Topology optimization based on deep representation learning (DRL) for compliance and stress-constrained design

This paper proposed a new topology optimization method based on geometry deep learning. The density distribution in design domain is described by deep neural networks. Compared to traditional density-based method, using geometry deep learning method to describe the density distribution function can guarantee the smoothness of the boundary and effectively overcome the checkerboard phenomenon. The design variables can be reduced phenomenally based on deep learning representation method. The numerical results for three different kernels including the Gaussian, Tansig, and Tribas are compared. The structural complexity can be directly controlled through the architectures of the neural networks, and minimum length is also controllable for the Gaussian kernel. Several 2-D and 3-D numerical examples are demonstrated in detail to demonstrate the effectiveness of proposed method from minimum compliance to stress-constrained problems.