Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials  

作　　者：Xu Xu Xiaoteng Wang Haitian Yang Zhenjun Yang Yiqian He 

机构地区：[1]State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian,116024,China [2]Hubei Key Laboratory of Geotechnical and Structural Safety,School of Civil Engineering,Wuhan University,Wuhan,430072,China [3]Mechanik–Materialtheorie,Ruhr-Universität Bochum,Bochum,44801,Germany

出　　处：《Computer Modeling in Engineering & Sciences》2024年第8期1831-1861,共31页工程与科学中的计算机建模（英文）

基　　金：NSFC Grants(12072063,11972109);Grant of State Key Laboratory of Structural Analysis for Industrial Equipment(S22403);National Key Research and Development Program of China(2020YFB1708304);Alexander von Humboldt Foundation(1217594).

摘　　要：The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

关 键 词：Three-dimensionalmultiscale viscoelastic analysis numerical base functions octree SBFEM image-based analysis temporally piecewise adaptive algorithm 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]