Topology optimization of multi-material structures with length-scale control based on Neural Style Transfer and element-free Galerkin method

A novel multi-material structures topology optimization framework considering length-scale control is proposed, based on Neural Style Transfer (NST) and element-free Galerkin method (EFGM). The alternating active-phase algorithm (AAPA) is used to achieve the multi-material distribution in topology structures, and the minimum length-scale control (MinLSC) filter is applied to improve the manufacturability of the topology. Convolutional neural networks in NST are used to extract style features from images. The effects of different convolutional layers in NST, the weight coefficient of style loss and content loss, and the MinLSC filter on the optimal topology configurations and performance are studied through numerical examples. The results demonstrate that the convolutional layer depth of style loss mainly affects the fine branches of the topology, while the convolutional layer depth of content loss mainly affects the overall layout of it. When the content and style weights satisfy the relation w(c) = 1 - w(s), as the weight of style loss w(s) gradually decreases, the fine branches in the topology gradually reduce, and the overall structural differences between the topology configuration and the reference image are more emphasized in the NST. The MinLSC filter can reduce the fine branches generated by NST in the topology. The maximum displacement in the topology structure changes by less than 2 %, and the maximum stress is reduced by about 17.96 %similar to 27.54 %.