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Stress-based topology optimization with the parameterized level-set method based on radial basis functions

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Abstract

Based on the parameterized level-set method using radial basis functions, a topology optimization method is proposed that can account for stress minimization and stress-constraint problems. First, the mathematical models of stress minimization and stress-constraint problems are separately established. In the mathematical model, the p-norm function is used as a stress aggregation function for both of the problems, and for the stress-constraint problem, the adaptive scaling constraint method to measure maximum stress in the structure is used. The shape derivative is then used to obtain the normal velocities in the parameterized level-set method, and an improved strategy based on weighted least square method is proposed to smooth the normal velocities at every nodal point in the design area in order to match the velocity in parameterized level-set method. Subsequently, an augmented Lagrange multiplier is given to make the transitions of both optimization problems stable during the convergence process. Finally, the effectiveness and efficiency of the proposed optimization method in solving stress minimization and stress-constraint problems are demonstrated through several classical numerical examples.

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Acknowledgements

The authors thank Professor Peng Wei et al. for providing the 88-line MATLAB source code for the parameterized level-set method based on topology optimization using radial basis functions.

Funding

The authors would like to deeply appreciate the support from the National Natural Sciences Foundation of China (U2067220, 51779139), Shanghai Talent Development Funding (2018029), the Young Talent Project of China National Nuclear Corporation and Top Young Talents of Ten Thousand Talents Plan.

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Authors and Affiliations

  1. State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Yuanteng Jiang & Min Zhao

  2. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration (CISSE), Shanghai, 200240, China

    Min Zhao

Authors
  1. Yuanteng Jiang
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  2. Min Zhao
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Correspondence to Min Zhao.

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Responsible Editor: Xiaojia Shelly Zhang

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Jiang, Y., Zhao, M. Stress-based topology optimization with the parameterized level-set method based on radial basis functions. Struct Multidisc Optim 65, 224 (2022). https://doi.org/10.1007/s00158-022-03313-x

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