Structural and Multidisciplinary Optimization

, Volume 59, Issue 3, pp 695–711 | Cite as

Robust topology optimization for multiple fiber-reinforced plastic (FRP) composites under loading uncertainties

  • Yanan Xu
  • Yunkai GaoEmail author
  • Chi Wu
  • Jianguang Fang
  • Qing Li
Research Paper


This study proposes a non-deterministic robust topology optimization of ply orientation for multiple fiber-reinforced plastic (FRP) materials, such as carbon fiber–reinforced plastic (CFRP) and glass fiber–reinforced plastic (GFRP) composites, under loading uncertainties with both random magnitude and random direction. The robust topology optimization is considered here to minimize the fluctuation of structural performance induced by load uncertainty, in which a joint cost function is formulated to address both the mean and standard deviation of compliance. The sensitivities of the cost function are derived with respect to the design variables in a non-deterministic context. The discrete material optimization (DMO) technique is extended here to accommodate robust topology optimization for FRP composites. To improve the computational efficiency, the DMO approach is revised to reduce the number of design variables by decoupling the selection of FRP materials and fiber orientations. In this study, four material design examples are presented to demonstrate the effectiveness of the proposed methods. The robust topology optimization results exhibit that the composite structures with the proper ply orientations are of more stable performance when the load fluctuates.


Robust topology optimization Non-deterministic design Load uncertainty Discrete material optimization (DMO) Ply orientation Carbon fiber–reinforced plastic (CFRP) and glass fiber–reinforced plastic (GFRP) 


Funding information

This work was supported by the National Key Research and Development Program of China (grant number 2016YFB0101602) and the National Natural Science Foundation of China (grant number 51575399).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yanan Xu
    • 1
    • 2
  • Yunkai Gao
    • 1
    • 2
    Email author
  • Chi Wu
    • 3
  • Jianguang Fang
    • 4
  • Qing Li
    • 3
  1. 1.School of Automotive StudiesTongji UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsTongji UniversityShanghaiChina
  3. 3.School of Aerospace, Mechanical and Mechatronic EngineeringThe University of SydneySydneyAustralia
  4. 4.School of Civil and Environmental EngineeringUniversity of Technology SydneySydneyAustralia

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