Topology optimization of shell–infill structures using an erosion-based interface identification method

Topology optimization of shell–infill structures has been a hot topic in the optimization community. The crucial issue of such design problem is how to accurately describe the material interfaces, which is often regarded as a relatively difficult problem in density-based topology optimization. This paper presents an erosion-based interface identification method to handle this difficulty by defining the different parts of the original and eroded structures as interfaces. The theoretical relation for determining the erosion parameters is derived to control the interface thickness accurately. It turns out that the erosion-based method offers excellent performance even for the extreme cases where the ratios of member sizes to a prescribed thickness are small, and at the same time, it is easy to implement since we only need to consider the frequently-used filtering and projection processes in the applied erosion operation. Then, we provide an improved SIMP-based topology optimization method for shell–infill structures based on the new idea of defining interfaces. In this paper, a tweak to the existing two-step filtering/projection process is made to separate the shell and infill, and a corresponding interpolation function is developed to model the whole composite objects. Enhanced by the worst-case based robust formulation, the minimum length scale of optimized structures can be controlled. Several 2D and 3D compliance optimization examples are provided to illustrate the effectiveness of the proposed method. •An erosion based method is proposed to describe material interfaces.•A theoretical relation between interface thickness and erosion parameters is derived.•An improved SIMP-based method for shell–infill structures is provided.•Effectiveness of the proposed method is demonstrated by several 2D and 3D examples.