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Truncated hierarchical B-spline–based topology optimization

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Abstract

This work presents a truncated hierarchical B-spline–based topology optimization (THB-TO) to address topology optimization (TO) for both minimum compliance and compliant mechanism. The sensitivity and density filters with a lower bound are adaptively consistent with the hierarchical levels of active elements to remove the checkboard pattern and reduce the gray transition area. By means of the maximum variation of design variables on two consecutive iterative steps and the density differences of adjacent active elements, a mark strategy is established, which triggers the hierarchical local refinement and identifies the elements to be refined during the course of THB-TO. Besides, a locally refined design space is constructed in terms of the parent–child relationship of the cells on consecutive hierarchical levels. Numerical examples are used to verify the effectiveness of the proposed THB-TO, where the resolution around the boundary of the optimized designs can be effectively improved by THB-TO. Compared with global refinement, the number of degree of freedoms (DOFs) and design variables are largely decreased for 2D and 3D cases by THB-TO, which demonstrates that the proposed THB-TO is a promising approach to solving 2D and 3D TO problems.

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Funding

This work has been supported by National Natural Science Foundation of China (No. 51675197, No. 51705158), the Fundamental Research Funds for the Central Universities (No. 2018MS45), and OpenFunds of National Engineering Research Centerof Near-Net-Shape Forming for Metallic Materials(No. 2018005).

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Authors and Affiliations

  1. School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Xianda Xie, Shuting Wang, Ning Jiang, Wei Zhao & Manman Xu

  2. National Engineering Research Center of Novel Equipment for Polymer Processing, Key Laboratory of Polymer Processing Engineering, Ministry of Education, Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing, South China University of Technology, Guangzhou, 510641, China

    Yingjun Wang

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  1. Xianda Xie
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  2. Shuting Wang
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  3. Yingjun Wang
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Correspondence to Shuting Wang or Yingjun Wang.

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Replication of results

The proposed framework is built on the truncated hierarchical B-spline and classical SIMP method, the combination of which has been fully expounded in this work, so the results can be easily reproduced. Moreover, the opening the source code of the proposed method is banned by a project.

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Xie, X., Wang, S., Wang, Y. et al. Truncated hierarchical B-spline–based topology optimization. Struct Multidisc Optim 62, 83–105 (2020). https://doi.org/10.1007/s00158-019-02476-4

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