This paper introduces a versatile multi-material topology optimization approach based on an Implicit Topology Description Function (ITDF). The proposed method employs a node-based topological descriptive function as a design variable, and uses a specialized interpolation model to represent the material distribution within the design domain. By decoupling the design variables from material properties, this approach addresses the limitations of traditional methods and accommodates a broader spectrum of material combinations. Notably, the method only requires a single set of design variables, regardless of the number of materials involved. The independence of the topology control mesh from the analysis mesh leads to a “multi-resolution” effect, significantly reducing the number of design variables compared to conventional techniques. The continuity and non-local characteristics of the chosen topology description function interpolation enable a relatively smooth transition between different materials without any filtering technique. Numerical examples demonstrate that the proposed method achieves satisfactory performance in further reducing the number of design variables, expanding the applicability of materials, and ensuring numerical stability.

中文翻译：

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一种基于隐式拓扑描述函数的多材料拓扑优化方法


该文介绍了一种基于隐式拓扑描述函数 （ITDF） 的通用多材料拓扑优化方法。所提出的方法采用基于节点的拓扑描述函数作为设计变量，并使用专门的插值模型来表示设计域内的材料分布。通过将设计变量与材料属性解耦，这种方法解决了传统方法的局限性，并适应了更广泛的材料组合。值得注意的是，该方法只需要一组设计变量，而不管涉及的材料数量如何。拓扑控制网格独立于分析网格，因此具有“多分辨率”效果，与传统技术相比，显著减少了设计变量的数量。所选拓扑描述函数插值的连续性和非局部特性使不同材料之间的过渡相对平滑，无需任何过滤技术。数值算例表明，所提方法在进一步减少设计变量数量、扩大材料的适用性、保证数值稳定性方面取得了令人满意的性能。