Self-supporting Topology Optimization for Additive Manufacturing
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The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such supports in general have to be created during the fabricating process so that the primary object can be manufactured layer by layer without collapse, which is very time-consuming and waste of material. The proposed approach resolves this problem by formulating the self-supporting requirements as a novel explicit quadratic continuous constraint in the topology optimization problem, or specifically, requiring the number of unsupported elements (in terms of the sum of squares of their densities) to be zero. Benefiting form such novel formulations, computing sensitivity of the self-supporting constraint with respect to the design density is straightforward, which otherwise would require lots of research efforts in general topology optimization studies. The derived sensitivity for each element is only linearly dependent on its sole density, which, different from previous layer-based sensitivities, consequently allows for a parallel implementation and possible higher convergence rate. In addition, a discrete convolution operator is also designed to detect the unsupported elements as involved in each step of optimization iteration, and improves the detection process 100 times as compared with simply enumerating these elements. The approach works for cases of general overhang angle, or general domain, and produces an optimized structures, and their associated optimal compliance, very close to that of the reference structure obtained without considering the self-supporting constraint, as demonstrated by extensive 2D and 3D benchmark examples.
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