Abstract
This paper presents a computationally efficient multi-resolution topology optimization framework by establishing a novel bi-directional evolutionary structure optimization (BESO) method based on extended finite element method (XFEM). In the proposed framework, the high-resolution designs preserving the topological complexity can be obtained with low degree of freedoms (DOFs). The implementation of the presented multi-resolution optimization framework takes good use of the ability of XFEM at accurately modeling material discontinuities within one element. On the basis of XFEM, a strategy of triangulated partition and a new material interpolation model are introduced to represent the finer material distribution. We employ the coarser finite element (FE) mesh to perform the finite element analysis, the sub-parts partitioned from finite elements to describe material properties and the nodal design variables to perform the optimization. To circumvent artificially stiff patterns, a modified sensitivity filter is applied to regularize the solution. The effectiveness and high efficiency of the presented approach are highlighted by typical 2D and 3D examples.
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Funding
This work was supported by the Key Program of National Natural Science Foundation of China (No. 11832009), the National Natural Science Foundation of China (No.11672104, 11902085), and the Chair Professor of Lotus Scholars Program in Hunan province (No.XJT2015408).
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The presented approach is a part of a new project such that we can not provide the source code. But, in order to help readers to reproduce the results, we attach the main framework of the source codes in the appendix. At the same time, numerical data for plots corresponding to Figs. 11, 15, 17, 19 and 20 are provided as supplementary material. Then, if the information provided in the paper is not sufficient, the readers can contact the authors for further explanations.
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Appendix
Appendix
Main framework of the source code (referring to the paper of Andreassen et al. 2011)
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Wang, H., Liu, J. & Wen, G. An efficient evolutionary structural optimization method for multi-resolution designs. Struct Multidisc Optim 62, 787–803 (2020). https://doi.org/10.1007/s00158-020-02536-0
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DOI: https://doi.org/10.1007/s00158-020-02536-0