Topological optimization of continuum structures with design-dependent surface loading - Part I: New computational approach for 2D problems

Structural and Multidisciplinary Optimization

Volumn 27, Issue 3, 2004, Pages 151-165

  Du, J ^a   Olhoff, N ^a  

^a AALBORG UNIVERSITY   (Denmark)

Author keywords

Design dependent loads; Loading surface; Sensitivities of loads; Topology design; Weighted unit cost constraints

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; OPTIMIZATION; POTENTIAL ENERGY; PROBLEM SOLVING; SENSITIVITY ANALYSIS; STRUCTURAL ANALYSIS; STRUCTURAL DESIGN; STRUCTURAL LOADS; TOPOLOGY;

DESIGN-DEPENDENT LOADS; LOADING SURFACES; SENSITIVITIES OF LOADS; TOPOLOGY DESIGN; WEIGHTED UNIT COST CONSTRAINTS;

CONTINUUM MECHANICS;

EID: 3042688151     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-004-0379-y     Document Type: Article

References (29)

1. Bendsøe, M.P.; Kikuchi, N. 1988: Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2), 19T-224
2. Bendsøe, M.P. 1989: Optimal shape design as a material distribution problem. Struct Optim 1, 193-202
3. Bendsøe, M.P.; Guedes, J.M.; Haber, R.B.; Pedersen, P.; Taylor, J.E, 1994: An analytical model to predict optimal material properties in the context of optimal structural design. J Appl Mech 61(4), 930-937
4. Bendsøe, M.P.; Diaz, A.R.; Lipton, R.; Taylor, J.E. 1995: Optimal design of material properties and material distribution for multiple loading conditions. Int J Numer Methods Eng 38, 1149-1170
5. Bendsøpe, M.P.; Sigmund, O. 1999: Material interpolation schemes in topology optimization. Arch Appl Mech 69, 635-654
6. Bendsøe, M.P.; Sigmund, O. 2003: Topology Optimization: Theory, Methods and Applications. Berlin, Heidelberg: Springer
7. Bourdin, B.; Chambolle, A. 2001: Design-dependent loads in topology optimization. Report, Cahiers du CEREMADE No. 01-21, 2001, Université de Paris-Dauphine, France
8. Burden, R.; Faires, J. 1985: Numerical Analysis. 3rd ed., Boston: Prindle, Weber and Schmidt
9. Chen, B.; Kikuchi, N. 2001: Topology optimization with design-dependent loads. Finite Elem Anal Des 37, 57-70
10. Cheng, G.; Olhoff, N. 1982: Regularized formulation for optimal design of axisymmetric plates. Int J Solids Struct 18, 153-169
11. Cherkaev, A. 2000: Variational Methods for Structural Optimization. Berlin Heidelberg New York: Springer
12. Du, J. 2001: An approach to computational solution for the optimal design of materials and topology of 2D and 3D continuum structures. In: Proc. WCSMO-4, Fourth World Congress of Structural and Multidisciplinary Optimization (held in Dalian, China, 4-8 June 2001)
13. Du, J.; Taylor, J.E. 2002: Application of an energy-based model for the optimal design of structural materials and topology. Struct Multidisc Optim 24, 277-292
14. Du, J.; Olhoff, N. 2004 (in press): Topological optimization of continuum structures with design-dependent surface loading - Part II: algorithm and examples for 3D problems. Struct Multidisc Optim. DOI 10.1007/s00158-004-0380-5
15. Eschenauer, H.; Olhoff, N. 2001: Topology optimization of continuum structures: A review. Appl Mech Rev 54(4) 331-389
16. Guedes, J.M.; Taylor, J.E. 1997: On the prediction of material properties and topology for optimal continuum structures. Struct Optim 14, 193-199
17. Hammer, V.B.; Olhoff, N. 1999: Topology optimization with design dependent loads. In: Proc. WCSMO-3, Third World Congress of Structural and Multidisciplinary Optimization (held in Buffalo, NY, May 17-21, 1999). State University of New York at Buffalo, Buffalo, New York
18. Hammer, V.B.; Olhoff, N. 2000: Topology optimization of continuum structures subjected to pressure loading. Struct Multidisc Optim 19(2), 85-92
19. Maute, K.; Ramm, E. 1995: Adaptive topology optimization. Struct Optim 10, 100-112
20. Olhoff, N.; Rønholt E.; Scheel, J. 1998: Topology optimization of three-dimensional structures using optimum microstructures. Struct Optim 16(1), 001-018
21. Rodrigues, H; Soto, C.A.; Taylor, J.E. 1999: A design model to predict optimal two-material composite structures. Struct Optim 17, 186-198
22. Rozvany, G.I.N.; Zhou, M. 1991: Applications of the COC method in layout optimization. In: Eschenauer, H.; Mattheck, C.; Olhoff, N. (eds.), Proc. Int. Conf. on Engineering Optimization in Design Processes (held in Karlsruhe, 1990), pp. 59-70, Berlin Heidelberg New York: Springer
23. Rozvany, G.I.N.; Zhou, M.; Birker, T. 1992: Generalized shape optimization without homogenization. Struct Optim 4, 250-252
24. Rozvany, G.I.N.; Bendsøe, M.P.; Kirsch, U. 1995: Layout optimization of structures. Appl Mech Rev 45, 41-119
25. Rozvany, G.I.N.; Olhoff, N. (eds.), Proc. NATO ARW on Topology Optimization of Structures and Composite Continua (Budapest, 2000), Dordrecht: Kluwer
26. Sigmund, O. 2000: A 99 line topology optimization code written in matlab. Struct Optim 21(2), 120-127
27. Taylor, J.E.; Washabaugh, P.D. 1995: A generalized expression of cost for prediction of the optimal material properties tensor. Proc. Summaries, ASME Summer Mechanics Meeting (held at UCLA)
28. Taylor, J.E. 1998: An energy model for the optimal design of linear continuum structures. Struct Optim 16(2-3), 116-127
29. Taylor, J.E. 2000: Addendum to: An energy model for the optimal design of linear continuum structures. Struct Multidisc Optim 19(4), 317-320