【摘要】 阐述一种适用于非均质材料力学性能分析的扩展的多尺度有限元法(Extended Multiscale Finite Element Method,EMsFEM)的基本原理.该方法的基本思想是利用数值方法构造能反映胞体单元内部材料非均质影响的多尺度基函数,在此基础上求得粗网格层次的等效单元刚度阵,从而在粗网格尺度上对原问题进行求解,很大程度地减少计算量.以该方法进行的具有周期和随机微观结构的材料计算示例,通过与传统有限元法的结果比较,说明这一方法的有效性.EMsFEM的优势在于,能容易地进行降尺度计算,可较准确地求得单元内部的微观应力应变信息,在非均质材料强度和非线性分析中有很大的应用潜力.更多还原

【Abstract】 The basic theory of Extended Multiscale Finite Element Method(EMsFEM) for mechanical analysis of heterogeneous materials is presented. The underlying idea is to construct numerically the multiscale base functions to capture the small scale heterogeneities of coarse elements in the multiscale finite element analysis. Then the problems are solved on the coarse-grid scale,thus resulting in a reduced number of degrees of freedom in the model. Both problems with periodic and random microstructures are considered and the numerical results verify the validity and accuracy of the developed method by comparing them with the traditional finite element method. An important feature of this work is that the downscaling computation could be performed easily and the micro stress and strain in the macro elements can be obtained simultaneously in the multiscale computation. Thus,the developed method has great potential for strength and nonlinear analysis of complicated heterogeneous materials.更多还原