Topology optimization using a mixed formulation: An alternative way to solve pressure load problems

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 13-16, 2007, Pages 1874-1889

  Sigmund, O ^a   Clausen, P M ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

Finite elements; Incompressibility; Mixed forms; Structural optimization; Topology optimization

Indexed keywords

FINITE ELEMENT METHOD; PRESSURE EFFECTS; STRUCTURAL OPTIMIZATION;

INCOMPRESSIBLE HYDROSTATIC FLUID; PRESSURE LOADS;

TOPOLOGY;

FINITE ELEMENT METHOD; PRESSURE EFFECTS; STRUCTURAL OPTIMIZATION; TOPOLOGY;

EID: 33846293326     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.09.021     Document Type: Article

References (28)

1. Bendsøe M.P., and Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Engrg. 71 2 (1988) 197-224
2. Bendsøe M.P., and Sigmund O. Topology Optimization - Theory, Methods and Applications (2003), Springer Verlag, Berlin Heidelberg pp. XIV+370
3. Hammer V.B., and Olhoff N. Topology optimization of continuum structures subjected to pressure loading. Struct. Multidisciplinary Optim. 19 (2000) 85-92
4. Du J., and Olhoff N. Topological optimization of continuum structures with design-dependent surface loading - Part I: New computational approach for 2D problems. Struct. Multidisciplinary Optim. 27 (2004) 151-165
5. Du J., and Olhoff N. Topological optimization of continuum structures with design-dependent surface loading - Part II: Algorithm and examples for 3D problems. Struct. Multidisciplinary Optim. 27 (2004) 166-177
6. Chen B., and Kikuchi N. Topology optimization with design-dependent loads. Finite Element Anal. Des. 37 (2001) 57-70
7. Fuchs M.B., and Shemesh N.N.Y. Density-based topological design of structures subjected to water pressure using a parametric loading surface. Struct. Multidisciplinary Optim. 28 1 (2004) 11-19
8. Bourdin B., and Chambolle A. Design-dependent loads in topology optimization, ESAIM: Control. Optim. Calculus Variations 9 (2003) 19-48
9. Allaire G., Jouve F., and Toader A.-M. Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys. 194 1 (2004) 363-393
10. Liu Z., Korvink J.G., and Huang R. Structure topology optimization: fully coupled level set method via FEMLAB. Struct. Multidisciplinary Optim. 29 6 (2005) 407-417
11. Sigmund O., and Torquato S. Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45 6 (1997) 1037-1067
12. Gibiansky L.V., and Sigmund O. Multiphase elastic composites with extremal bulk modulus. J. Mech. Phys. Solids 48 3 (2000) 461-498
13. Sigmund O. Design of multiphysics actuators using topology optimization - Part II: two-material structures. Comput. Methods Appl. Mech. Engrg. 190 49-50 (2001) 6605-6627
14. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method (Parts 1-3) (2000), Butterworth Heinemann, Oxford
15. Jog C.S., and Haber R.B. Stability of finite element models for distributed-parameter optimization and topology design. Comput. Methods Appl. Mech. Engrg. 130 3-4 (1996) 203-226
16. Sigmund O. On the design of compliant mechanisms using topology optimization. Mech. Struct. Mach. 25 4 (1997) 493-524
17. Bendsøe M.P. Optimal shape design as a material distribution problem. Struct. Optim. 1 (1989) 193-202
18. Zhou M., and Rozvany G.I.N. The COC algorithm, Part II: Topological, geometry and generalized shape optimization. Comput. Methods Appl. Mech. Engrg. 89 1-3 (1991) 309-336
19. Mlejnek H.P., and Schirrmacher R. An engineering approach to optimal material distribution and shape finding. Comput. Methods Appl. Mech. Engrg. 106 (1993) 1-26
20. Bendsøe M.P., and Sigmund O. Material interpolation schemes in topology optimization. Arch. Appl. Mech. 69 9-10 (1999) 635-654
21. Stolpe M., and Svanberg K. An alternative interpolation scheme for minimum compliance optimization. Struct. Multidisciplinary Optim. 22 2 (2001) 116-124
22. Bruyneel M., and Duysinx P. Note on topology optimization of continuum structures including self-weight. Struct. Multidisciplinary Optim. 29 4 (2005) 245-256
23. Pedersen N.L. Maximization of eigenvalues using topology optimization. Struct. Multidisciplinary Optim. 20 1 (2000) 2-11
24. Svanberg K. The method of moving asymptotes - a new method for structural optimization. Int. J. Numer. Methods Engrg. 24 (1987) 359-373
25. Olesen L.H., Okkels F., and Bruus H. A high-level programming-language implementation of topology optimization applied to steady-state Navier-Stokes flow. Int. J. Numer. Methods Engrg. 65 7 (2006) 975-1001 10.1002/nme.1468
26. Sigmund O., and Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards mesh-dependencies and local minima. Struct. Optim. 16 1 (1998) 68-75
27. Yoon G.H., Jensen J.S., and Sigmund O. Topology optimization for acoustic structure interaction problems. In: Bendsøe M.P., Olhoff N., and Sigmund O. (Eds). Topological Design Optimization of Structures, Machines and Materials - Status and Perspectives. Solid Mechanics and its Applications (2005), Springer
28. G.H. Yoon, J.S. Jensen, O. Sigmund, Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation, International Journal for Numerical Methods in Engineering, in press, doi:10.1002/nme.1900.