This paper presents a model for generating strut-based lattice structures using topology optimization and their efficient direct slicing. These structures exhibit better physical properties and can represent the partial densities at the macro-scale level, which often appear in designs based on topology optimization. The fabrication of such large member structures with intricate geometries is possible by the additive manufacturing technologies which offer design freedom to produce the optimized parts for engineering applications. However, these structures generate millions of planer manifolds describing the strut members and result in large data files, thus making conventional procedures in additive manufacturing highly ineffective. Therefore, the design process for such structures requires efficient data manipulation and storage of the lattice topology. In the current work, a mathematical model for the strut primitive which connects two nodes in a cell is developed. Based on the proposed strut model, a structural optimization formulation is presented for lattice structures design under volume fraction constraint. A matrix-oriented compact data structure to express the lattice topology and the direct slicing algorithm which makes queries on the proposed compact data structure is presented as part of this work. The slicing kernel has been tailored for parallel implementation to handle engineering-scale applications which often consist of structures over a million struts. The article is organized into the “Introduction” section explaining the requirement and the novelty of this work. Following which, the automated design framework based on topology optimization procedure for lattice structures is given. The mathematical derivations and data structure of the strut-based lattice will be explained and the operations on model data for the direct slicing procedure are elaborated. Numerical experiments verifying the proposed method will be presented toward the end.

本文提出了一种使用拓扑优化及其有效的直接切片生成基于支撑的网格结构的模型。这些结构表现出更好的物理性能，并可以代表宏观级别的部分密度，这些密度通常出现在基于拓扑优化的设计中。这种具有复杂几何形状的大型构件结构的制造可以通过增材制造技术来实现，该技术提供了设计自由度，可以生产用于工程应用的优化零件。但是，这些结构生成了数百万个描述支杆构件的平面歧管，并导致数据文件很大，从而使增材制造中的常规过程极为无效。因此，这种结构的设计过程需要有效的数据处理和晶格拓扑的存储。在当前的工作中，开发了用于将单元中的两个节点连接起来的支撑原语的数学模型。基于所提出的支撑模型，提出了一种在体积分数约束下进行晶格结构设计的结构优化公式。作为工作的一部分，提出了一种表达矩阵拓扑结构的面向矩阵的紧凑数据结构和对所提出的紧凑数据结构进行查询的直接切片算法。切片内核已针对并行实现进行了量身定制，以处理通常由百万个支柱组成的工程规模应用程序。本文分为“简介”部分，解释了这项工作的要求和新颖性。接着，给出了基于拓扑优化程序的晶格结构自动设计框架。将解释基于支杆的晶格的数学推导和数据结构，并阐述对模型数据进行直接切片的操作。数值实验将验证提出的方法将在最后提出。