Dynamical systems and topology optimization

Structural and Multidisciplinary Optimization

Volumn 42, Issue 2, 2010, Pages 179-192

  Klarbring, Anders ^b   Torstenfelt, Bo ^a  

^a LINKÖPING INSTITUTE OF TECHNOLOGY   (Sweden)

^b NONE

Author keywords

Optimality criteria Dynamical systems; Topology optimization

Indexed keywords

ALGORITHMIC ISSUES; BONE REMODELING; BOX CONSTRAINTS; DAMAGE EVOLUTION; DYNAMICAL SYSTEMS APPROACH; EULER APPROXIMATION; EVOLUTION PROBLEM; MATERIAL DISTRIBUTION; NATURAL EVOLUTION; NUMERICAL EXAMPLE; OBJECTIVE FUNCTIONS; OPTIMALITY CRITERIA; OPTIMALITY CRITERIA DYNAMICAL SYSTEMS; OPTIMIZATION PROBLEMS; PROJECTION TECHNIQUES; TOPOLOGY OPTIMIZATION;

ALGORITHMS; BIOLOGY; BONE; EULER EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; STRUCTURAL OPTIMIZATION; TOPOLOGY;

DYNAMICAL SYSTEMS;

EID: 77956617222     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-010-0479-9     Document Type: Article

References (28)

1. Achtziger W, Bendsøe MP, Taylor JE (1998) Bounds on the effect of progressive structural degradation. J Mech Phys Solids 46(6):1055-1087
2. Bejan A (2000) Shape and structure, from engineering to nature. Cambridge University Press, Cambridge
3. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Heidelberg
4. Borrvall T (2001) Topology optimization of elastic continua using restriction. Arch Comput Methods Eng 8:351-385
5. Brown AA, Bartholomew-Biggs MC (1989) Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations. J Optim Theory Appl 62(2):211-224
6. Chen G, Pettet G, Pearcy M, McElwain DLS (2007) Comparison of two numerical approaches for bone remodelling. Med Eng Phys 29(1):134-139
7. Christensen PW, Klarbring A (2009) An introduction to structural optimization. Springer, Heidelberg
8. Dontchev A, Lempio F (1992) Difference methods for differential inclusions: a survey. SIAM Rev 34(2):263-294
9. Francfort GA, Bourdin B, Marigo J-J (2008) The variational approach to fracture. J Elast 91(1-3):5-148
10. Harrigan TP, Hamilton JJ (1992) Optimality conditions for finite ele ment simulation of adaptive bone remodeling. Int J Solids Struct 29(23):2897-2906
11. Harrigan TP, Hamilton JJ (1994a) Necessary and sufficient conditions for global stability and uniqueness in finite element simulations of adaptive bone remodeling. Int J Solids Struct 31(1):97-107
12. Harrigan TP, Hamilton JJ (1994b) Bone remodeling and structural optimization. J Biomech 27(3):323-328
13. Klarbring A (2009) Topology optimization, dynamical systems, thermodynamics and growth. In: Damkilde L, Andersen L, Kristensen AS, Lund E (eds) Proceedings of the twenty second nordic seminar on computational mechanics, Aalborg, pp 337-344
14. Klarbring A, Petersson J, Torstenfelt B, Karlsson M (2003) Topology optimization of flow networks. Comput Methods Appl Mech Eng 192:3909-3932
15. Liao L-Z, Qi H, Qi L (2004) Neurodynamical optimization. J Glob Optim 28:175-195
16. Mullender MG, Huiskes R, Weinans H (1994) A physiological approach to the simulation of bone remodeling as a self-organizationalcontrolprocess. J Biomech 27(11):1389-1394
17. Nagurney A, Zhang D (1996) Projected dynamical systems and varia-tional inequalities with applications. Kluwer
18. Dordrecht Pang J-S, Stewart DE (2008) Differential variational inequalities. Math Program 113(2):345-24
19. Pappalardo M, Passacantando M (2002) Stability for equilibrium problems: from variational inequalities to dynamical systems. J Optim TheoryAppl 113(3):567-582
20. Payten WM, Ben-Nissan B, Mercer DJ (1998) Optimal topology design using a global self-organisational approach. Int J Solids Struct 35(3-4):219-237
21. Pettermann HE, Reiter TJ, Rammerstorfer FG (1997) Computational simulation of internal bone remodeling. Arch Comput Methods Eng 4(4):295-323
22. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401-424
23. Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidisc Optim 22(2):116-124
24. Svanberg K (1994) On the convexity and concavity of compliances. Struct Optim 7(1-2):42-46
25. Torstenfelt B (2009) The TRINITAS project. http://www.solid.iei.liu.se/ Offered-services/Trinitas/index.html
26. Wang S, Yang XQ, Teo KL (2003) A unified gradient flow approach to constrained nonlinear optimization problems. Comput Optim Appl 25:251-268
27. Xia YS (2004) Further results on global convergence and stability of globally projected dynamical systems. J Optim Theory Appl 122(3):637-649
28. Xinghua Z, He G, Dong Z, Bingzhao G (2002) A study of the effect of non-linearity in the equations of bond remodeling. J Biomech 35:951-960