Topology optimization using the variable substitution among three fields can achieve a design with desired solid and/or void features. This paper proposes a three-field floating projection topology optimization (FPTO) method using the linear material interpolation. The implicit floating projection constraint is used as an engine for generating a 0/1 solution at the design field. The substitution filtering and projection schemes enhance the length scale and solid/void features to accelerate the formation of structural topology in the physical field. Meanwhile, the three-field FPTO method can be extended to robust formulation, which obtains the eroded, intermediate, and dilated designs with the same topology. The most distinct feature of the FPTO method lies in the adoption of the linear material interpolation scheme, which makes many topology optimization problems straightforward. As an example, the proposed three-field FPTO algorithm is further applied to the design of shell-infill structures using the linear multi-material interpolation scheme. The distribution of the shell material is generated through a simple filtering scheme, and the shell thickness is accurately controlled by the filter radius. Numerical examples are presented to demonstrate the effectiveness and advantage of the proposed three-field FPTO method.

使用三个字段之间的变量替换的拓扑优化可以实现具有所需实体和/或空洞特征的设计。本文提出了一种使用线性材料插值的三场浮动投影拓扑优化（FPTO）方法。隐式浮动投影约束用作在设计领域生成 0/1 解决方案的引擎。替代过滤和投影方案增强了长度尺度和实体/空洞特征，以加速物理场中结构拓扑的形成。同时，三场 FPTO 方法可以扩展到鲁棒公式，获得具有相同拓扑的侵蚀、中间和扩张设计。FPTO方法最显着的特点在于采用了线性材料插值方案，这使得许多拓扑优化问题变得简单。例如，所提出的三场 FPTO 算法进一步应用于使用线性多材料插值方案设计壳填充结构。外壳材料的分布是通过简单的过滤方案生成的，外壳厚度由过滤器半径精确控制。数值例子展示了所提出的三场 FPTO 方法的有效性和优势。