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Clustering Solver for Displacement-based Numerical Homogenization
用于基于位移的数值均质化的聚类求解器
変位ベースの数値均質化のためのクラスタリングソルバー
변위 기반 수치 균질화를 위한 클러스터링 솔버
Solucionador de clústeres para homogeneización numérica basada en desplazamiento
Solveur de clustering pour l'homogénéisation numérique basée sur le déplacement
Кластерный решатель для численного усреднения на основе смещения
Shaoqiang Tang 唐少强, Xi Zhu 朱熙
HEDPS, CAPT and LTCS, College of Engineering, Peking University, Beijing 100871, China
北京大学工学院
Theoretical and Applied Mechanics Letters, 25 November 2021
Abstract

Based on strain-clustering via k-means, we decompose computational domain into clusters of possibly disjoint cells. Assuming cells in each cluster take the same strain, we reconstruct displacement field. We further propose a new way to condensate the governing equations of displacement-based finite element method to reduce the complexity while maintain the accuracy.

Numerical examples are presented to illustrate the efficiency of the clustering solver. Numerical convergence studies are performed for the examples. Avoiding complexities which is common in existing clustering analysis methods, the proposed clustering solver is easy to implement, particularly for numerical homogenization using commercial softwares.
Theoretical and Applied Mechanics Letters_1
Theoretical and Applied Mechanics Letters_2
Theoretical and Applied Mechanics Letters_3
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