密度法に基づくトポロジー最適化における境界形状の特定手法

抄録

Topology optimization is an advanced design method that is used to generate lightweight and high-performance structures by determining the material distribution. However, one of important drawbacks of the topology optimization, especially performed by the density approach, is that distinct and smooth boundaries cannot be directly obtained owing to checkerboard patterns, grayscales, and irregular shapes with thin parts (point-point connections) or disconnected parts (isolated islands). This drawback makes it difficult manufacture the results of topology optimization. In this paper, a novel methodology is proposed to automatically obtain optimal smooth boundaries of topology optimization results using an efficient boundary smoothing technique and the H¹ gradient method, which is a node-based parameter-free optimization method. With this methodology, distinct and smooth optimal boundaries can be determined without any shape design parameterization. Moreover, re-mesh is not necessary in the shape updating process and the process is fully automatic. The validity and practical utility of this method is verified through three numerical examples with respect to a mean compliance minimization problem. They were calculated under the volume constraint, and a shape with a smooth outer shape was obtained with the average compliance reduced while satisfying the volume constraint. It was also confirmed that the shape obtained by using this methodology can be directly manufactured by a home 3D printer by converting it into an STL file.