The parameterized level set method for structural topology optimization with shape sensitivity constraint factor

  • Mingtao CuiEmail author
  • Chenchun Luo
  • Guang Li
  • Min Pan
Original Article


In recent years, the parameterized level set method (PLSM) has attracted widespread attention for its good stability, high efficiency and the smooth result of topology optimization compared with the conventional level set method. In the PLSM, the radial basis functions (RBFs) are often used to perform interpolation fitting for the conventional level set equation, thereby transforming the iteratively updating partial differential equation (PDE) into ordinary differential equations (ODEs). Hence, the RBFs play a key role in improving efficiency, accuracy and stability of the numerical computation in the PLSM for structural topology optimization, which can describe the structural topology and its change in the optimization process. In particular, the compactly supported radial basis function (CS-RBF) has been widely used in the PLSM for structural topology optimization because it enjoys considerable advantages. In this work, based on the CS-RBF, we propose a PLSM for structural topology optimization by adding the shape sensitivity constraint factor to control the step length in the iterations while updating the design variables with the method of moving asymptote (MMA). With the shape sensitivity constraint factor, the updating step length is changeable and controllable in the iterative process of MMA algorithm so as to increase the optimization speed. Therefore, the efficiency and stability of structural topology optimization can be improved by this method. The feasibility and effectiveness of this method are demonstrated by several typical numerical examples involving topology optimization of single-material and multi-material structures.


Compactly supported radial basis function Parameterized level set method Shape sensitivity constraint factor MMA algorithm Structural topology optimization 



This work was supported by the Project of China Scholarship Council (201506965015). The authors are also grateful to the anonymous reviewers for their valuable suggestions for improving the manuscript.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechano-electronic EngineeringXidian UniversityXi’anPeople’s Republic of China
  2. 2.Department of Mechanical EngineeringMcGill UniversityMontrealCanada

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