Topology optimization of incompressible media using mixed finite elements

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 33-34, 2007, Pages 3151-3164

  Bruggi, Matteo ^a   Venini, Paolo ^a  

^a UNIVERSITY OF PAVIA   (Italy)

Author keywords

Incompressible media; Mixed finite elements; Topology optimization

Indexed keywords

FINITE ELEMENT METHOD; PRESSURE; SHAPE OPTIMIZATION;

INCOMPRESSIBLE MEDIA; METHOD OF MOVING ASYMPTOTES; MIXED FINITE ELEMENTS;

STRUCTURE (COMPOSITION);

FINITE ELEMENT METHOD; PRESSURE; SHAPE OPTIMIZATION; STRUCTURE (COMPOSITION);

EID: 34249052292     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.02.013     Document Type: Article

References (31)

1. Arnold D.N., Brezzi F., and Douglas J.D. PEERS: a new mixed finite element for plane elasticity. Japan J. Appl. Math. 1 (1984) 347-367
2. Bendsøe M., and Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engrg. 71 2 (1988) 197-224
3. Bendsøe M., and Sigmund O. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69 (1999) 635-654
4. Bendsøe M., and Sigmund O. Topology Optimization - Theory, Methods and Applications (2003), Springer, EUA, New York
5. Borrvall T., and Petersson J. Topology optimization of fluids in Stokes flow. Int. J. Numer. Methods Engrg. 41 (2003) 77-107
6. Braess D. Finite Elements (1997), Cambridge University Press
7. Brezzi F., and Fortin M. Mixed and Hybrid Finite Element Methods (1991), Springer-Verlag, New York
8. Bruns T.E., and Tortorelli D.A. Topology optimization of nonlinear elastic structures and compliant mechanisms. Comput. Methods Appl. Mech. Engrg. 190 (2001) 3443-3459
9. Bruns T.E., Sigmund O., and Tortorelli D.A. Numerical methods for the topology optimization of structures that exhibit snap-through. Int. J. Numer. Methods Engrg. 55 (2002) 1215-1237
10. Bruyneel M., and Duysinx P. Note on topology optimization of continuum structures including self-weight design. Struct. Multidisc. Optim. 29 4 (2005) 245-256
11. Cheng B.-C., and Kikuchi N. Topology optimization with design dependent loads. Comput. Methods Appl. Mech. Engrg. 37 (2001) 57-70
12. Diaz A., and Kikuchi N. Solution to shape and topology eigenvalue optimization problems using a homogenization method. Int. J. Numer. Methods Engrg. 35 3 (1992) 1487-1502
13. G. Duvaut, Mécanique de Milieux Continus, Masson. 1992.
14. Duysinx P., and Bendsøe M. Topology optimization of continuum structures with local stress constraints. Int. J. Numer. Methods Engrg. 43 (1998) 1453-1478
15. Gensborg-Hansen A., Sigmund O., and Haber R.B. Topology optimization of channel flow problems. Struct. Multidisc. Optim. 30 3 (2005) 181-192
16. V.B. Hammer, Checkmate? Nodal densities in topology optimization, in: Proc. II Max Planck Workshop on Engineering Design Optimization 2001; Dept. of Mathematics, DTU, Denmark.
17. Hammer V.B., and Olhoff N. Topology optimization of continuum structures subjected to pressure loading. Struct. Multidisc. Optim. 19 (2000) 85-92
18. Han W., and Reddy B.D. On the finite element method for mixed variational inequalities arising in elastoplasticity. SIAM J. Numer. Anal. 32 6 (1995) 1778-1807
19. Johnson C., and Mercier B. Some equilibrium finite elements methods for two dimensional elasticity problems. Numer. Math. 30 (1978) 103-116
20. Olhoff N., and Eschenauer H.A. Topology optimization of continuum structures - a review. Appl. Mech. Rev. 54 (2001) 331-390
21. Pedersen N.L. Maximization of eigenvalues using topology optimization. Struct. Multidisc. Optim. 20 1 (2001) 2-11
22. Petersson J. Some convergence results in perimeter-controlled topology optimization. Comput. Methods Appl. Mech. Engrg. 171 (1999) 123-140
23. Schwarz S., Maute K., and Ramm E. Topology and shape optimization for elastoplastic structural response. Comput. Methods Appl. Mech. Engrg. 190 (2001) 2135-2155
24. Schenk O., and Gärtner K. Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Generation Comput. Syst. 20 3 (2004) 475-487
25. Schenk O., and Gärtner K. On fast factorization pivoting methods for symmetric indefinite systems. Elec. Trans. Numer. Anal. 23 (2006) 158-179
26. Sigmund O. A new class of extremal composites. J. Mech. Phys. Solids 48 2 (2000) 397-428
27. Sigmund O., and Clausen P.M. Topology optimization using a mixed formulation: an alternative way to solve pressure load problems. Comput. Methods Appl. Mech. Engrg. 196 13-16 (2007) 1874-1889
28. Sigmund O., and Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct. Multidisc. Optim. 16 1 (1998) 68-75
29. Stolpe M., and Svanberg K. An alternative interpolation scheme for minimum compliance optimization. Struct. Multidisc. Optim. 22 (2001) 116-124
30. Svamberg K. Method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Methods Engrg. 24 3 (1987) 359-373
31. G.H. Yoon, J.S. Jensen, O. Sigmund, Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation, Int. J. Numer. Methods Engrg., in press, doi:10.1002/nme.1900.