Structural and Multidisciplinary Optimization

, Volume 59, Issue 2, pp 647–658 | Cite as

Evolutionary topology optimization of continuum structures with stress constraints

  • Zhao Fan
  • Liang XiaEmail author
  • Wuxing Lai
  • Qi Xia
  • Tielin Shi
Research Paper


In this work, we propose to extend the bi-directional evolutionary structural optimization (BESO) method for compliance minimization design subject to both constraints on volume fraction and maximum von Mises stress. To this end, the aggregated p-norm global stress measure is first adopted to approximate the maximum stress. The conventional compliance design objective is augmented with p-norm stress measures by introducing one or multiple Lagrange multipliers. The Lagrange multipliers are employed to yield compromised designs of the compliance and the p-norm stress. An empirical scheme is developed for the determination of the Lagrange multipliers such that the maximum von Mises stress could be effectively constrained through the controlling of the aggregated p-norm stress. To further enforce the satisfaction of stress constraints, the stress norm parameter p is assigned to a higher value after attaining the objective volume. The update of the binary design variables lies in the computationally efficient sensitivity numbers derived using the adjoint method. A series of comparison studies has been conducted to validate the effectiveness of the method on several benchmark design problems.


Topology optimization Stress constraint BESO Multiple constraints 


Funding information

This work is supported by the National Natural Science Foundation of China (51705165, 51405170, 51790171, 5171101743) and the Natural Science Foundation for Distinguished Young Scholars of Hubei province of China (2017CFA044).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Digital Manufacturing Equipment and TechnologyHuazhong University of Science and TechnologyWuhanChina

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