Advertisement

Acta Mechanica Solida Sinica

, Volume 32, Issue 6, pp 698–712 | Cite as

Bi-material Topology Optimization Using Analysis Mesh-Independent Point-Wise Density Interpolation

  • Xiaoyu Suo
  • Zhan KangEmail author
  • Xiaopeng Zhang
  • Yaguang Wang
Article
First Online:
  • 46 Downloads

Abstract

This paper extends the independent point-wise density interpolation to the bi-material topology optimization to improve the structural static or dynamic properties. In contrast to the conventional elemental density-based topology optimization approaches, this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain. To be specific, the density design variable points can be freely positioned, independently of the field points used for discretization of the displacement field. By this means, a material interface description of relatively high quality can be achieved, even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain. Numerical examples, regarding the minimum static compliance design and the maximum fundamental eigen-frequency design, are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques. It is shown that this method is free of numerical difficulties such as checkerboard patterns and the “islanding” phenomenon.

Keywords

Topology optimization Bi-material Independent point-wise density interpolation Topology description Material interface Dynamic topology optimization 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The financial support of the National Natural Science Foundation of China (11425207, U1508209) is gratefully acknowledged.

References

  1. 1.
    Bendsøe MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng. 1988;71:197–224.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bendsøe MP. Optimal shape design as a material distribution problem. Struct Optim. 1989;1:193–202.CrossRefGoogle Scholar
  3. 3.
    Rozvany GI, Zhou M, Birker T. Generalized shape optimization without homogenization. Struct Optim. 1992;4:250–2.CrossRefGoogle Scholar
  4. 4.
    Bendsøe MP, Sigmund O. Material interpolation schemes in topology optimization. Arch Appl Mech. 1999;69:635–54.CrossRefGoogle Scholar
  5. 5.
    Xie Y, Steven G. Evolutionary structural optimization for dynamic problems. Comput Struct. 1996;58:1067–73.CrossRefGoogle Scholar
  6. 6.
    Allaire G, Jouve F, Toader AM. Structural optimization using sensitivity analysis and a level-set method. J Comput Phys. 2004;194:363–93.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang MY, Wang X, Guo D. A level set method for structural topology optimization. Comput Methods Appl Mech Eng. 2003;192:227–46.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Luo Z, Wang MY, Wang S, Wei P. A level set-parameterization method for structural shape and topology optimization. Int J Numer Methods Eng. 2008;76:1–26.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Luo Z, Tong L, Kang Z. A level set method for structural shape and topology optimization using radial basis functions. Comput Struct. 2009;87:425–34.CrossRefGoogle Scholar
  10. 10.
    Zhou S, Li W, Li Q. Level-set based topology optimization for electromagnetic dipole antenna design. J Comput Phys. 2010;229:6915–30.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bruns TE. Topology optimization of convection-dominated, steady-state heat transfer problems. Int J Heat Mass Transf. 2007;50:2859–73.CrossRefGoogle Scholar
  12. 12.
    Jeong SH, Choi DH, Yoon GH. Fatigue and static failure considerations using a topology optimization method. Appl Math Model. 2015;39:1137–62.CrossRefGoogle Scholar
  13. 13.
    Makihara K, Takezawa A, Shigeta D, Yamamoto Y. Power evaluation of advanced energy-harvester using graphical analysis. Mech Eng J. 2015;2:14–00444.CrossRefGoogle Scholar
  14. 14.
    Thomsen J. Topology optimization of structures composed of one or two materials. Struct Optim. 1992;5:108–15.CrossRefGoogle Scholar
  15. 15.
    Sigmund O. Design of multiphysics actuators using topology optimization-part II: two-material structures. Comput Methods Appl Mech Eng. 2001;190:6605–27.CrossRefGoogle Scholar
  16. 16.
    Luo Y, Kang Z. Layout design of reinforced concrete structures using two-material topology optimization with Drucker–Prager yield constraints. Struct Multidiscip Optim. 2013;47:95–110.MathSciNetCrossRefGoogle Scholar
  17. 17.
    Sun S, Zhang W. Multiple objective topology optimal design of multiphase microstructures. Acta Mech Sin. 2006;38:633–8.Google Scholar
  18. 18.
    Sun S, Zhang W. Investigation of perimeter control methods for structural topology optimization with multiphase materials. Hangkong Xuebao/Acta Aeronautica et Astronautica Sinica. 2006;27:963–8.Google Scholar
  19. 19.
    Molter A, Fonseca J, Fernandez L. Simultaneous topology optimization of structure and piezoelectric actuators distribution. Appl Math Model. 2016;40:5576–88.MathSciNetCrossRefGoogle Scholar
  20. 20.
    Gao T, Zhang W. A mass constraint formulation for structural topology optimization with multiphase materials. Int J Numer Methods Eng. 2011;88:774–96.CrossRefGoogle Scholar
  21. 21.
    Stegmann J, Lund E. Discrete material optimization of general composite shell structures. Int J Numer Methods Eng. 2005;62:2009–27.CrossRefGoogle Scholar
  22. 22.
    Long K, Wang X, Gu X. Multi-material topology optimization for the transient heat conduction problem using a sequential quadratic programming algorithm. Eng Optim. 2018;50:2091–107.MathSciNetCrossRefGoogle Scholar
  23. 23.
    Huang X, Xie Y. Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech. 2009;43:393–401.MathSciNetCrossRefGoogle Scholar
  24. 24.
    Radman A, Huang X, Xie Y. Topological design of microstructures of multi-phase materials for maximum stiffness or thermal conductivity. Comput Mater Sci. 2014;91:266–73.CrossRefGoogle Scholar
  25. 25.
    Sethian JA, Wiegmann A. Structural boundary design via level set and immersed interface methods. J Comput Phys. 2000;163:489–528.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wang MY, Wang X. Color level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng. 2004;193:469–96.MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zhou P, Du J, Lü Z. A generalized DCT compression based density method for topology optimization of 2D and 3D continua. Comput Methods Appl Mech Eng. 2018;334:1–21.MathSciNetCrossRefGoogle Scholar
  28. 28.
    Antonietti PF, Bruggi M, Scacchi S, Verani M. On the virtual element method for topology optimization on polygonal meshes: a numerical study. Comput Math Appl. 2017;74(5):1091–109.MathSciNetCrossRefGoogle Scholar
  29. 29.
    Kang Z, Wang Y. Structural topology optimization based on non-local Shepard interpolation of density field. Comput Methods Appl Mech Eng. 2011;200:3515–25.MathSciNetCrossRefGoogle Scholar
  30. 30.
    Kang Z, Wang Y. A nodal variable method of structural topology optimization based on Shepard interpolant. Int J Numer Methods Eng. 2012;90:329–42.MathSciNetCrossRefGoogle Scholar
  31. 31.
    Wang Y, Kang Z, He Q. Adaptive topology optimization with independent error control for separated displacement and density fields. Comput Struct. 2014;135:50–61.CrossRefGoogle Scholar
  32. 32.
    He Q, Kang Z, Wang Y. A topology optimization method for geometrically nonlinear structures with meshless analysis and independent density field interpolation. Comput Mech. 2014;54:629–44.MathSciNetCrossRefGoogle Scholar
  33. 33.
    Pedersen NL. Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim. 2000;20:2–11.CrossRefGoogle Scholar
  34. 34.
    Jensen JS. Topology optimization of dynamics problems with Padé approximants. Int J Numer Methods Eng. 2007;72:1605–30.CrossRefGoogle Scholar
  35. 35.
    Svanberg K. The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng. 1987;24:359–73.MathSciNetCrossRefGoogle Scholar
  36. 36.
    Du J, Olhoff N. Minimization of sound radiation from vibrating bi-material structures using topology optimization. Struct Multidiscip Optim. 2007;33:305–21.CrossRefGoogle Scholar
  37. 37.
    Pedersen NL, Nielsen AK. Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling. Struct Multidiscip Optim. 2003;25:436–45.CrossRefGoogle Scholar
  38. 38.
    Jensen JS, Pedersen NL. On maximal eigenfrequency separation in two-material structures: the 1D and 2D scalar cases. J Sound Vib. 2006;289:967–86.CrossRefGoogle Scholar
  39. 39.
    Gao T, Zhang W. A mass constraint formulation for structural topology optimization with multiphase materials. Int J Numer Methods Eng. 2011;88(8):774–96.CrossRefGoogle Scholar
  40. 40.
    Luo Y, Kang Z, Yue Z. Maximal stiffness design of two-material structures by topology optimization with nonprobabilistic reliability. AIAA J. 2012;50:1993–2003.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  • Xiaoyu Suo
    • 1
    • 2
  • Zhan Kang
    • 1
    Email author
  • Xiaopeng Zhang
    • 1
  • Yaguang Wang
    • 1
  1. 1.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianChina
  2. 2.The 41st Institute of the Sixth Academy of China Aerospace Science & Industry CorporationHohhotChina

Personalised recommendations

Cite article

Buy options