Structural and Multidisciplinary Optimization

, Volume 56, Issue 4, pp 865–884 | Cite as

A novel displacement constrained optimization approach for black and white structural topology designs under multiple load cases

  • Jian Hua Rong
  • Liaohong Yu
  • Xuan Pei Rong
  • Zhi Jun Zhao


The gray problem of displacement constrained topology volume minimization under multiple load cases still is an opening topic of research. A series of topologies with clear profiles generated from an optimization process are very beneficial to method engineering applications. In this paper, a novel displacement constrained optimization approach for black and white structural topology designs under multiple load cases, is proposed to obtain a series of topologies with clear profiles. Firstly, a distribution feature of constraint displacement derivatives is investigated. Secondly, an adaptive adjusting approach of design variable bounds is proposed, and an improved approximate model with varied constraint limits and a volume penalty objective function are constructed. Thirdly, an improved density-based optimization method is proposed for the displacement constrained topology volume minimization under multiple load cases. Finally, several examples are given to demonstrate that the results obtained by the proposed method provide a series of topologies with clear profiles during an optimization process. It is concluded from examples that the proposed method is effective and robust for generating an optimal topology.


Structural topology optimization Feasible domain adjustment Trust region Multiple constraints Dual algorithm 



This work is supported by the National Natural Science Foundation of China (11372055 and 11302033). Very thanks reviewers for their comments on the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Jian Hua Rong
    • 1
    • 2
  • Liaohong Yu
    • 1
    • 3
  • Xuan Pei Rong
    • 1
    • 2
  • Zhi Jun Zhao
    • 2
    • 4
  1. 1.School of Automotive and Mechanical EngineeringChangsha University of Science and TechnologyChangshaPeople’s Republic of China
  2. 2.Key Laboratory of Lightweight and Reliability Technology for Engineering VehicleCollege of Hunan ProvinceChangshaChina
  3. 3.School of Physical Science and TechnologyYichun UniversityYichunPeople’s Republic of China
  4. 4.Department of Civil EngineeringChangsha UniversityChangshaPeople’s Republic of China

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