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

Abstract

SUMMARYA 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

Deep learning for determining a near-optimal topological design without any iteration

“…Kwak (2006, 2007) proposed a design space optimization method that involves conducting a series of design space adjustments and refinements during optimization. Kim et al (2012) proposed a new convergence criterion to reduce computational expense by adaptively reducing the number of design variables on the basis of the optimization history of each design variable. Wu et al (2016) proposed a new method of performing topology optimization with a high-performance GPU solver.…”

Multimaterial multijoint topology optimization

“…Wong et al used topology optimization and the equivalent static loading method to reduce both mass and cost of an aircraft landing gear assembly under dynamic loading . Kim et al developed the reducible design variable (DV) method to reduce computational expense in topology optimization problems by not considering DVs that quickly converge as DVs in future iterations …”

“…10 Kim et al developed the reducible design variable (DV) method to reduce computational expense in topology optimization problems by not considering DVs that quickly converge as DVs in future iterations. 11 Most types of topology optimization in continuum structures can be divided into four categories, ie, (i) density-based methods, including the solid isotropic material with penalization (SIMP) interpolation scheme; (ii) boundary variation methods, including the level set and phase field methods; (iii) hard-kill methods, including evolutionary structural optimization; and (iv) nongradient methods, including ant colony and genetic algorithms (GAs). The density-based method utilizing the SIMP interpolation scheme has become the predominant topology optimization approach in both the literature and industrial applications due to its performance and computational efficiency.…”

RDVM Topology Optimization for Optimal Damping Treatment

“…In order to demonstrate the effectiveness and efficiency of RDVM topology optimization, optimal damping layouts and computational expenses are compared between conventional and RDVM topology optimization. 5,6) . …”

“…위해서 reducible design variable method(RDVM) 위상최적설계 기법을 제안하였고, 컴플라이언스 (compliance) 최소화 및 고윳값(eigenvalue) 최대화 의 문제에 적용하여 타당성을 입증하였다 (6) . (2,7,8) .…”