On the Study of the Geometrical Continuity of the Two-Level Topology Optimization Method
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Engineers and companies today face mounting pressure to provide high definition optimized mechanical components. While standard Topology Optimization (TO) effectively determines material distribution within a design domain, it encounters significant scalability issues. Specifically, the computational cost becomes prohibitive when the design requires the resolution of fine-scale topological features, such as trabecular micro-structures. In order to improve numerical performance, the two-level Topology Optimization is developed in three main steps. The first one decomposes the domain into square cells and performs a coarse low-definition material distribution using the standard SIMP method [1]. The second one allows to obtain continuous lateral tractions across neighboring cells by means of the equilibrating traction method [2]. In third place, each cell is finely optimized using the SIMP method again [3], starting from the cell densities obtained at the coarse level. After the fulfillment of a first two-level TO, the continuity of the resulting internal members across adjacent unit cells may be enhanced. This is achieved by restricting the distribution of lateral tractions to the appropriate segments of the cell boundary. In this work, some discussion about two concurrent criteria of segment selection and further matching of boundary voxels between neighboring interfaces is presented. Therefore, the required mechanical continuity is assured by optimizing again under these new loading conditions. It must be noticed that no density constraints are imposed between two neighboring cells, so that the geometrical continuity of final members is not thoroughly enforced. However, this study reaches a sharper density distribution of members across each cell contour, in comparison with [4].
