimality Criteria, Kluwer Academic Publishers, Dordrecht.
16. Rozvany, G.I.N. (1996) Some shortcomings of Michell's truss theory, Struct. Optim., 12, 244-250. (Pubitemid 126650490)
17. Rozvany, G.I.N. (1998) Exact analytical solutions for some popular benchmark problems in topology optimization, Struct. Optim., 15, 42-48. (Pubitemid 128647615)
18. Rozvany, G.I.N. and Gollub, W. (1990) Michell layouts for various combinations of line supports. Part I, Int. J. Mech. Sci., 32, 1021-1043.
19. Rozvany, G.I.N. and Zhou, M. (1991) Applications of COC method in layout optimization, in Proc. Conf. on Eng. Optim. in Design Processes, Karlsruhe, 1990, H. Eschenauer, C. Mattheck and N. Olhoff (eds), Springer, Berlin, pp. 59-70.
20. Rozvany, G.I.N., Querin, O.M., Gaspar, Z. and Pomezanski, V. (2002) Extended optimality in topology design, Struct. Multidisc. Optim., 24, 257-261. (Pubitemid 35186134)
21. Rozvany, G.I.N., Querin, O.M., Gaspar, Z. and Pomezanski, V. (2003) Weight increasing effect of topology simplification, Struct. Multidisc. Optim., 25, 459-465.
22. Rozvany, G.I.N., Pomezanski V., Gaspar Z. and Querin, O.M. (2005) Some pivotial issues in structural optimization, in 6th World Congress on Structural and Multidisciplinary Optimization, Book of Abstracts and CD-ROM Proceedings, Rio de Janeiro, 30 May-3 June 2005, p. 147. Short paper: http://www.wcsmo6.org/ Papers/5951Rozvany.pdf (2 pp.)
23. Rozvany, G.I.N., Querin, O.M., Logo, J. and Pomezanski, V. (2006) Exact analytical theory of topology optimization with some pre-existing members or elements, Struct. Multidisc. Optim., in press.
24. Sigmund, O. (1994) Design of material structures using topology optimization, Ph.D. Thesis, Dept. Solid Mech., TU Denmark.
25. Sigmund, O. and Petersson, J. (1998) Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Struct. Optim., 16, 68-75. (Pubitemid 128647652)
26. Sved, G. (1954) The minimum weight of certain redundant structures, Aust. J. Appl. Sci., 5, 1-3.