Partition Density Modified Sensitivity Filtering Method for Topology Optimization of Continuum Structure
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摘要: 变密度法因设计变量少、效率高等优点，已成为解决连续体结构拓扑优化问题的一种有效方法。传统变密度法在优化过程中常出现数值不稳定问题，其优化结果常具有灰度单元，使得优化模型提取较为困难。Sigmund敏度过滤方法虽然能有效减少数值不稳定现象，但该方法容易产生边界扩散的问题，不具备良好的可制造性。为得到边界清晰的拓扑优化结果，提出一种面向连续体结构的分区密度修正敏度过滤方法，该方法将原过滤区域进行划分，采取新的复合卷积因子对不同区域处理，进一步采用一种带有预设密度修正权值的方法，有效弱化边界扩散的问题。通过对多个算例及不同处理方法进行比较分析，验证该方法的可行性及稳定性。Abstract: The SIMP method has become an efficient method to solve the topology optimization issue of the continuum because of its advantages such as less design constraints and high performance. In the traditional SIMP method, numerical instability often occurs during the optimization process, and the optimization results often have gray units, which make it difficult to extract the optimization model and have not good manufacturability. Although the Sigmund sensitivity filtering method can effectively improve the checkerboard phenomenon, this method is prone to the problem of boundary diffusion. In order to achieve the topological optimization results with clear boundaries, a partition density correction sensitivity filtering method for continuum structure is proposed in this study. This method divides the original filtering area, uses a new mixed convolution index to process different areas, and further adopts a method with preset density correction weights that effectively weakens the problem of boundary diffusion. By combining and analyzing multiple analytical examples and different filtering methods, the feasibility and reliability of the method are verified.
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Key words:
- topology optimization /
- continuum /
- SIMP /
- sensitivity filtering /
- gray-scale suppression
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表 1 不同参数计算结果
k λ 迭代次数 柔度值 离散率/% 灰度率/% 1 0.3 96 79.0042 1.076 1.889 0.4 86 78.9768 1.196 2.332 0.5 93 79.4472 1.336 2.557 0.6 63 79.5954 1.617 2.889 0.7 87 79.4244 1.458 2.556 2 0.3 102 79.0653 0.757 1.111 0.4 100 79.0425 0.698 1.000 0.5 97 78.9228 0.761 1.111 0.6 94 79.0349 0.819 1.444 0.7 68 79.0741 1.185 1.666 3 0.3 74 79.2295 0.902 1.111 0.4 69 79.2480 1.012 1.223 0.5 105 79.1645 0.882 1.223 0.6 98 79.1335 0.932 0.889 0.7 99 79.0865 0.806 1.222 
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表 3 算例2优化结果
序号 处理
方法网格
划分过滤
半径迭代
次数柔度值 离散
率/%灰度
率/%a 变密度法 120×80 3 64 34.4529 11.892 17.753 b 本文方法 120×80 3 66 33.3438 0.400 0.457 c 120×80 2 51 33.6056 0.310 0.209 d 120×80 5 91 33.1421 0.465 0.416 e 60×40 3 96 32.9673 0.745 1.000 f 180×120 3 115 33.7790 0.223 0.130
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