This thesis a method is described to include manufacturing constraints of the additive manufacturing process into topology optimization. Topology optimization often results in complex structures, which can only be produced by additive manufacturing. Although additive manufacturing has much fewer design restrictions compared to conventional manufacturing methods, it has its own limitations. The most prominent limitation is the overhang constraint, which causes the need for support structures. In this thesis front propagation is utilized to crudely mimic the printing process. Making use of existing numerical methods for front propagation, a numerically efficient algorithm is produced that can identify parts of the structure that do not adhere to the overhang constraint, during the topology optimization process. Since the sensitivities of the algorithm are available, it can be used in the gradient based topology optimization to ensure printability of the final part. Due to the continuous description of the constraint, it can be applied to unstructured meshes and for variable overhang angles. Furthermore, it is shown that the constraint can be parallelized which is demonstrated on large scale 3D problems.@en

Additive manufacturing (AM) and topology optimization (TO) have a synergetic relation, as AM can produce complex TO designs, and TO provides high-performance parts that utilize the form freedom provided by AM. Recently, TO has been tailored more toward AM with the inclusion of the minimum allowable overhang angle as a design constraint: resulting designs can be built without any support structures. This work is an extension thereof, by allowing support structures only if they are accessible, such that they can be removed after manufacturing. This is achieved by applying a conventional overhang filter twice, combined with basic operations such as geometry inversion, union, and intersection. The result is an accessibility-aware overhang filter that can be incorporated in TO. Compared with conventional overhang filtered designs, the accessibility filter results in increased part performance and better convergence behavior. Furthermore, a modular filter structure is presented to easily construct the accessibility filter, and its effectiveness is demonstrated on several numerical cases.

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An important cause of failure in powder bed additive manufacturing is the distortion of the part due to thermal shrinkage during printing and the relaxation of residual stresses after its release from the base plate. In this paper, Additive Manufacturing simulations are coupled with Topology Optimization in order to generate designs that are not susceptible to failure associated with distortion. Two possible causes of failure are accounted for: recoater collision and global distortion of the product. Both are considered by simulation of the build process and defined as constraints in the context of a Solid Isotropic Material with Penalization method based topological optimization. The adjoint method is used to derive the sensitivities of the additive manufacturing constraints. The method is demonstrated with the 2D and 3D optimization of a bracket. Next to global topological changes, the obtained designs show features that are aimed at facilitating the printing process. These features resemble supports that are routinely applied to powder bed additive manufacturing. The formulated constraints were found to prevent excessive part distortion and associated build failures in all cases, against a modest increase in the compliance of the bracket.

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Although additive manufacturing (AM) allows for a large design freedom, there are some manufacturing limitations that have to be taken into consideration. One of the most restricting design rules is the minimum allowable overhang angle. To make topology optimization suitable for AM, several algorithms have been published to enforce a minimum overhang angle. In this work, the layer-by-layer overhang filter proposed by Langelaar (Struct Multidiscip Optim 55(3):871–883, 2017), and the continuous, front propagation-based, overhang filter proposed by van de Ven et al. (Struct Multidiscipl Optim 57(5):2075–2091, 2018) are compared in detail. First, it is shown that the discrete layer-by-layer filter can be formulated in a continuous setting using front propagation. Then, a comparison is made in which the advantages and disadvantages of both methods are highlighted. Finally, the continuous overhang filter is improved by incorporating complementary aspects of the layer-by-layer filter: continuation of the overhang filter and a parameter that had to be user-defined are no longer required. An implementation of the improved continuous overhang filter is provided.

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It is attractive to combine topology optimization (TO) with additive manufacturing (AM), due to the design freedom provided by AM, and the increased performance that can be achieved with TO. One important aspect is to include the design rules associated with the process restrictions of AM to prevent the requirement of relatively large support volumes during printing. This paper presents a TO filter that enforces a minimum overhang angle, resulting in an optimized topology that is printable without the need for support structures. The filter is based on front propagation, which, as it is described by a PDE, allows for a straightforward application on unstructured meshes, to enforce an arbitrary overhang angle. Efficient algorithms developed for front propagation are used in combination with adjoint sensitivities, in order to have a minor influence on the total computational cost. The focus of this work is on the implementation of the filter for high resolution 3D cases, which requires development of the front propagation for tetrahedral elements, and its parallelization.

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Additive manufacturing enables the nearly uncompromised production of optimized topologies. However, due to the overhang limitation, some designs require a large number of supporting structures to enable manufacturing. Because these supports are costly to build and difficult to remove, it is desirable to find alternative designs that do not require support. In this work, a filter is presented that suppresses non-manufacturable regions within the topology optimization loop, resulting in designs that can be manufactured without the need for supports. The filter is based on front propagation, can be evaluated efficiently, and adjoint sensitivities are calculated with almost no additional computational cost. The filter can be applied also to unstructured meshes and the permissible degree of overhang can be freely chosen. The method is demonstrated on several compliance minimization problems in which its computational efficiency and flexibility are shown. The current applications are in 2D, and the proposed method is readily extensible to 3D.

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Additive Manufacturing allows for considerably more form freedom compared to existing manufacturing technologies but still faces the limitation of building overhanging parts. The overhang limitation in additive manufacturing prevents the direct production of topology optimized parts. We present an overhang constraint that incorporates this manufacturing limitation into topology optimization. The overhanging regions in a design iteration are detected using front propagation and a global constraint is formulated by aggregating the local constraints within the design domain. Since the constraint is formulated in a continuous manner, it can be discretized for any type of mesh, and with an arbitrary minimum allowable overhang angle. Furthermore, it is easily extensible to 3D. The Ordered Upwind Method is used to solve the constraint, and adjoint sensitivities are used for efficient evaluation. The newly developed constraint is demonstrated on 2D examples having an unstructured mesh. Overhang free designs are obtained with smooth convergence behaviour.@en

Designing transient thermal mechanical systems is a challenging task. Material can have many different functions: it can provide heat capacity, heat conduction, mechanical stiffness or even function as an actuator. Topology optimization can provide the engineer with valuable insight on such a problem. One of the most popular topology optimization approaches is the density method. This method is applied to a transient thermal mechanical problem. In order to ensure manufacturability, penalization is applied to suppress intermediate densities in the final design. However, for transient thermal mechanical optimization problems, conventional penalization does not work for most objective functions. A new penalization method, material penalization, is presented that does suppress intermediate densities in the transient thermal mechanical domain. Each element is given its own unique set of penalization parameters which are optimized to maximize the objective function for a minimization problem. By reusing sensitivity information from the density variables, the additional computational cost is limited.@en