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XFEM schemes for level set based structural optimization

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Abstract

In this paper, some elegant extended finite element method (XFEM) schemes for level set method structural optimization are proposed. Firstly, two-dimension (2D) and three-dimension (3D) XFEM schemes with partition integral method are developed and numerical examples are employed to evaluate their accuracy, which indicate that an accurate analysis result can be obtained on the structural boundary. Furthermore, the methods for improving the computational accuracy and efficiency of XFEM are studied, which include the XFEM integral scheme without quadrature sub-cells and higher order element XFEM scheme. Numerical examples show that the XFEM scheme without quadrature sub-cells can yield similar accuracy of structural analysis while prominently reducing the time cost and that higher order XFEM elements can improve the computational accuracy of structural analysis in the boundary elements, but the time cost is increasing. Therefore, the balance of time cost between FE system scale and the order of element needs to be discussed. Finally, the reliability and advantages of the proposed XFEM schemes are illustrated with several 2D and 3D mean compliance minimization examples that are widely used in the recent literature of structural topology optimization. All numerical results demonstrate that the proposed XFEM is a promising structural analysis approach for structural optimization with the level set method.

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Authors and Affiliations

  1. Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China

    Li Li & Michael Yu Wang

  2. School of Mechatronics Engineering and Automation, Shanghai University, Shanghai, 200072, China

    Li Li

  3. State Key Laboratory of Subtropical Building Science, School of Civil Engineering and Transportation, South China University of Technology, Guangzhou, 510641, China

    Peng Wei

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  1. Li Li
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  2. Michael Yu Wang
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  3. Peng Wei
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Correspondence to Michael Yu Wang.

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Li, L., Wang, M.Y. & Wei, P. XFEM schemes for level set based structural optimization. Front. Mech. Eng. 7, 335–356 (2012). https://doi.org/10.1007/s11465-012-0351-2

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  • DOI: https://doi.org/10.1007/s11465-012-0351-2

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