The recent drive for producing lightweight and high performance designs on reduced timelines has promoted the need for computational design generation tools such as Multi‐Material Topology Optimization (MMTO). However, MMTO has drawn some industry skepticism as it assumes different material elements to be perfectly fused together. To address this concern, in this article, a novel pseudo‐cost domain (PCD) method is proposed which mathematically determines individual material interfaces in MMTO solutions. The proposed methodology employs a user defined joint cost model to weigh the distinct material interfaces relative to each other. An innovative approach to tailor the MMTO design considering the relative cost of each material interface is presented. The proposed methodology can consider any number of materials and their respective interfaces, and it is defined in such a way that increasing the number of materials has minimal effect on computational time. The methodology is formulated in a smooth and differentiable manner and the sensitivity expressions required by gradient‐based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.

中文翻译：

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使用伪成本域方法的多材料拓扑优化中的材料界面控制

最近在减少时间轴上生产轻量级和高性能设计的动力推动了对诸如多材料拓扑优化（MMTO）之类的计算设计生成工具的需求。但是，MMTO假设某些不同的材料元素完美地融合在一起，因此引起了业界的怀疑。为了解决这个问题，本文提出了一种新颖的伪成本域（PCD）方法，该方法可以数学确定MMTO解决方案中的各个材料界面。所提出的方法采用用户定义的联合成本模型来权衡不同材料界面之间的相对关系。提出了一种考虑每种材料界面的相对成本来定制MMTO设计的创新方法。拟议的方法可以考虑任何数量的材料及其各自的界面，并且以这样的方式定义：增加材料的数量对计算时间的影响最小。该方法以平滑和可微的方式制定，并给出了基于梯度的优化求解器所需的灵敏度表达式。提供了一系列示例问题，以证明所提出方法的有效性。