Clustering-based concurrent topology optimization with macrostructure, components, and materials

This paper proposes a clustering-based concurrent topology optimization method for designing additive manufacturable cellular structures. In the context of multiscale topology optimization, the macrodesign domain can be divided into several subdomains (components) to reduce the number of microstructures which are needed to be optimized. However, in previous works, the division pattern is either artificially decided and fixed during the iteration process or updated according to a fixed parameter range. In this paper, a dynamic clustering strategy is developed to automatically divide the macrodesign domain into several subdomains according to the directions and ratio of the principal stress. K-means algorithm is adopted here for clustering; the advantages are that no predefined range is needed to group the microstructures and the number of microstructures used in the optimization can be arbitrarily specified. The macrostructure and the representative microstructures are optimized simultaneously using a density-based method. Each iteration consists of three sequential steps: First, the macrovariables are updated one step forward. Then, get the stress tensors from the macrovariables updating step and perform the clustering analysis. In the end, update the microvariables one step forward under the current clustering pattern and start the next iteration until the optimization converges. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.