Fast structural optimization with frequency constraints by genetic algorithm using adaptive eigenvalue reanalysis methods

• Published in: Structural and multidisciplinary optimization Vol. 43; no. 6; pp. 799 - 810
• Main Authors: Zuo, Wenjie, Xu, Tao, Zhang, Hao, Xu, Tianshuang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2011; Springer Nature B.V
• Subjects: Adaptive algorithms; Computational efficiency; Computational Mathematics and Numerical Analysis; Computing time; Eigenvalues; Engineering; Engineering Design; Genetic algorithms; Global optimization; Mathematical programming; Nonlinear dynamics; Nonlinear programming; Optimality criteria; Research Paper; Theoretical and Applied Mechanics; Vectors (mathematics); Fast structural optimization; Adaptive eigenvalue reanalysis; Frequency constraints; Genetic algorithm
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-010-0610-y

Structural optimization with frequency constraints is highly nonlinear dynamic optimization problems. Genetic algorithm (GA) has greater advantage in global optimization for nonlinear problem than optimality criteria and mathematical programming methods, but it needs more computational time and numerous eigenvalue reanalysis. To speed up the design process, an adaptive eigenvalue reanalysis method for GA-based structural optimization is presented. This reanalysis technique is derived primarily on the Kirsch’s combined approximations method, which is also highly accurate for case of repeated eigenvalues problem. The required number of basis vectors at every generation is adaptively determined and the rules for selecting initial number of basis vectors are given. Numerical examples of truss design are presented to validate the reanalysis-based frequency optimization. The results demonstrate that the adaptive eigenvalue reanalysis affects very slightly the accuracy of the optimal solutions and significantly reduces the computational time involved in the design process of large-scale structures.