Topology optimization of shell structures using adaptive inner-front (AIF) level set method

Structural and Multidisciplinary Optimization

Volumn 36, Issue 1, 2008, Pages 43-58

  Park, Kang Soo ^a   Youn, Sung Kie ^a  

^a Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Inner front creation; Level set method; LSFEM; Topology optimization

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; LEAST SQUARES APPROXIMATIONS; PARTIAL DIFFERENTIAL EQUATIONS; SHELLS (STRUCTURES); TOPOLOGY;

INNER-FRONT CREATION; LEAST-SQUARES FINITE ELEMENT METHOD (LSFEM); LEVEL SET METHOD;

SHAPE OPTIMIZATION;

EID: 44349090909     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0169-4     Document Type: Conference Paper

References (35)

1. Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level set method. J Comput Phys 194:363-393
2. Allaire G, Jouve F, Toader AM (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cyber 34:59-80
3. Amstutz V, Andra H (2006) A new algorithm for topology optimization using a level-set method. J Comput Phys 216:573-588
4. Aubert G, Kornprobst P (2001) Mathematical problems in image processing: partial differential equations and the calculus of variations. Springer, Berlin
5. Belblidia F, Bulman S (2002) A hybrid topology optimization algorithm for static and vibrating shell structures. Int J Numer Methods Eng 54:835-852
6. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197-224
7. Bendsøe MP, Sigmund O (2003) Topology optimization-theory, methods and applications. Springer-Verlag, Berlin
8. Burger M, Hackl B, Ring W (2004) Incorporating topological derivatives into level set methods. J Comput Phys 194:344-362
9. Céa J, Garreau S, Guillaume P, Masmoudi M (2000) The shape and topological optimizations connection. Comput Methods Appl Mech Eng 188:713-726
10. Ha SH, Cho SH (2005) Topological shape optimization of heat conduction problems using level set approach. Numer Heat Trans Part B 48:67-88
11. Haftka RT, Gürdal Z (1992) Elements of structural optimization. Kluwer, Dordrechet
12. Harber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Optim 11:1-12
13. Haug EJ, Choi KK, Komkov V (1986) Design sensitivity analysis of structural systems. Academic, Orlando
14. Jiang BN (1998) The least-squares finite element method. Springer, Berlin
15. Kwak JH, Cho SH (2005) Topological shape optimization of geometrically nonlinear structures using level set method. Comput Struct 83:2257-2268
16. Lee S, Soni BK (1997) Governing equation of fluid mechanics in physical curvilinear coordinate system. In: Proceedings of the 3rd Mississippi state conference on difference equations and computational simulations. Mississippi State, USA, pp 149-157
17. Lee SJ, Bae JE, Hinton E (2000) Shell topology optimization using the layered artificial material model. Int J Numer Methods Eng 47:843-867
18. Li Q, Steven GP, Querin OM (1999) Optimization of thin shell structures subjected to thermal loading. Struct Eng Mech 7:401-412
19. Maute K, Ramm E (1996) Adpative topology optimization of shell structures. In: Proceedings of the 6th AIAA/NASA/ISSMO symposium on multidisciplinary analysis and optimization. Bellevue, USA, pp 1133-1141
20. Mei Y, Wang XM (2004) Level set method for structural topology optimization and its applications. Adv Eng Softw 35:415-441
21. Novotny AA, Feijoo RA, Taroco E, Padra C (2003) Topological sensitivity analysis. Comput Methods Appl Mech Eng 192:803-829
22. Oden JT, Demkowicz LF (1996) Applied functional analysis. CRC Press, Florida
23. Osher S, Fedkiw R (2003) Level set methods and dynamic implicit surfaces. Springer, Berlin
24. Osher S, Sethian JA (1998) Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12-49
25. Rosen JB (1960) The gradient projection method for nonlinear programming, part I, linear constraints. J Soc Industrial Appl Math 8:181-217
26. Sethian JA (1999) Level set methods and fast marching methods: evolution interfaces in computational geometry, fluid mechanics, computer vision, and meterail science. Cambridge Univ. Press, Cambridge
27. Sethian JA, Wiegmann (2000) A structural boundary design via level se and immersed interface method. J Comput Phys 163:489-528
28. Simon J (1980) Differentiation with respect to the domain in boundary value problems. Numer Function Anal Optim 2:649-687
29. Sokołowski J, Zochowski A (1999) On the topological derivative in shape optimization. SIAM J Control Optim 37:1251-1272
30. Takahira H, Horiuchi T, Banerjee S (2004) An improved three-dimensional level set method for gas-liquid two-phase flows. J Fluids Eng 126:578-585
31. Tenek LH, Hagiwara I (1994) Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization. Comput Methods Appl Mech Eng 115:111-124
32. Wang MY, Wang XM (2004) Color level sets: a multi-phase level set method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193:469-496
33. Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227-246
34. Youn SK, Park SH (1997) A study on the shape extraction process in the structural topolgy optimization using homogenized material. Comput Struct 62:527-538
35. Yue W, Lin CL, Patel VC (2005) Coherent structures in open-channel flows over a fixed dune. J Fluids Eng 127:858-864