This paper extends the independent point-wise density interpolation to the bi-material topology optimization to improve the structural static or dynamic properties. In contrast to the conventional elemental density-based topology optimization approaches, this method employs an analysis-mesh-separated material density field discretization model to describe the topology evolution of bi-material structures within the design domain. To be specific, the density design variable points can be freely positioned, independently of the field points used for discretization of the displacement field. By this means, a material interface description of relatively high quality can be achieved, even when unstructured finite element meshes and irregular-shaped elements are used in discretization of the analysis domain. Numerical examples, regarding the minimum static compliance design and the maximum fundamental eigen-frequency design, are presented to demonstrate the validity and applicability of the proposed formulation and numerical techniques. It is shown that this method is free of numerical difficulties such as checkerboard patterns and the “islanding” phenomenon.

中文翻译：

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使用与分析无关的点明智密度插值的双材料拓扑优化

本文将独立的点密度插值扩展到双材料拓扑优化，以改善结构的静态或动态特性。与传统的基于元素密度的拓扑优化方法不同，此方法采用分析网格分隔的材料密度场离散模型来描述设计域内双材料结构的拓扑演化。具体而言，密度设计变量点可以自由定位，而与用于离散化位移场的场点无关。通过这种方式，即使在分析域的离散化中使用非结构化有限元网格和不规则形状的单元时，也可以获得相对高质量的材料界面描述。数值示例 关于最小静态柔度设计和最大基本本征频率设计，旨在证明所提出的公式和数值技术的有效性和适用性。结果表明，该方法没有出现诸如棋盘格图案和“孤岛”现象的数值困难。