One crucial advantage of additive manufacturing regarding the optimization of lattice structures is that there is a reduction in manufacturing constraints compared to classical manufacturing methods. To make full use of these advantages and to exploit the resulting potential, it is necessary that lattice structures are designed using optimization. Against this backdrop, two mixed integer programs are developed in order to use the methods of mathematical optimization in the context of topology optimization on the basis of a fitted ground structure method. In addition, an algorithm driven product design process is presented to systematically combine the areas of mathematical optimization, computer aided design, finite element analysis and additive manufacturing. Our developed computer aided design tool serves as an interface between state-of-the-art mathematical solvers and computer aided design software and is used for the generation of design data based on optimization results. The first mixed integer program focuses on powder-based additive manufacturing, including a preprocessing that allows a multi-material topology optimization. The second mixed integer program generates support-free lattice structures for additive manufacturing processes usually depending on support structures, by considering geometry-based design rules for inclined and support-free cylinders and assumptions for location and orientation of parts within a build volume. The problem to strengthen a lattice structure by local thickening or beam addition or both, with the objective function to minimize costs, is modeled. In doing so, post-processing is excluded. An optimization of a static area load with a practice-oriented number of connection nodes and beams was manufactured using the powder-based additive manufacturing system EOS INT P760.

增材制造在优化晶格结构方面的一个关键优势是，与传统制造方法相比，制造限制有所减少。为了充分利用这些优势并利用产生的潜力，有必要使用优化来设计晶格结构。在这种背景下，开发了两个混合整数程序，以便在基于拟合地面结构方法的拓扑优化中使用数学优化方法。此外，提出了一种算法驱动的产品设计过程，以系统地结合数学优化，计算机辅助设计，有限元分析和增材制造等领域。我们开发的计算机辅助设计工具可充当最先进的数学求解器和计算机辅助设计软件之间的接口，并用于根据优化结果生成设计数据。第一个混合整数程序专注于基于粉末的增材制造，包括允许进行多材料拓扑优化的预处理。第二个混合整数程序通过考虑倾斜和无支撑圆柱体的基于几何的设计规则以及在构建体积内零件的位置和方向的假设，生成通常用于支撑结构的无支撑晶格结构，通常用于支撑结构。对通过局部增厚或添加梁或同时使用二者来加强晶格结构的问题进行了建模，其目的是使成本最小化。在这样做，后处理不包括在内。使用基于粉末的增材制造系统EOS INT P760，通过针对实践中数量的连接节点和梁来优化静态面积载荷。