Topological design of structures and composite materials with multiobjectives

International Journal of Solids and Structures

Volumn 44, Issue 22-23, 2007, Pages 7092-7109

  de Kruijf, Niek ^a   Zhou, Shiwei ^b   Li, Qing ^b   Mai, Yiu Wing ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b UNIVERSITY OF SYDNEY   (Australia)

Author keywords

Inverse homogenization; Material conduction; Microstructural composites; Multiobjective; Nonlinear diffusion; Topology optimization

Indexed keywords

BOUNDARY CONDITIONS; ELASTIC MODULI; MULTIOBJECTIVE OPTIMIZATION; SHAPE OPTIMIZATION; THERMAL CONDUCTIVITY;

INVERSE HOMOGENIZATION; MATERIAL CONDUCTION; MICROSTRUCTURAL COMPOSITES; NONLINEAR DIFFUSION;

COMPOSITE MATERIALS;

EID: 34548818744     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.03.028     Document Type: Article

References (51)

1. Allaire G., Jouve F., and Toader A. Structural optimization using sensitivity analysis and a level-set method. Journal of Computational Physics 194 (2004) 363-393
2. Aubert G., and Kornprobst P. Mathematical Problems in Image Processing (2000), Springer, Berlin
3. Belytschko T., Xiao S., and Parimi C. Topology optimization with implicit functions and regularization. International Journal for Numerical Methods in Engineering 57 8 (2003) 1177-1196
4. Bendsøe M. Optimal shape design as a material distribution problem. Structural Optimization 1 (1989) 193-202
5. Bendsøe M., and Kikuchi N. Generating optimal topologies in optimal design using a homogenization method. Computational Methods in Applied Mechanics and Engineering 71 (1988) 197-224
6. Bendsøe M., and Sigmund O. Material interpolation schemes in topology optimization. Achieve of Applied Mechanics 69 (1999) 635-654
7. Bendsøe M., and Sigmund O. Topology Optimization Theory Methods and Applications (2003), Springer, Berlin
8. Bensoussan A., Lions J., and Papanicolaou G. Asymptotic Analysis for Periodic Structures (1978), North-Holland, Amsterdam
9. Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering 50 (2001) 2143-2158
10. Charbonnier P., Blanc-Feraud L., Aubert G., and Barlaud M. Deterministic edge-reserving regularization in computed imaging. IEEE Transactions on Image Processing 6 2 (1997) 298-311
11. Chen, B., 2000. Optimal design of material microstructures and optimization of structural topological for design-dependent loads. Ph.D. Thesis, The University of Michigan.
12. Chen X., and Mai Y. Micromechanics of rubber-toughened polymers. Journal of Materials Science 33 14 (1998) 3529-3539
13. Cho S., and Choi J. Efficient topology optimization of thermo-elasticity problems using coupled field adjoint sensitivity analysis method. Finite Elements in Analysis and Design 41 15 (2005) 1481-1495
14. Gibiansky L., and Sigmund O. Multiphase elastic composites with extremal bulk modulus. Journal of the Mechanics and Physics of Solids 48 (2000) 461-498
15. Guest J., and Prévost J. Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. International Journal of Solids and Structures 43 (2006) 7028-7047
16. Guest J., Prévost J., and Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering 61 (2004) 238-254
17. Haber R., Jog C., and Bendsøe M. A new approach to variable-topology shape design using a constraint on perimeter. Structural Optimization 11 (1996) 1-12
18. Hashin Z., and Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of Mechanics and Physics of Solids 11 (1963) 127-140
19. Hassani B., and Hinton E. Homogenization and Structural Topology Optimization (1999), Springer-Verlag, London
20. Haug E., Choi K., and Komkov V. Design Sensitivity Analysis of Structural Systems (1986), Academic press, New York
21. Jonsmann J., Sigmund O., and Bouwstra S. Compliant thermal microactuators. Sensors and Actuators 76 (1999) 463-469
22. Larsen U., Sigmund O., and Bouwstra S. Design and fabrication of compliant micromechanisms and structures with negative poisson's ratio. Journal of Microelectromechanical Systems 6 2 (1997) 99-106
23. Li Q., Steven G., and Xie Y. Thermoelastic topology optimization for problems with varying temperature fields. Journal of Thermal Stresses 24 (2001) 347-366
24. Li Q., Steven G., Xie Y., and Querin O. Evolutionary topology optimization for temperature reduction of heat conducting fields. International Journal of Heat and Mass Transfer 47 (2004) 5071-5083
25. Li Q., Steven G., Xie Y., and Qurein O. Shape and topology design for heat conduction by evolutionary structural optimization. International Journal of Heat and Mass Transfer 42 (1999) 3361-3371
26. Lurie K., and Cherkaev A. Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion. Proceedings of the Royal Society Edinburg A 99 71 (1984)
27. Lyu N., and Saitou K. Topology optimization of multicomponent beam structure via decomposition-based assembly synthesis. Journal of Mechanical Design 127 2 (2005) 170-183
28. Moulton T., and Ananthasuresh G. Micromechanical devices with embedded electro-thermal-compliant actuation. Sensors and Actuators 90 (2001) 38-48
29. Pareto V. Manual of Political Economy (1971), Macmillan, New York (Ch. Manuale di Economia Politica. Societa Editrice Libria, Milano)
30. Petersson J., and Sigmund O. Slope constrained topology optimization. International Journal for Numerical Methods in Engineering 41 (1998) 1417-1434
31. Prager W., and Taylor J. Problems of optimal structural design. Journal of Applied Mechanics 35 (1968) 102-106
32. Rodrigues H., and Fernades P. A material based model for topology optimization of thermoelastic structures. International Journal of Numerical Methods in Engineering 38 12 (1995) 1951-1965
33. Sanchez-Palencia E. Non-homogeneous media and vibration theory. Lecture Notes in Physics vol. 127 (1980), Springer Verlag, Berlin
34. Saxena A. Synthesis of compliant mechanisms for path generation using genetic algorithm. Journal of Mechanical Design 127 4 (2005) 745-752
35. Sethian J., and Wiegmann A. Structural boundary design via level set and immersed interface methods. Journal of Computational Physics 163 2 (2000) 489-528
36. Sigmund, O., 1994a. Design of material structures using topology optimization. Ph.D. Thesis, Technical University of Denmark.
37. Sigmund O. Materials with prescribed constitutive parameters: an inverse homogenization problem. International Journal of Solids and Structures 31 (1994) 2313-2329
38. Sigmund O. Tailoring materials with prescribed elastic properties. Mechanics of Materials 20 (1995) 351-368
39. Sigmund O. A new class of extremal composites. Journal of the Mechanics and Physics of Solids 48 (2000) 397-428
40. Sigmund O., and Torquato S. Design of materials with extreme thermal expansion using a three-phase topology optimization method. Journal of the Mechanics and Physics of Solids 45 (1997) 1037-1067
41. Song Y.S., and Youn J.R. Evaluation of effective thermal conductivity for carbon nanotube/polymer composites using control volume finite element method. Carbon 44 35 (2006) 710-717
42. Svanberg K. The method of moving asymptotes - a new method for structural optimization. International Journal for Numerical Methods in Engineering 24 (1987) 359-373
43. Torquato S., Hyun S., and Donev A. Multifunctional composites: optimizing microstructures for simultaneous transport of heat and electricity. Physical Review Letters 98 (2002) 266601
44. Torquato S., Hyun S., and Donev A. Optimal design of manufacturable three-dimensional composites with multifunctional characteristics. Journal of Applied Physics 94 9 (2003) 5748-5755
45. Wang M., Wang X., and Guo D. A level set method for structural topology optimization. Computer Methods in Applied and Engineering 192 (2003) 227-246
46. Wang M., Zhou S., and Ding H. Nonlinear diffusion in topology optimization. Structural Multidisciplinary Optimization 28 (2004) 262-276
47. Weickert J. A review of nonlinear diffusion filtering, Scale-Space, Theory in Computer Vision. Lecture Notes in Computer Science vol. 1252 (1997), Springer Berlin 3-28
48. Xie Y., and Steven G. A simple evolutionary procedure for structural optimization. Computers and Structures 49 (1993) 885-896
49. Yoo J., and Lee C. Topology optimization of a swing arm type actuator using the response surface method. Microsystem Technologies-Micro-and-Nanosystems-Information Storage and Processing Systems 13 1 (2007) 21-31
50. Zhou M., and Rozvany G. Dcoc: an optimality criteria method for large systems, part i: theory. Structural Optimization 5 (1993) 12-25
51. Zhou, S., Li, Q., 2006. Design of microstructure composites with tailored thermal conductivity by topological optimization. In: Proceedings of the 7th World Congress on Computational Mechanics, LA, USA.