1.3.3 Topology optimization considering AM constraints

Although AM has extraordinary ability to fabricate lattice-infilled parts, there are a number of constraints to be addressed.

Typical AM constraints include the minimum length scale constraint, overhangfree constraint and connectivity constraint. AM fabricates parts by joining materials layerby-layer, and hence, the minimum layer thickness and printing resolution impose the minimum length scale restriction to design. In addition, the layer-by-layer manufacturing requires the material deposition to be supported by its below materials, and if the below materials are non-solidified, the so-called overhang structure is formed that collapses easily and fails the printing. Hence, a maximum inclination angle restriction is applied to the overhang surfaces to enable the self-support property. On the other hand, sacrificial support structures can be added to facilitate the printing of large-angle overhangs. However, additional supports reduce material utilization efficiency and the post-processing to remove supports degrades the surface quality. For power-based or liquid-based AM, it is impossible to remove materials from enclosed voids. Thus, the connectivity constraints are crucial to these AM processes.

The above constraints have been integrated into topology optimization. For density-based topology optimization, applying multi-morphology density filters to build the robust formulation is an effective approach to constrain the minimum length scale[10]. To ensure the self-support property, the overhang-free constraint for topology optimization has been developed by enforcing the magnitude relationship between the overhang element and its below three elements[15]. The connectivity constraint can be formulated by the virtual temperature method. Assumed heat sources are added to the structure and high temperatures would appear inside the enclosed voids since heats cannot be dissipated to the ambience. Hence, the method can eliminate enclosed voids by restricting the maximum local temperature[16]. The connectivity constraint can also be realized by creating tunnels to connect voids[17].

The above constraints have been partially or fully included in the later presented lattice structure topology optimization algorithms.