基于20节点辛元的复合材料层合板应力分析  

20-Node Hexahedron Symplectic Elements for Stress Analysis of Composite Laminates

作　　者：童瑶[1] 姚玉喆 TONG Yao;YAO Yuzhe(Shanghai Aircraft Design&Research Institute,Shanghai 201206,P.R.China;College of Aeronautical Engineering,Civil Aviation University of China,Tianjin 300300,P.R.China)

机构地区：[1]上海飞机设计研究院,上海201206 [2]中国民航大学航空工程学院,天津300300

出　　处：《应用数学和力学》2020年第5期509-516,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11502286)。

摘　　要：通常情况下,常规位移有限元法获得的应力结果比位移精度低一阶次,且面外应力难以满足连续性要求.联合最小势能原理和H-R变分原理,构造出包含位移和3个面外应力两类变量的20节点六面体辛元.由于两类变量采用高阶插值函数近似,无需引入单元内部的非协调位移项,因此相关理论的推导过程非常简单.与Hamilton部分混合元不同,该辛元涉及的变量沿3个坐标方向均做离散处理,不受单元厚度和结构几何形状的限制.数值实例表明20节点辛元的数值结果收敛稳定.在粗糙网格的情况下,与20节点位移元相比,该文单元的面外应力更接近精确解.Usually,the accuracy of the stresses obtained with the conventional displacement finite element method is one-order lower than that of the displacements,and the out-of-plane stresses can hardly meet the continuity requirements.Then,combined with the minimum potential energy principle and the H-R variational principle,a 20-node hexahedral symplectic element involving displacement and out-of-plane stress variables was established.Incompatible displacement terms are needless in the element since the 2 kinds of variables are approximated with higher-order interpolation functions.Hence,the derivation process of the theory is very simple.Unlike in the partially mixed Hamiltonian element,the variables involved in the symplectic element are discretized in 3 coordinate directions without restriction of the element thickness and the structure geometry.Numerical examples show that,the 20-node symplectic elements exhibit stable convergence.Under the coarse mesh,the out-of-plane stresses obtained with the proposed element are closer to the exact solution than those by the incompatible 8-node symplectic element.

关 键 词：复合材料 面外应力 H-R变分原理 20节点辛元 位移法 混合法 

分 类 号：O342[理学—固体力学] O343[理学—力学]