An efficient multiscale topology optimization method for frequency response minimization of cellular composites

IF 8.7 2区 工程技术 Q1 Mathematics
Xiliang Liu, Liang Gao, Mi Xiao
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引用次数: 0

Abstract

It is vital to control the vibration of cellular composites under harmonic excitation in engineering. Due to numerous design variables and expensive frequency domain integration operation, the majority of multiscale topology optimization methods for frequency response minimization of cellular composites tend to be conservative, where a small number of types of microstructures are considered. This paper proposes an efficient multiscale topology optimization method to minimize the frequency response of cellular composites over specified frequency intervals. This method utilizes multiclass graded lattice unit cells (LUCs) as design candidates, offering great design space to improve the dynamic performance of cellular composites. At microscale, the proposed method leverages Kriging metamodels to replace the the homogenization method in each iteration step, thus accelerating the performance estimation of multiclass graded LUCs. At macroscale, the second-order Krylov subspace with moment-matching Gram-Schmidt orthonormalization (SOMMG) method is introduced to expedite the frequency response analysis of cellular composites. Two types of design variables are employed to construct the Kriging metamodel assisted Uniform Multiphase Materials Interpolation (KUMMI) model, facilitating the concurrent updating of LUCs’ classes and relative densities. Several numerical examples are presented to validate the effectiveness and efficiency of the proposed method in minimizing the frequency response of cellular composites.

Abstract Image

最小化蜂窝复合材料频率响应的高效多尺度拓扑优化方法
在工程中,控制谐波激励下蜂窝复合材料的振动至关重要。由于设计变量众多且频域积分操作成本高昂,大多数用于蜂窝复合材料频率响应最小化的多尺度拓扑优化方法都趋于保守,只考虑了少量类型的微结构。本文提出了一种高效的多尺度拓扑优化方法,可在指定频率区间内最小化蜂窝复合材料的频率响应。该方法利用多类分级晶格单元(LUC)作为设计候选,为改善蜂窝复合材料的动态性能提供了巨大的设计空间。在微观尺度上,所提出的方法利用克里金元模型取代了每个迭代步骤中的均质化方法,从而加速了多类分级 LUC 的性能估计。在宏观尺度上,引入了二阶克雷洛夫子空间与矩匹配格拉姆-施密特正交化(SOMMG)方法,以加快蜂窝复合材料的频率响应分析。利用两类设计变量构建克里金元模型辅助均匀多相材料插值(KUMMI)模型,便于同时更新 LUC 的类别和相对密度。通过几个数值示例,验证了所提方法在最小化蜂窝复合材料频率响应方面的有效性和效率。
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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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