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Abstract Topology optimization (TO) has rapidly evolved from an academic exercise into an exciting discipline with numerous industrial applications. Various TO algorithms have been established, and several commercial TO software packages are now available. However, a major challenge in TO is the post-processing of the optimized models for downstream applications. Typically, optimal topologies generated by TO are faceted (triangulated) models, extracted from an underlying finite element mesh. These triangulated models are dense, poor quality, and lack feature/parametric control. This poses serious challenges to downstream applications such as prototyping/testing, design validation, and design exploration. One strategy to address this issue is to directly impose downstream requirements as constraints in the TO algorithm. However, this not only restricts the design space, it may even lead to TO failure. Separation of post-processing from TO is more robust and flexible. The objective of this paper is to provide a critical review of various post-processing methods and categorize them based both on targeted applications and underlying strategies. The paper concludes with unresolved challenges and future work. 

A fundamental requirement in standard finite element method (FEM) over four‐node quadrilateral meshes is that every element must be convex, else the results can be erroneous. A mesh containing concave element is said to betangled, and tangling can occur, for example, during: mesh generation, mesh morphing, shape optimization, and/or large deformation simulation. The objective of this article is to introduce a tangled finite element method (TFEM) for handling concave elements in four‐node quadrilateral meshes. TFEM extends standard FEM through two concepts. First, the ambiguity of the field in the tangled region is resolved through a careful definition, and this naturally leads to certain correction terms in the FEM stiffness matrix. Second, an equality condition is imposed on the field at re‐entrant nodes of the concave elements. When the correction terms and equality conditions are included, we demonstrate that one can achieve accurate results, and optimal convergence, even over severely tangled meshes. The theoretical properties of the proposed TFEM are established, and the implementation, that requires minimal changes to standard FEM, is discussed in detail. Several numerical experiments are carried out to illustrate the robustness of the proposed method.

 

Abstract Lattice structures exhibit unique properties including a large surface area and a highly distributed load-path. This makes them very effective in engineering applications where weight reduction, thermal dissipation, and energy absorption are critical. Furthermore, with the advent of additive manufacturing (AM), lattice structures are now easier to fabricate. However, due to inherent surface complexity, their geometric construction can pose significant challenges. A classic strategy for constructing lattice structures exploits analytic surface–surface intersection; this, however, lacks robustness and scalability. An alternate strategy is voxel mesh-based isosurface extraction. While this is robust and scalable, the surface quality is mesh-dependent, and the triangulation will require significant postdecimation. A third strategy relies on explicit geometric stitching where tessellated open cylinders are stitched together through a series of geometric operations. This was demonstrated to be efficient and scalable, requiring no postprocessing. However, it was limited to lattice structures with uniform beam radii. Furthermore, existing algorithms rely on explicit convex-hull construction which is known to be numerically unstable. In this paper, a combinatorial stitching strategy is proposed where tessellated open cylinders of arbitrary radii are stitched together using topological operations. The convex hull construction is handled through a simple and robust projection method, avoiding expensive exact-arithmetic calculations and improving the computational efficiency. This is demonstrated through several examples involving millions of triangles. On a typical eight-core desktop, the proposed algorithm can construct approximately up to a million cylinders per second. 

Cerebral aneurysm clips are biomedical implants applied by neurosurgeons to re-approximate arterial vessel walls and prevent catastrophic aneurysmal hemorrhages in patients. Current methods of aneurysm clip production are labor intensive and time-consuming, leading to high costs per implant and limited variability in clip morphology. Metal additive manufacturing is investigated as an alternative to traditional manufacturing methods that may enable production of patient-specific aneurysm clips to account for variations in individual vascular anatomy and possibly reduce surgical complication risks. Relevant challenges to metal additive manufacturing are investigated for biomedical implants, including material choice, design limitations, postprocessing, printed material properties, and combined production methods. Initial experiments with additive manufacturing of 316 L stainless steel aneurysm clips are carried out on a selective laser melting (SLM) system. The dimensions of the printed clips were found to be within 0.5% of the dimensions of the designed clips. Hardness and density of the printed clips (213 ± 7 HV1 and 7.9 g/cc, respectively) were very close to reported values for 316 L stainless steel, as expected. No ferrite and minimal porosity is observed in a cross section of a printed clip, with some anisotropy in the grain orientation. A clamping force of approximately 1 N is measured with a clip separation of 1.5 mm. Metal additive manufacturing shows promise for use in the creation of custom aneurysm clips, but some of the challenges discussed will need to be addressed before clinical use is possible.