Study of key algorithms in topology optimization

• Published in: International journal of advanced manufacturing technology 2007-04, Vol.32 (7-8), p.787-796
• Main Authors: Zuo, Kong-Tian, Chen, Li-Ping, Zhang, Yun-Qing, Yang, Jingzhou
• Format: Article
• Language: English
• Subjects: Algorithms; Asymptotes; Control methods; Control stability; Convolution; Convolution integrals; Isotropic material; Iterative methods; Topology optimization
• ISSN: 0268-3768; 1433-3015
• DOI: 10.1007/s00170-005-0387-0

The theory of topology optimization based on the solid isotropic material with penalization model (SIMP) method is thoroughly analyzed in this paper. In order to solve complicated topology optimization problems, a hybrid solution algorithm based on the method of moving asymptotes (MMA) approach and the globally convergent version of the method of moving asymptotes (GCMMA) approach is proposed. The numerical instability, which always leads to a non-manufacturing result in topology optimization, is analyzed, along with current methods to control it. To eliminate the numerical instability of topology results, a convolution integral factor method is introduced. Meanwhile, an iteration procedure based on the hybrid solution algorithm and a method to eliminate numerical instability are developed. The proposed algorithms are verified with illustrative examples. The effect and function of the hybrid solution algorithm and the convolution radius in optimization are also discussed.