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Shape optimization of axisymmetric solids with the finite cell method using a fixed grid

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Abstract

In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion. Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant 51275424), 973 Program (Grant 2011CB610304), Research Fund for the Doctoral Program of Higher Education of China (Grant 20126102130003) and the opening project (Grant KFJJ13-6M) of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology). The first author is greatly thankful to Professor Piotr BREITKOPF, Université de Technologie de Compiègne, France.

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  1. Engineering Simulation and Aerospace Computing (ESAC), Northwestern Polytechnical University, Xi’an, 710072, China

    Liang Meng, Wei-Hong Zhang, Ji-Hong Zhu, Zhao Xu & Shou-Hu Cai

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  1. Liang Meng
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  2. Wei-Hong Zhang
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  3. Ji-Hong Zhu
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  4. Zhao Xu
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  5. Shou-Hu Cai
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Correspondence to Ji-Hong Zhu.

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Meng, L., Zhang, WH., Zhu, JH. et al. Shape optimization of axisymmetric solids with the finite cell method using a fixed grid. Acta Mech. Sin. 32, 510–524 (2016). https://doi.org/10.1007/s10409-015-0549-8

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  • DOI: https://doi.org/10.1007/s10409-015-0549-8

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