A hierarchical multilevel finite element method for mechanical analyses of periodical composite structures
A hierarchical multilevel finite element method for mechanical analyses of periodical composite structures
复制标题
周期性复合结构力学分析的分层多级有限元方法
DOI：
10.1016/j.compstruct.2015.05.001
复制
发表时间：
2015-11-01
影响因子：
6.3
通讯作者：
Chu, Xihua
中科院分区：
文献类型：
--
作者：
Liu, Hui;Sun, Xiaoyu;Chu, Xihua
提出了一种分层多层有限元方法(HMM)来模拟周期性复合材料结构的力学行为。该方法是基于多尺度有限元中提出的数值构造形函数的思想而建立的。为了提高计算精度，除了原有的形函数外，还在子网格域上构造了分层形函数和振型形函数。然后在提出的隐马尔可夫模型中引入了三种数值形函数。相应地，粗略单元的宏观位移可分为三部分，分别由节点(原始)形函数、层次形函数和振型函数贡献。借助于这些函数，可以方便地确定单个粗单元的等效质量矩阵、刚度矩阵和外荷载向量。将每个粗单元的宏观量进行组合，得到整个组合结构的总体宏观量。最终在宏观尺度上解决原问题，从而节省大量的计算成本。为了验证所提出的隐马尔可夫模型的有效性和有效性，对其进行了静态分析、广义特征值分析和暂态响应分析。(C)2015爱思唯尔有限公司。保留所有权利。
A hierarchical multilevel finite element method (HMM) is developed for simulating mechanical behaviors of periodical composite structures. This method is established based on the idea of constructing shape function numerically which is proposed in the multiscale finite element method (MsFEM). In order to improve the computational accuracy, a hierarchical shape function and a modal shape function are also constructed numerically on sub-grids domain in addition to the original shape function. Then totally three kinds of numerical shape function are introduced in the proposed HMM. Correspondingly, the macroscopic displacement of coarse element can be divided into three parts which are contributed by nodal (original), hierarchical and modal shape functions, respectively. By virtue of these functions, the equivalent mass matrix, stiffness matrix and external loading vector of one single coarse element can be determined easily. The overall macroscopic quantities of whole composite structure are obtained by assembling those of each coarse element. Finally the original problems can be solved at the macroscopic scale, which will save amount of computational cost. To verify the validation and efficiency of the developed HMM, the static analysis, generalized eigenvalue analysis and transient response analysis are investigated. (C) 2015 Elsevier Ltd. All rights reserved.