Topology optimization of hyperelastic bodies including non-zero prescribed displacements

Structural and Multidisciplinary Optimization

Volumn 47, Issue 1, 2013, Pages 37-48

  Klarbring, Anders ^a   Strömberg, Niclas ^b  

^a LINKÖPING INSTITUTE OF TECHNOLOGY   (Sweden)

^b JÖNKÖPING UNIVERSITY   (Sweden)

Author keywords

Compliance; Hyperelasticity; Optimality criteria; Potential energy

Indexed keywords

COMPLIANCE; DESIGN CONCEPT; EXTERNAL FORCE; HYPER ELASTIC; HYPER-ELASTICITY; LARGE DEFORMATIONS; LARGE ROTATION; LINEAR ELASTICITY; NUMERICAL RESULTS; OPTIMAL DESIGN; OPTIMALITY CRITERIA; PRESCRIBED DISPLACEMENTS; SMALL DISPLACEMENT; STRAIN ENERGY FUNCTIONS;

DEFORMATION; ELASTICITY; STIFFNESS;

POTENTIAL ENERGY;

EID: 84871979511     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-012-0819-z     Document Type: Article

References (27)

1. Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:193-202
2. Bendsøe M, Sigmund O (2002) Topology optimization, theory, methods and applications. Springer, New York
3. Bonet J, Wood RD (2008) Nonlinear continuum mechanics for finite element analysis. Cambridge University Press, Cambridge
4. Bruns TE, Sigmund O (2004) Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng 193:3973-4000 (Pubitemid 39142609)
5. Bruns TE, Sigmund O, Tortorelli DA (2002) Numerical methods for the topology optimization of structures that exhibit snap-through. Int J Numer Methods Eng 55:1215-1237 (Pubitemid 35326717)
6. Bruns TE, Tortorelli D (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190:3443-3459 (Pubitemid 32379192)
7. Buhl T, Pedersen CB, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidisc Optim 19:93-104
8. Cho S, Jung H-S (2003) Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures. Comput Methods Appl Mech Eng 192:2539-2553 (Pubitemid 36738599)
9. Christensen P, Klarbring A (2008) An introduction to structural optimization. Springer, New York
10. Curnier A (1994) Computational methods in solid mechanics. Kluwer Academic, Dordrecht
11. Fleury C (1979) Structural weight optimization by dual methods of convex programming. Int J Numer Methods Eng 14:1761-1783 (Pubitemid 10436659)
12. Fleury C, Braibant V (1986) Structural optimization: a new dual method using mixed variables. Int J Numer Methods Eng 23:409-428 (Pubitemid 16517200)
13. Gea HC, Luo J (2001) Topology optimization of structures with geometrical nonlinearities. Comput Struct 79:1977-1985 (Pubitemid 32922965)
14. Groenwold AA, Etman LFP (2008) On the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem. Int J Numer Methods Eng 73:297-316
15. Haftka RT, Gürdal Z (1992) Elements of structural optimization. Kluwer Academic, Dordrecht
16. Holzapfel GA (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, New York
17. Huang X, Xie YM (2008) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30:2057-2068
18. Jung D, Gea HC (2004) Topology optimization of nonlinear structures. Finite Elem Anal Des 40:1417-1427
19. Kemmler R, Lipka A, Ramm E (2005) Large deformations and stability in topology optimization. Struct Multidisc Optim 30:459-476 (Pubitemid 41720547)
20. Klarbring A, Strömberg N (2011) A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements. Struct Multidisc Optim. doi: 10.1007/s00158-011-0674-3
21. Lee WS, Youn SK (2004) Topology optimization of rubber isolators considering static and dynamic behaviours. Struct Multidisc Optim 27:284-294
22. Niu F, Xu S, Cheng G (2011) A general formulation of structural topology optimization for maximizing structural stiffness. Struct Multidisc Optim 43:561-572
23. Pajot JM, Maute K (2006) Analytical sensitivity analysis of geometrically nonlinear structures based on the co-rotational finite element method. Finite Elem Anal Des 42:900-913
24. Pedersen C, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50:2683-2705 (Pubitemid 32277245)
25. Pedersen P, Pedersen N (2011) Design objectives with non-zero prescribed support displacements. Struct Multidisc Optim 43:205-214
26. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidisc Optim 21:120-127 (Pubitemid 32535047)
27. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89:309-336 (Pubitemid 21721598)