基于相邻单元高斯点方案的应力恢复方法  

A stress recovery method based on the programme of Gauss points in adjacent elements

作　　者：卿光辉[1] 徐靖峪 QING Guanghui;XU Jingyu(College of Aeronautical Engineering,CAUC,Tianjin 300300,China)

机构地区：[1]中国民航大学航空工程学院,天津300300

出　　处：《中国民航大学学报》2022年第2期58-64,共7页Journal of Civil Aviation University of China

基　　金：国家自然科学基金项目(11502286)

摘　　要：针对二维非协调4节点四边形单元模型,采用节点外相邻单元的高斯点构造新的等参元,可以直接计算包含在单元内的节点应力。这种节点应力恢复算法避免了常规的外推法中相邻单元在公共节点处应力结果取平均值的过程,计算程序更加简便;由模型内部节点应力计算边界节点应力时采用简单的线性插值方法。算例表明:模型中应力计算结果的精度较外推法有所提高;收敛性分析证明了该方法的正确性和有效性,具有较好的普遍适用性;在运用该方法分析含孔平板应力集中问题时,所得的应力集中系数比外推法更接近理论解。For the two-dimensional incompatible 4-nodes quadrilateral element model,a new isoparametric element is constructed using the Gaussian points in adjacent elements around the nodes,and the stresses of the nodes included in the element can be calculated directly.This method avoids the calculation process of average value of stress results of adjacent elements at common nodes in the common extrapolation method and the program is easier.A simple linear interpolation method is used to calculate the boundary node stress from the internal node stress of the model.Examples show that the accuracy of the stress in the model is higher than that of the extrapolation method,and the convergence analysis of the stress proves the correctness and effectiveness of the method,which is a method with universal applicability.When the method is used to analyze the stress concentration problem of plate with holes,the stress concentration factor obtained is closer to the theoretical solution than that of the extrapolation method.

关 键 词：应力恢复 二维问题 四边形单元 高斯点 插值函数 

分 类 号：O302[理学—力学] O343