Scale-related topology optimization of cellular materials and structures

International Journal for Numerical Methods in Engineering

Volumn 68, Issue 9, 2006, Pages 993-1011

  Zhang, Weihong ^a   Sun, Shiping ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Cellular material design; Homogenization method; Scale effect; Topology optimization; Unit cell

Indexed keywords

ASYMPTOTIC STABILITY; LIGHT WEIGHT STRUCTURES; NUMERICAL METHODS; STRUCTURAL OPTIMIZATION; TOPOLOGY;

CELLULAR MATERIAL DESIGN; DESIGN ELEMENT CONCEPT; HOMOGENIZATION METHOD; SCALE EFFECT;

STRUCTURAL ANALYSIS;

ASYMPTOTIC STABILITY; LIGHT WEIGHT STRUCTURES; NUMERICAL METHODS; STRUCTURAL ANALYSIS; STRUCTURAL OPTIMIZATION; TOPOLOGY;

EID: 37349026991     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1743     Document Type: Article

References (24)

1. Bendsøe MP. Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering 1988; 71(2):197-224.
2. Bensoussan A, Lions JL, Papanicolaou G. Asymptotic Analysis for Periodic Structures. North-Holland: Amsterdam, 1978.
3. Sanchez-Palencia E. Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer: Berlin, 1980.
4. Bendsøe MP. Optimal shape design as a material distribution problem. Structural Optimization 1989; 1: 193-202.
5. Rozvany GIN, Zhou M, Birker T. Generalized shape optimization without homogenization. Structural Optimization 1992; 4:250-254.
6. Swan CC, Kosaka I. Voigt-Reuss topology optimization for structures with linear elastic material behaviours. International Journal for Numerical Methods in Engineering 1997; 40:3033-3057.
7. Rozvany GIN. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization 2001; 21:90-108.
8. Bendsøe MP. Sigmund O. Topology Optimization: Theory, Methods and Applications. Springer: Berlin, 2003.
9. Sigmund O. Materials with prescribed constitutive parameters: an inverse homogenization problem. International Journal of Solids and Structures 1994; 31(17):2313-2329.
10. Sigmund O, Torquato S. Design of materials with extreme thermal expansion using a three-phase topology optimization method. Journal of the Mechanics and Physics of Solids 1997; 45(6):1037-1067.
11. Silva ECN, Fonseca JSO, Kikuchi N. Optimal design of piezoelectric microstructures. Computational Mechanics 1997; 19(5):397-410.
12. Fujii D, Chen BC, Kikuchi N. Composite material design of two-dimensional structures using the homogenization design method. International Journal for Numerical Methods in Engineering 2001; 50: 2031-2051.
13. Rodrigues H, Guedes JM, Bendsøe MP. Hierarchical optimisation of material and structure. Structural and Multidisciplinary Optimization 2002; 24:1-10.
14. Neves MM, Sigmund O, Bendsøe MP. Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. International Journal for Numerical Methods in Engineering 2002; 54:809-834.
15. Sutherland LS, Shenoi RA, Lewis SM. Size and scale effects in composites - I. Literature review. Composites Science and Technology 1999; 59:209-220.
16. Pecullan S, Gibiansky LV, Torquato S. Scale effects on the elastic behavior of periodic and hierarchical two-dimensional composites. Journal of the Mechanics and Physics of Solids 1999; 47:1509-1542.
17. Tantikom K, Aizawa T, Mukai T. Symmetric and asymmetric deformation transition in the regularly cell-structured materials. Part I: experimental study. International Journal of Solids and Structures 2005; 42: 2199-2210.
18. Burgueno R, Quagliata MJ, Mohanty AK, Mehta G, Drzal LT, Misra M. Hierarchical cellular designs for load-bearing biocomposite beams and plates. Materials Science and Engineering A 2005; 390(1-2):178-187.
19. Bendsøe MP, Triantafyllidis N. Scale effects in the optimal design of a microstructured medium against buckling. International Journal of Solids and Structures 1990; 26(7):725-741.
20. Nemat-Nasser S, Hori M. Micromechanics: Overall Properties of Heterogeneous Materials. Elsevier: Amsterdam, 1993.
21. Fleury C, Braibant V. Structural optimization: a new dual method using mixed variables. International Journal for Numerical Methods in Engineering 1986; 23:409-428.
22. Beckers M. Dual methods for discrete structural optimization problems. International Journal for Numerical Methods in Engineering 2000; 48:1761-1784.
23. Zhang WH, Duysinx P. Dual approach using a variant perimeter constraint and efficient sub-iteration scheme for topology optimization. Computers and Structures 2003; 81(22/23):2173-2181.
24. Michell AGM. The limit of economy of material in frame structures. Philosophical Magazine 1904; 8(6): 589-597.