An Efficient Strategy for Non-probabilistic Reliability-Based Multi-material Topology Optimization with Evidence Theory

  • Qinghai Zhao
  • Hongxin ZhangEmail author
  • Tiezhu Zhang
  • Qingsong Hua
  • Lin Yuan
  • Wenyue Wang


It is essential to consider the effects of incomplete measurement, inaccurate information and inadequate cognition on structural topology optimization. For the multi-material structural topology optimization with non-probability uncertainty, the multi-material interpolation model is represented by the ordered rational approximation of material properties (ordered RAMP). Combined with structural compliance minimization, the multi-material topology optimization with reliability constraints is established. The corresponding non-probability uncertainties are described by the evidence theory, and the uniformity processing method is introduced to convert the evidence variables into random variables. The first-order reliability method is employed to search the most probable point under the reliability index constraint, and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information. Therefore, the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format, followed by the ordered RAMP method to solve the optimization problem. Finally, through numerical examples of 2D and 3D structures, the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.


Multi-material Topology optimization Non-probabilistic Reliability Evidence theory 



This work is supported by the Natural Science Foundation of China (Grant No. 51705268), Shandong Provincial Natural Science Foundation, China (Grant No. ZR2016EEB20), and China Postdoctoral Science Foundation Funded Project (Grant No. 2017M612191). The authors are thankful to the anonymous reviewers for their helpful and constructive comments.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2019

Authors and Affiliations

  1. 1.National and Local Union Engineering Research Center of Electric Vehicle Intelligent Power Integration TechnologyQingdao UniversityQingdaoChina
  2. 2.Mechanical and Electrical CollegeQingdao UniversityQingdaoChina

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