In this paper, we delve into the appearance of sharp ‘V’ features at joint areas in multi-material topology optimization, originating from independent minimum length scale control. To mitigate these undesirable features, three approaches have been studied: a hybrid strategy combining independent control with entire void control for parallel distributions, a fusion of independent control and entire solid control for parallel and wrapped distributions, and a local relaxation method employing a two-step filtering scheme. The modified minimum length scale controls for multi-material problems are proposed based on geometric constraints and the indicator functions with a normalization gradient norm. To validate the effectiveness of these methods, four numerical tests have been conducted. The results indicate that the combinations of two minimum length scale controls cannot achieve the parallel distribution and wrapped distribution due to the limited ability to modify the material layout. While local relaxation is feasible, which results in a significant reduction in stress concentration at joint areas.

中文翻译：

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通过最小长度尺度控制提高基于密度的多材料拓扑优化的接头质量


在本文中，我们深入研究了多材料拓扑优化中接头区域尖锐“V”特征的出现，该特征源于独立的最小长度尺度控制。为了减轻这些不良特征，研究了三种方法：将独立控制与并行分布的整体空控制相结合的混合策略、并行和缠绕分布的独立控制和整体固体控制的融合，以及采用二元函数的局部松弛方法。步进过滤方案。基于几何约束和具有归一化梯度范数的指示函数，提出了针对多材料问题的改进的最小长度尺度控制。为了验证这些方法的有效性，进行了四次数值试验。结果表明，由于修改材料布局的能力有限，两个最小长度尺度控制的组合无法实现平行分布和缠绕分布。虽然局部松弛是可行的，但这会导致接头区域的应力集中显着减少。