Engineering with Computers

, Volume 35, Issue 1, pp 21–33 | Cite as

Maximizing the first eigenfrequency of structures subjected to uniform boundary erosion through the level set method

  • Zhenhua Li
  • Tielin Shi
  • Liang Xia
  • Qi XiaEmail author
Original Article


Erosion of structure may result in non-trivial loss of performance. For instance, erosion may make structure members break apart and results in localized vibration eigenmodes, which will make the first eigenfrequency of eroded structure become smaller. To obtain a robust design whose first eigenfrequency is not disproportionately affected by boundary erosion, we first examine a generic deterministic structural optimization problem defined in the level-set framework. Relying on the analysis of the first-order shape derivative and the optimality conditions, several important conclusions are obtained. Then, the optimization problem of maximizing the first eigenfrequency of structures subjected to uniform erosion is introduced. In each iteration of optimization, erosion is intentionally created, and a mode recognition technique is employed to identify the actual first eigenfrequency, i.e., not belonging to localized eigenmodes. The boundary of the un-eroded structure is optimized to improve the performance of the eroded structure. The shape derivative defined on the boundary of the eroded structure is mapped to the boundary of the un-eroded one by resorting to velocity extension of the level set method.


Robust topology optimization Eroded boundary Level set Eigenfrequency maximization 



This research work is supported by the National Natural Science Foundation of China (Grant No. 51575203) and the Natural Science Foundation for Distinguished Young Scholars of Hubei province of China (Grant No. 2017CFA044).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

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

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