Isogeometric topology optimization based on energy penalization for symmetric structure

Abstract

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.

Keywords

topology optimization / moving morphable component / isogeometric analysis / energy penalization method / symmetric constraint

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (Grant Nos. 51675197 and 51705158), the National Engineering Research Center of Near-Net-Shape Forming for Metallic Materials, Ministry of Education Key Laboratory of High Efficient Near-Net-Shape Forming Technology and Equipment for Metallic Materials (Category B) Opening Foundation (Grant No. 2018005). The support is gratefully acknowledged.ƒ

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