A new efficient convergence criterion for reducing computational expense in topology optimization: reducible design variable method

• Published in: International journal for numerical methods in engineering 2012-05, Vol.90 (6), p.752-783
• Main Authors: Kim, Sun Yong, Kim, Il Yong, Mechefske, Chris K.
• Format: Article
• Language: English
• Subjects: Applied sciences; computational expense; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; convergence criterion; Exact sciences and technology; Fundamental areas of phenomenology (including applications); numerical efficiency; Physics; reducible design variable method; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; topology optimization; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.3343

SUMMARY A new efficient convergence criterion, named the reducible design variable method (RDVM), is proposed to save computational expense in topology optimization. There are two types of computational costs: one is to calculate the governing equations, and the other is to update the design variables. In conventional topology optimization, the number of design variables is usually fixed during the optimization procedure. Thus, the computational expense linearly increases with respect to the iteration number. Some design variables, however, quickly converge and some other design variables slowly converge. The idea of the proposed method is to adaptively reduce the number of design variables on the basis of the history of each design variable during optimization. Using the RDVM, those design variables that quickly converge are not considered as design variables for the next iterations. This means that the number of design variables can be reduced to save the computational costs of updating design variables. Then, the iteration will repeat until the number of design variables becomes 0. In addition, the proposed method can lead to faster convergence of the optimization procedure, which indeed is a more significant time saving. It is also revealed that the RDVM gives identical optimal solutions as those by conventional methods. We confirmed the numerical efficiency and solution effectiveness of the RDVM with respect to two types of optimization: static linear elastic minimization, and linear vibration problems with the first eigenvalue as the objective function for maximization. Copyright © 2012 John Wiley & Sons, Ltd.