Skip to main content
SpringerLink
Log in

Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

  • Research paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the independent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization interpolation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimization model based on the minimum structural compliance and the specified fiber material volume constraint has been established. The sensitivity information about the two geometrical scales design variables are also deduced considering the characteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can further explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultra-light design of the composite frame structure. The novel two geometrical scales optimization model provides a new opportunity for the design of composite structure in aerospace and other industries.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Du, S.Y.: Advanced composite materials and aerospace engineering. Acta Mater. Compos. Sin. 24, 1–12 (2007)

    Google Scholar 

  2. Chen, C.Y., Li, Z., Shi, Q., et al.: Static test method for the satellite frame structure subjected to multi-point load. J. Shanghai Jiaotong Univ. 34, 140–142 (2000)

    Google Scholar 

  3. Ibrahim, S., Polyzois, D., Hassan, S.: Development of glass fiber reinforced plastic poles for transmission and distribution lines. Can. J. Civ. Eng. 27, 850–858 (2000)

    Article  Google Scholar 

  4. Hu, B., Xue, J.X., Yan, D.Q.: Structural materials and design study for space station. Fiber Compos. 21, 60–64 (2004)

    Google Scholar 

  5. Liu, Q., Ren, Z.D., Mo, Z.L.: The research of FRP applied in the transmission tower. FRP/CM 1, 53–56 (2012)

    Google Scholar 

  6. Jensen, F.M., Falzon, B.G., Ankersen, J., et al.: Structural testing and numerical simulation of a 34m composite wind turbine blade. Compos. Struct. 76, 52–61 (2006)

    Article  Google Scholar 

  7. Bendsøe, M., Sigmund, O.: Topology Optimization—Theory, Methods, and Applications. Springer, Berlin (2003)

    MATH  Google Scholar 

  8. Dong, Y.F., Huang, H.: Truss topology optimization by using multi-point approximation and GA. Chin. J. Comput. Mech. 21, 746–751 (2004)

    Google Scholar 

  9. Sui, Y.K., Yang, D.Q., Sun, H.C.: Truss geometry optimization based on two-step method linked with sensitivity of optimal objective. Acta Mech. Sin. 29, 87–92 (1997)

    Google Scholar 

  10. Zhou, K.M., Li, J.F., Li, X.: A review on topology optimization of structures. Adv. Mech. 35, 69–76 (2005)

    Google Scholar 

  11. An, H.C., Chen, S.Y., Huang, H.: Simultaneous optimization of stacking sequences and sizing with two-level approximations and a genetic algorithm. Compos. Struct. 123, 180–189 (2015)

    Article  Google Scholar 

  12. Todoroki, A., Terada, Y.: Improved fractal branch and bound method for stacking-sequence optimizations of laminates. AIAA J. 42, 141–148 (2004)

    Article  Google Scholar 

  13. Deng, S., Pai, P.F., Lai, C.C., et al.: A solution to the stacking sequence of a composite laminate plate with constant thickness using simulated annealing algorithms. Int. J. Adv. Manuf. Technol. 26, 499–504 (2005)

    Article  Google Scholar 

  14. Aymerich, F., Serra, M.: Optimization of laminate stacking sequence for maximum buckling load using the ant colony optimization (ACO) meta heuristic. Compos. Part A 39, 262–272 (2008)

    Article  Google Scholar 

  15. Chang, N., Wang, W., Yang, W., et al.: Ply stacking sequence optimization of composite laminate by permutation discrete particle swarm optimization. Struct. Multidiscip. Optim. 41, 179–187 (2010)

    Article  MathSciNet  Google Scholar 

  16. Tsai, S.W., Pagano, N.J.: Invariant properties of composite materials. In: Composite materials workshop, p. 233 (1968)

  17. Miki, M., Sugiyamat, Y.: Optimum design of laminated composite plates using lamination parameters. AIAA J. 31, 921–922 (1993)

    Article  Google Scholar 

  18. Lund, E., Stegmann, J.: On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy 8, 109–124 (2005)

    Article  MATH  Google Scholar 

  19. Stegmann, J., Lund, E.: Discrete material optimization of general composite shell structures. Int. J. Numer. Methods Eng. 62, 2009–2027 (2005)

    Article  MATH  Google Scholar 

  20. Bruyneel, M.: SFP-a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct. Multidiscip. Optim. 43, 17–27 (2011)

    Article  Google Scholar 

  21. Gao, T., Zhang, W., Duysinx, P.: A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int. J. Numer. Methods Eng. 91, 98–114 (2012)

    Article  MATH  Google Scholar 

  22. Rodrigues, H., Guedes, J.M., Bendsoe, M.: Hierarchical optimization of material and structure. Struct. Multidiscip. Optim. 24, 1–10 (2002)

    Article  Google Scholar 

  23. Ferreira, R.T.L., Rodrigues, H.C., Guedes, J.M., et al.: Hierarchical optimization of laminated fiber reinforced composites. Compos. Struct. 107, 246–259 (2014)

    Article  Google Scholar 

  24. Liu, L., Yan, J., Cheng, G.D.: Optimum structure with homogeneous optimum truss-like material. Compos. Struct. 86, 1417–1425 (2008)

    Article  Google Scholar 

  25. Deng, J.D., Yan, J., Cheng, G.D.: Multi-objective concurrent topology optimization of thermos elastic structures composed of homogeneous porous material. Struct. Multidiscip. Optim. 47, 583–597 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  26. Huo, F., Yang, D.Q.: Laminate component method for materials selection optimum design of hybrid skeletal structures. China Sci. Pap. 8, 1179–1196 (2013)

    Google Scholar 

  27. Ni, C.H., Yan, J., Cheng, G.D., et al.: ntegrated size and topology optimization of skeletal structures with exact frequency constraints. Struct. Multidiscip. Optim. 50, 113–128 (2014)

    Article  Google Scholar 

  28. Gao, T., Zhang, W.H.: A mass constraint formulation for structural topology optimization with multiphase materials. Int. J. Numer. Methods Eng. 88, 774–796 (2011)

    Article  MATH  Google Scholar 

  29. Niu, B., Yan, J., Cheng, G.D.: Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Struct. Multidiscip. Optim. 39, 115–132 (2009)

    Article  Google Scholar 

  30. An, H.C., Chen, S.Y., Huang, H.: Laminate stacking sequence optimization with strength constraints using two-level approximations and adaptive genetic algorithm. Struct. Multidiscip. Optim. 1, 1–16 (2014)

    Google Scholar 

  31. An, H.C., Chen, S.Y., Huang, H.: Simultaneous optimization of stacking sequences and sizing with two-level approximations and a genetic algorithm. Compos. Struct. 123, 180–189 (2015)

    Article  Google Scholar 

  32. Baker, A.A.B., Kelly, D.W.: Composite materials for aircraft structures. AIAA, Reston (2004)

    Google Scholar 

  33. Duan, Z.Y., Yan, J., Niu, B., Xin, X., et al.: Design optimization of composite materials based on improved discrete materials optimization model. Acta Mater. Compos. Sin. 33, 2221–2229 (2012)

    Google Scholar 

  34. Duan, Z.Y., Yan, J., Zhao, G.Z.: Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct. Multidiscip. Optim. 51, 721–732 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  36. Gao, T., Zhang, W., Duysinx, P.: Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Struct. Multidiscip. Optim. 48, 1075–1088 (2013)

    Article  MathSciNet  Google Scholar 

  37. Hvejsel, C.F., Lund, E., Stolpe, M.: Optimization strategies for discrete multi-material stiffness optimization. Struct. Multidiscip. Optim. 44, 149–163 (2011)

    Article  Google Scholar 

  38. Guest, J.K., Prevost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int. J. Numer. Methods Eng. 61, 238–254 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. Sigmund, O.: Morphology-based black and white filters for topology optimization. Struct. Multidiscip. Optim. 33, 401–424 (2007)

    Article  Google Scholar 

  40. Bendsoe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  41. Lund, E.: Finite Element based design sensitivity analysis and optimization: Videnbasen for Aalborg Universitety VBN. Aalborg University, Denmark (1994)

    Google Scholar 

  42. Cheng, G.D., Olhoff, N.: Rigid body motion test against error in semianalytical sensitivity analysis. Comput. Struct. 6, 515–527 (1993)

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The financial support for this research was provided by the Program (Grants 11372060, 91216201) of the National Natural Science Foundation of China, Program (LJQ2015026 ) for Excellent Talents at Colleges and Universities in Liaoning Province, the Major National Science and Technology Project (2011ZX02403-002), 111 project (B14013), Fundamental Research Funds for the Central Universities (DUT14LK30), and the China Scholarship Fund.

Author information

Authors and Affiliations

  1. Dalian University of Technology, Dalian, 116024, China

    Jun Yan, Zunyi Duan & Guozhong Zhao

  2. Aalborg University, 9220, Aalborg, Denmark

    Erik Lund

Authors
  1. Jun Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zunyi Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Erik Lund
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guozhong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, J., Duan, Z., Lund, E. et al. Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model. Acta Mech. Sin. 32, 430–441 (2016). https://doi.org/10.1007/s10409-015-0485-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-015-0485-7

Keywords

Search

Navigation