基于光滑位移场的应力恢复方法  

Stress recovery based on smoothed basic solutions

作　　者：李涛[1] 左正兴[1] 廖日东[1] 蒲大宇[1] 王舒妍[1] 

机构地区：[1]北京理工大学机械与车辆工程学院,北京100081

出　　处：《计算力学学报》2007年第5期674-677,共4页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(59978038)资助项目

摘　　要：为了提高位移元的应力精度,提出了一种应力求解的新方法。首先在一取定的单元小片内对基本解进行多项式拟合光滑处理,使得基本解在单元交界处获得更高的光滑性,进而通过微分运算获得节点的应力值;最后按此方法遍历所有的节点得到全求解域应力场。数值算例表明该方法是可行的,并且计算结果的精度较高。该方法计算量小,普适性强,具有较强的理论意义与工程应用价值。　Postprocessing techniques in traditional finite element method,smoothing process is always adopeted after differential operation,such as the nodal average method,SPR,etc.The difference between them is mainly on how to smooth the discontinuous stresses.In order to enhance finite element stress accuracy,a new method is proposed in this paper.First,the basic solutions are smoothed under a small element patch with polynomial fitting method;as a result,the basic solutions get differentiability on element boundaries.Then,the stress value on the node can be calculated though differential operation.According to this way,the stress value on nodes＇ can be given over the whole domain.The numerical examples illustrated the applicability and higher accuracy can be achieved.Moreover,this method needs less computing time and can be used widely.

关 键 词：应力恢复 超收敛 单元片 光滑位移场 

分 类 号：O242.21[理学—计算数学]