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论文类型：期刊论文

发表时间：2014-09-01

发表刊物：JOURNAL OF ENGINEERING MECHANICS

收录刊物：SCIE、Scopus

卷号：140

期号：9

ISSN号：0733-9399

关键字：Multilevel adaptive analysis; Extended multiscale finite-element method (EMSFEM); Numerical base function (NBF); Hierarchical linear equation solver

摘要：A multilevel adaptive FEM is proposed for multiscale mechanical analysis of heterogeneous materials. The algorithm is developed based on the extended multiscale FEM (EMSFEM), which has been proven to be an efficient method for multiscale mechanical analysis. A residual force-based error estimate is introduced, which is able to detect both global and local errors economically. The concept of microscopic numerical base function (NBF) is introduced, which can be used to refine the local results at the regions with a high-stress gradient level by level. Two efficient methods for updating the microscopic NBFs were developed, i.e., the hierarchical NBFs scheme and the residual force NBFs scheme. A hierarchical linear solver is designed to solve the multilevel equation system in each iteration step. In the algorithm, the calculations at the current iteration step take full advantage of the results of previous iteration steps, which is helpful to save computational resources. The numerical examples demonstrate the stability, flexibility, and convergence of the method. (C) 2014 American Society of Civil Engineers.