Optimization of material distribution in functionally graded structures with stress constraints

Communications in Numerical Methods in Engineering

Volumn 23, Issue 6, 2007, Pages 535-551

  Stump, Fernando V ^a   Silva, Emílio C N ^a   Paulino, Glaucio H ^b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

Functionally graded materials; Stress constraint; Topology optimization

Indexed keywords

APPROXIMATION ALGORITHMS; FINITE ELEMENT METHOD; INTERPOLATION; MICROSTRUCTURE; SHAPE OPTIMIZATION; STRESS CONCENTRATION; STRUCTURAL DESIGN;

MATERIAL DISTRIBUTION; STRESS CONSTRAINT;

FUNCTIONALLY GRADED MATERIALS;

APPROXIMATION ALGORITHMS; FINITE ELEMENT METHOD; FUNCTIONALLY GRADED MATERIALS; INTERPOLATION; MICROSTRUCTURE; SHAPE OPTIMIZATION; STRESS CONCENTRATION; STRUCTURAL DESIGN;

EID: 34250355959     PISSN: 10698299     EISSN: 10990887     Source Type: Journal    
DOI: 10.1002/cnm.910     Document Type: Conference Paper

References (36)

1. Cho JR, Choi JH. A yield-criteria tailoring of the volume fraction in metal-ceramic functionally graded material. European Journal of Mechanics - A/Solids 2004; 23(2):271-281.
2. Durodola JF, Attia O. Deformation and stresses in functionally graded rotating disks. Composites Science and Technology 2000; 60(7):987-995.
3. Horgan CO, Chan AM. The stress response of functionally graded isotropic linearly elastic rotating disks. Journal of Elasticity 1999; 55(3):219-230.
4. Turteltaub S. Functionally graded materials for prescribed field evolution. Computer Methods in Applied Mechanics and Engineering 2002; 191(21-22):2283-2296.
5. Paulino GH, Silva ECN. Design of functionally graded structures using topology optimization. Materials Science Forum 2005; 492-493:435-440.
6. Stump FV. Otimização topológica aplicada ao projeto de estruturas tradicionais e estruturas com gradação funcional sujeitas a restrição de tensão. MS Thesis, Universidade de São Paulo, Brazil, 2006.
7. 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.
8. Bendsøe MP, Sigmund O. Topology Optimization: Theory Methods and Applications. Springer: Berlin, 2003.
9. Duysinx P, Bendsøe MP. Topology optimization of continuum structures with local stress constraints. International Journal for Numerical Methods in Engineering 1998; 43(8):1453-1478.
10. Sved G, Ginos Z. Structural optimization under multiple loading. International Journal of Mechanical Sciences 1968; 10(10):803-805.
11. Pereira JT, Fancello EA, Barcellos CS. Topology optimization of continuum structures with material failure constraints. Structural and Multidisciplinary Optimization 2004; 26(1-2):50-66.
12. Yang RJ, Chen CJ. Stress-based topology optimization. Structural Optimization 1996; 12(2-3):98-105.
13. Cheng GD, Guo X. ε-Relaxed approach in structural topology optimization. Structural Optimization 1997; 13(4):258-266.
14. Allaire G. Shape Optimization by the Homogenization Method. Series: Applied Mathematical Sciences, vol. 146. Springer: New York, 2002.
15. Torquato S. Random Heterogeneous Materials: Microstucture and Macroscopic Properties. Series: Interdisciplinary Applied Mathematics, vol. 16. Springer: New York, 2002.
16. Matsui K, Terada K. Continuous approximation of material distribution for topology optimization. International Journal for Numerical Methods in Engineering 2004; 59(14):1925-1944.
17. Rahmatalla S, Swan CC. Form finding of sparse structures with continuum topology optimization. Journal of Structural Engineering (ASCE) 2003; 129(12):1707-1716.
18. Kim JH, Paulino GH. Isoparametric graded finite elements for nonhomogeneous isotropic and orthotropic materials. Journal of Applied Mechanics - Transactions of the ASME 2002; 69(4):502-514.
19. Hashin Z, Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. Journal of the Mechanics and Physics of Solids 1963; 11:127-140.
20. Zuiker J, Dvorak G. The effective properties of functionally graded composites. I. Extension of the Mori-Tanaka method to linearly varying fields. Composites Engineering 1994; 4:19-35.
21. Reiter T, Dvorak GJ, Tvergaard V. Micromechanical models for graded composite materials. Journal of the Mechanics and Physics of Solids 1997; 45:1281-1302.
22. Reiter T, Dvorak GJ. Micromechanical models for graded composite materials: II. Thermomechanical loading. Journal of the Mechanics and Physics of Solids 1998; 46(9):1655-1673.
23. Tanaka K, Watanabe H, Sugano Y, Poterasu V. A multicriterial material tailoring of a hollow cylinder in functionally gradient materials: scheme to global reduction of thermoelastic stresses. Computer Methods in Applied Mechanics and Engineering 1996; 135(3-4):369-380.
24. Kim JH, Paulino GH. An accurate scheme for mixed-mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models. International Journal for Numerical Methods in Engineering 2003; 58(10):1457-1497.
25. Zuiker JR. Functionally graded materials: choice of micromechanics model and limitations in property variation. Composites Engineering 1995; 5:807-819.
26. Aboudi J, Pindera MJ, Arnold SM. Higher-order theory for functionally graded materials. Composites Part B - Engineering 1999; 30(8):777-832.
27. Yin HM, Sun LZ, Paulino GH. Micromechanics-based elastic model for functionally graded materials with particle interactions. Acta Materialia 2004; 52(12):3535-3543.
28. Benveniste Y. A new approach to the application of Mori-Tanaka's theory in composite materials. Mechanics of Materials 1987; 6:147-157.
29. Lipton R. Design of functionally graded composite structures in the presence of stress constraints. International Journal of Solids and Structures 2002; 39(9):2575-2586.
30. Allaire G, Jouve F, Maillot H. Topology optimization for minimum stress design with the homogenization method. Structural and Multidisciplinary Optimization 2004; 28(2-3):87-98.
31. Swan CC, Kosaka I. Voigt-Reuss topology optimization for structures with linear elastic material behaviours. International Journal for Numerical Methods in Engineering 1997; 40(16):3033-3057.
32. Swan CC, Kosaka I. Voigt-Reuss topology optimization for structures with nonlinear material behaviours. International Journal for Numerical Methods in Engineering 1997; 40(20):3785-3814.
33. Vanderplaats GN. Numerical Optimization Techniques for Engineering Design. Mcgraw-Hill: New York, 2002.
34. Cardoso EL. Controle de complexidade na otimização topológica de estruturas contínuas. MS Thesis, Universidade Federal do Rio Grande do Sul, Brazil, 2000.
35. Liu JS, Parks GT, Clarkson PJ. Optimization of turbine disk profiles by metamorphic development. Journal of Mechanical Design 2002; 124(2):192-200.
36. Ashby MF. Materials Selection in Mechanical Design. Butterworth-Heinemann: Stoneham, MA, 1999.