
Non-intrusive shape and size optimization of non-conforming stiffener meshes in the context of hybrid manufacturing
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In hybrid manufacturing (additive + conventional manufacturing), one notable use case for structural applications, involves utilizing additive manufacturing to fabricate stiffeners (or ribs). The primary advantage is that these structures can be ”simply” added to a part, without it necessitating geometrical alterations or new tooling, which is often a costly drawback in conventional manufacturing processes, and all whilst enhancing its stiffness. From an industrial perspective, this approach allows for improving mechanical performance without modifying the original geometry of the conventionally manufactured part. The 3D printed stiffeners can be seamlessly integrated into designs that previously did not meet the mechanical and structural requirements. Similarly, in computational processes, the goal is to optimize the shapes and paths of stiffeners based on an existing geometry. The challenge arises from the typical limitation of using FEM. When stiffeners and base structure are coupled by sharing nodes, any design update of the stiffener path perturbs the mesh of the base structure. To address this, the objective is to mesh the stiffeners independently from the base mesh, i.e., using non-conforming meshes. One approach that can facilitate this “independence” of meshes is to use Lagrange multipliers that enforce the coupling of both meshes. However, this strategy requires exact knowledge of the shape functions of the elements, and in a commercial software, their formulation is often unavailable due to proprietary restrictions. In this work, we present a method to replicate the coupling in a viable manner for usage in commercial software by using a mesh subdivision scheme of the base model mesh. As in the Lagrange multipliers, it only affects the base model mesh at the elements where the stiffener nodes are inserted. Additionally, meaningful manufacturing constraints, regarding the fact that the stiffeners are manufactured using Wire and Arc Additive Manufacturing (WAAM), are considered to ensure that the designs remain feasible for production.