Highly accurate symplectic element based on two variational principles

作     者：Guanghui Qing Jia Tian 

作者机构：College of Aeronautical Engineering Civil Aviation University of China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2018年第34卷第1期

页      面：151-161页

核心收录：

学科分类：08[工学] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundations of China (Grant 11502286) 

主　　题：Modified H-R mixed variational principle Partial-mixed element Noncompatible symplectic element Finite element method Nearly incompressible material 

摘      要：For the stability requirement of numerical resultants, the mathematical theory of classical mixed methods are relatively complex. However, generalized mixed methods are automatically stable, and their building process is simple and straightforward. In this paper, based on the seminal idea of the generalized mixed methods, a simple, stable, and highly accurate 8-node noncompatible symplectic element(NCSE8) was developed by the combination of the modified Hellinger-Reissner mixed variational principle and the minimum energy principle. To ensure the accuracy of in-plane stress results, a simultaneous equation approach was also suggested. Numerical experimentation shows that the accuracy of stress results of NCSE8 are nearly the same as that of displacement methods, and they are in good agreement with the exact solutions when the mesh is relatively fine. NCSE8 has advantages of the clearing concept, easy calculation by a finite element computer program, higher accuracy and wide applicability for various linear elasticity compressible and nearly incompressible material problems. It is possible that NCSE8 becomes even more advantageous for the fracture problems due to its better accuracy of stresses.