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Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures

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Abstract

An alternative strain energy method is proposed for the prediction of effective elastic properties of orthotropic materials in this paper. The method is implemented in the topology optimization procedure to design cellular solids. A comparative study is made between the strain energy method and the well-known homogenization method. Numerical results show that both methods agree well in the numerical prediction and sensitivity analysis of effective elastic tensor when homogeneous boundary conditions are properly specified. Two dimensional and three dimensional microstructures are optimized for maximum stiffness designs by combining the proposed method with the dual optimization algorithm of convex programming. Satisfactory results are obtained for a variety of design cases.

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References

  1. Bensoussan A., Lions J.L. and Papanicolaou G. (1978). Asymptotic Analysis for Periodic structures. North Holland, Amsterdam

    MATH  Google Scholar 

  2. Fazekas A., Dendieveel R., Salvo L. and Bréchet Y. (2002). Effect of microstructural topology upon the stiffness and strength of 2D cellular structures. Int. J. Mech. Sci. 44: 2047–2066

    Article  MATH  Google Scholar 

  3. Hashin Z. (1983). Analysis of composite materials. J. Appl. Mech. T ASME 50: 481–505

    Article  MATH  Google Scholar 

  4. Hassani B. and Hinton E. (1998). A review of homogenization and topology optimization II—analytical and numerical solution of homogenization equations. Comput. Struct. 69: 719–738

    Article  Google Scholar 

  5. Hazanov S. (1998). Hill condition and overall properties of composites. Arch. Appl. Mech. 68: 385–394

    Article  MATH  Google Scholar 

  6. Hohe J. and Becker W. (2002). Effective stress-strain relations for two-dimensional cellular sandwich cores: Homogenization, material models and properties. Appl. Mech. Rev. 55(1): 61–87

    Article  Google Scholar 

  7. Kalamkarov A.L. and Georgiades A.V. (2002). Modeling of smart composites on account of actuation, thermal conductivity and hygroscopic absorption. Compos. Part B-Eng. 33: 141–152

    Article  Google Scholar 

  8. Nemat-Nasser S. and Hori M. (1993). Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland, London

    MATH  Google Scholar 

  9. Sanchez-Palencia E. (1980). Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer, Heidelberg

    Google Scholar 

  10. Vigdergauz S. (2001). The effective properties of a perforated elastic plate. Numerical optimization by genetic algorithm. Int. J. Solids Struct. 38: 8593–8616

    Article  MATH  Google Scholar 

  11. Gibson L.J. and Ashby M.F. (1997). Cellular Solids: Structure and Properties. Cambridge University Press, Cambridge

    Google Scholar 

  12. Sigmund O. (1994). Materials with prescribed constitutive parameters: an inverse homogenization problem. Int. J. Solids Struct. 31(17): 2313–2329

    Article  MATH  MathSciNet  Google Scholar 

  13. Sigmund O. (1995). Tailoring materials with prescribed elastic properties. Mech. Mater. 20(4): 351–368

    Article  MathSciNet  Google Scholar 

  14. Silva E., Nishiwaki S., Fonseca J. and Kikuchi N. (1999). Optimization methods applied to material and flextensional actuator design using the homogenization method. Comput. Method Appl. M 172: 241–271

    Article  MATH  MathSciNet  Google Scholar 

  15. Neves M.M., Sigmund O. and Bendsoe M.P. (2002). Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. Struct. Multidiscip. O 54: 809–834

    MATH  MathSciNet  Google Scholar 

  16. Pedersen N. (2000). Maximization of eigenvalue using topology optimization. Struct. Multidiscip O 20(1): 2–11

    Article  Google Scholar 

  17. Sigmund O. and Torquato S. (1997). Design of materials with extreme thermal expansion using a three-phase topology optimization method. J. Mech. Phys. Solids 45: 1037–1067

    Article  MathSciNet  Google Scholar 

  18. Zhang W.H. and Duysinx P. (2003). Dual approach using a variant perimeter constraint and efficient sub-iteration scheme for topology optimization. Comput. Struct. 81(22/23): 2173–2181

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Mechatronic Engineering, Northwestern Polytechnical University, Xi’an, 710072, China

    Weihong Zhang, Gaoming Dai, Fengwen Wang & Shiping Sun

  2. FEMTO-ST, Department of LMARC, UMR—CNRS 6174, 25000, Besancon, France

    Hicham Bassir

Authors
  1. Weihong Zhang
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  2. Gaoming Dai
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  3. Fengwen Wang
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  4. Shiping Sun
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  5. Hicham Bassir
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Corresponding author

Correspondence to Weihong Zhang.

Additional information

The project supported by the National Natural Science Foundation of China (10372083, 90405016), 973 Program (2006CB601205) and the Aeronautical Science Foundation (04B53080). The English text was polished by Keren Wang.

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Zhang, W., Dai, G., Wang, F. et al. Using strain energy-based prediction of effective elastic properties in topology optimization of material microstructures. Acta Mech Sin 23, 77–89 (2007). https://doi.org/10.1007/s10409-006-0045-2

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  • DOI: https://doi.org/10.1007/s10409-006-0045-2

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