title: Optimization and generation of cellular structures for additive manufacturing with mechanical and thermomechanical applications
title: Optimierung und Generierung zellulärer Strukturen für die Additive Fertigung mit mechanischen und thermomechanischen Anwendungen
Creators: name: Vu, Bich Ngoc
Publisher: name: Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU)
Year: 2024
Subjects: subject: Topology optimization
subject: Additive manufacturing
subject: Cellular structures

description: Weight reduction plays an important role in the aerospace industry because total aircraft weight has a significant impact on kerosene consumption. Ideally, the amount of material can be reduced while the properties of an aircraft component, such as stiffness or temperature distribution, remain constant. Components are often only produced in small quantities, making additive manufacturing (3D printing) technologies ideal for such applications. In particular, these types of processes enable the fabrication of three-dimensional components with different levels of detail, which are barely achievable using conventional material processing methods such as injection molding or milling. Additional tools, such as a negative mold for injection molding or a multitude of milling heads, are not required. By-products and waste, which tend to accumulate quickly in machining processes such as milling or drilling, are also kept to a minimum. In conventional processes, a component often has to be split and manufactured as sub-components, which are then reassembled in post-production. The resulting joint interfaces become the mechanical weak spots of the final result. In additive manufacturing, a full component is built by depositing materials layer by layer, without the necessity for subdivisions. However, the prerequisite for this deposition is that each new layer is supported by the layer below it. For this reason, additional support structures are required to prevent the upper layers from collapsing. Powder bed systems with high-precision lasers enable the fabrication of structures with delicate and complex details. The unmelted powder serves as a support structure and can mostly be reused. In this work, we focus on gradient-based optimization of the topology or layout of a component. In particular, we investigate the potential of utilizing physics-based optimization combined with additive manufacturing's capability to produce cellular structures, that is, porous structures with specified patterns, with filigree details. To this end, we incorporate manufacturing restrictions into the formulation of the optimization problem. We refer to the numerical solution of such a problem as a design. A further goal is the interpretation of a topology optimized result to obtain a geometric description, which is stored in data format and can be directly imported by a slicer. Slicer is the abbreviated term for a slicing software package that adds necessary support structures and creates the layers for the manufacturing process. In this case, it is sufficient to consider only the component's enclosing surface, which we describe and approximate using point coordinates and triangles. From a mechanical point of view, our assumption is that a material can be regarded as a periodic structure on the microscopic level (also referred to as a micro-structure). It is therefore completely described by the geometry and material composition of a periodic unit cell, which is the smallest representative unit. This has the advantage of allowing us to formulate parametrizations and local manufacturing constraints at the unit cell level. We determine the material properties as a function of the unit cell variables by implementing an established homogenization approach. It is evident from the literature that the use of laminates, that is, materials constructed of layers with different length scales, is ideal in terms of mechanical stiffness. However, such laminates cannot be realized using the current manufacturing technologies; even additive process are not viable. The restriction to periodic cellular structures is therefore also a compromise between technical feasibility and structural complexity. Hence, from a technical point of view, we evaluate a design using a numerical solution of the underlying physical models and partial differential equations. We use the finite element method as a discretization approach because of the substantial number of previous works in the research field of topology optimization. In our case, an optimization algorithm selects the best feasible choice of design variable values,that is, the variables of the unit cell, in each discretized location of the component. However, the resulting spatial material variation violates the assumption of periodicity and thus introduces a model error. Connections between the unit cells are not explicitly modeled in our optimization problems. Therefore, subsequent interpretation and post-processing steps are necessary to avoid interfaces and transition areas with artificially induced weak material behavior in the final component description. The post-processing algorithms rely on heuristics and may cause arbitrary deviations from the homogenized optimization result. It is therefore important to evaluate the final design description through numerical simulation to assess the quality of the design. Overall, the specific contribution of our work is a holistic consideration of each step in the homogenization-based optimization workflow. This includes selecting and parametrizing unit cells, formulating an algorithm for solving such an optimization problem, interpreting the optimized variables to obtain a smooth geometric description, and evaluating the final design. We propose our own ideas for each of these steps and combine them with existing approaches from the literature. An essential aspect of this work is performing a thorough search for a representative load case that clearly demonstrates the mechanical stiffness benefits of cellular structures. For this purpose, we conducted a variety of numerical optimization experiments to fill components with spatially varying cellular structures. In terms of mechanical stiffness, we determine that the use of cellular structures does not provide any advantage because the manufacturing options are too restrictive. This supposition persists, even if we also allow topological changes in the design and thereby violate manufacturability. Finally, to demonstrate that the prospects of additive manufacturing can be exploited in a different context, we conclude this thesis with a thermomechanical example of an injection mold component. Cellular structures show promise in thermal applications due to their large surface area supporting the exchange of thermal energy with the surroundings.