In this paper, a new method is presented to concurrently determine the structural layout and joint interface during the multi-material topology optimization (MMTO) process. Although the development of additive manufacturing techniques allows the fabrication of multi-material structures for soft materials with graded properties, joint materials for joining metals or composites are still needed. This paper proposes a novel material interpolation scheme for defining the joint area between dissimilar materials using a two-step filtering process. The general MMTO process is performed in the first filtering step. Furthermore, the filtered variables generate the joint area, and the filter radius controls the thickness of the area in the second filtering step. A modified discrete material optimization (DMO) approach is developed to control the different materials independently and to expand the applicability of the method to cases with more than two design materials. To demonstrate the performance of the proposed method, a compliance minimization problem is formulated for various volume constraints, joint thicknesses, material properties, mesh types, and number of materials. To show the scalability, 3-D design and compliant mechanism design examples are adopted. Based on numerical examples, it was confirmed that the proposed method performs well in various cases; moreover, the results demonstrate that the concurrent designing of the structural layout and joint interface leads to better performance than when joint stiffness is not considered.

在本文中，提出了一种在多材料拓扑优化 (MMTO) 过程中同时确定结构布局和接头界面的新方法。尽管增材制造技术的发展允许为具有渐变特性的软材料制造多材料结构，但仍然需要用于连接金属或复合材料的接头材料。本文提出了一种新的材料插值方案，用于使用两步过滤过程定义不同材料之间的连接区域。一般的 MMTO 过程在第一个过滤步骤中执行。此外，过滤后的变量生成联合区域，过滤半径控制第二次过滤步骤中区域的厚​​度。改进的离散材料优化 (DMO) 方法被开发用于独立控制不同的材料，并将该方法的适用性扩展到具有两种以上设计材料的情况。为了证明所提出方法的性能，针对各种体积约束、接头厚度、材料特性、网格类型和材料数量制定了一个最小化问题。为了显示可扩展性，采用了 3-D 设计和兼容机制设计示例。基于数值例子，证实了所提出的方法在各种情况下都表现良好；此外，结果表明，结构布局和接头界面的同时设计比不考虑接头刚度时具有更好的性能。