Modeling of fluid flows in density-based topology optimization forms a longstanding challenge. Methods based on the Navier–Stokes equations with Darcy penalization (NSDP equations) are widely used in fluid topology optimization. These methods use porous materials with low permeability to represent the solid domain. Consequently, they suffer from flow leakage in certain areas. In this work, the governing equations for solid/fluid density-based topology optimization are reevaluated and reinterpreted. The governing equations are constructed using the volume averaged Navier–Stokes (VANS) equations, well known in the field of porous flow modeling. Subsequently, we simplify, interpret and discretize the VANS equations in the context of solid/fluid topology optimization, and analytically derive lower bounds on the Darcy penalization to sufficiently prevent flow leakage. Based on both the NSDP and VANS equations, two flow solvers are constructed using the Finite Volume method. Their precision and the lower bound on the Darcy penalization are investigated. Subsequently, the solvers are used to optimize flow channels for minimal pressure drop, and the resulting designs and convergence behavior are compared. The optimization procedure using the VANS equations is found to show less tendency to converge to inferior local optima for more precise flow solutions and is less sensitive to its parameter selection.

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.

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.

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.

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.