Second-order two-scale method for bending behavior analysis of composite plate with 3-D periodic configuration and its approximation  

作　　者：WANG ZiQiang CUI JunZhi 

机构地区：[1]College of Science, Guizhou Minzu University [2]LSEC,ICMSEC, Academy of Mathematics and Systems Science,Chinese Academy of Sciences

出　　处：《Science China Mathematics》2014年第8期1713-1732,共20页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(GrantNo.90916027);the Special Funds for National Basic Research Program of China(Grant No.2010CB832702);Foundation of Guizhou Science and Technology Department(Grant No.[2013]2144);the State Key Laboratory of Science and Engineering Computing

摘　　要：This paper considers the bending behaviors of composite plate with 3-D periodic configuration.A second-order two-scale(SOTS)computational method is designed by means of construction way.First,by 3-D elastic composite plate model,the cell functions which are defined on the reference cell are constructed.Then the effective homogenization parameters of composites are calculated,and the homogenized plate problem on original domain is defined.Based on the Reissner-Mindlin deformation pattern,the homogenization solution is obtained.And then the SOTS’s approximate solution is obtained by the cell functions and the homogenization solution.Second,the approximation of the SOTS’s solution in energy norm is analyzed and the residual of SOTS’s solution for 3-D original in the pointwise sense is investigated.Finally,the procedure of SOTS’s method is given.A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate.It shows that SOTS’s method can capture the 3-D local behaviors caused by3-D micro-structures well.This paper considers the bending behaviors of composite plate with 3-D periodic configuration. A second-order two-scale（SOTS） computational method is designed by means of construction way. First, by 3-D elastic composite plate model, the cell functions which are defined on the reference cell are constructed. Then the effective homogenization parameters of composites are calculated, and the homogenized plate problem on original domain is defined. Based on the Reissner-Mindlin deformation pattern, the homogenization solution is obtained. And then the SOTS＇s approximate solution is obtained by the cell functions and the homogenization solution. Second, the approximation of the SOTS＇s solution in energy norm is analyzed and the residual of SOTS＇s solution for 3-D original in the pointwise sense is investigated. Finally, the procedure of SOTS＇s method is given. A set of numerical results are demonstrated for predicting the effective parameters and the displacement and strains of composite plate. It shows that SOTS＇s method can capture the 3-D local behaviors caused by3-D micro-structures well.

关 键 词：second-order two-scale computational method Reissner-Mindlin deformation pattern composite plate approximation analysis 

分 类 号：TB33[一般工业技术—材料科学与工程]