A generalized DCT compression based density method for topology optimization of 2D and 3D continua

In this paper, a novel topology optimization method based on discrete cosine transform (DCT) and density interpolation is proposed for layout designs of 2D and 3D continua. As one of the most frequently used transforms in digital image compression, the DCT may significantly reduce the number of design variables in density-based topology optimization, and can hereby improve the efficiency of solving the topology optimization problems to a great extent. This way the DCT compression based density method (DCDM) could be quite attractive in the topology optimization of large-scale engineering structures where a huge number of design variables may present. Effectiveness and efficiency of the proposed method is demonstrated with several 2D and 3D examples including both mechanical and heat conduction problems. Through these examples, some interesting features of DCDM are revealed and discussed. Since high frequency components are inherently filtered in DCDM, there is no need to introduce additional density filter or sensitivity filter in the present model. It is shown by numerical examples that there is no sharp corners present in the final optimized layout obtained by DCDM, which is beneficial when considering the stress of structures.