The topology of a structure is defined by its genus or number of handles. When the topology of a structure is optimized, its topology might be changed if the material state of a design cell is switched from solid to void or vice versa. In discrete topology optimization, each design cell is either solid or void and there is no topology uncertainty from any grey design cell. Point connection might cause topology uncertainty and is eradicated when hybrid discretization model is used for discrete topology optimization. However, the topology solution of an optimized structure might be uncertain when its design domain is discretized differently, which is commonly called mesh dependence problem. In this paper, the degree of genus based topology optimization strategy is introduced to circumvent this topology uncertainty. With this strategy, the genus of an optimized structure is constrained during its topology optimization process. There is no topology uncertainty even if different design domain discretizations are used. The introduced strategy is used for discrete topology optimization of structures that have multiple loading points in this paper. The presented discrete topology optimization procedure is demonstrated by examples with different degrees of genus and loading conditions.
Discrete Topology Optimization of Structures Without Uncertainty
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Zhou, H, & Kolavennu, ST. "Discrete Topology Optimization of Structures Without Uncertainty." Proceedings of the ASME 2013 International Mechanical Engineering Congress and Exposition. Volume 4A: Dynamics, Vibration and Control. San Diego, California, USA. November 15–21, 2013. V04AT04A022. ASME. https://doi.org/10.1115/IMECE2013-62824
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