A hybrid-stress element based on Hamilton principle

作     者：Song Cen Tao Zhang Chen-Feng Li Xiang-Rong Fu Yu-Qiu Long 

作者机构：Department of Engineering Mechanics School of Aerospace Tsinghua University Beijing 100084 China Civil and Computational Engineering Centre School of Engineering Swansea University Swansea SA2 8PP UK College of Water Conservancy and Civil Engineering China Agriculture University Beijing 100083 China Department of Civil Engineering Tsinghua University Beijing 100084 China 

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

年 卷 期：2010年第26卷第4期

页      面：625-634页

核心收录：

学科分类：01[哲学] 0101[哲学-哲学] 010104[哲学-逻辑学] 07[理学] 08[工学] 080104[工学-工程力学] 070104[理学-应用数学] 0815[工学-水利工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 

基　　金：supported by the National Natural Science Foundation of China (10872108,10876100) the Program for New Century Excellent Talents in University (NCET-07-0477) the National Basic Research Program of China (2010CB832701) 

主　　题：Finite element Hamilton variational principle Hybrid stress element Post processing schemes 

摘      要：A novel hybrid-stress finite element method is proposed for constructing simple 4-node quadrilateral plane elements, and the new element is denoted as HH4-3fl here. Firstly, the theoretical basis of the traditional hybrid-stress elements, i.e., the Hellinger-Reissner variational principle, is replaced by the Hamilton variational principle, in which the number of the stress variables is reduced from 3 to 2. Secondly, three stress parameters and corresponding trial functions are introduced into the system equations. Thirdly, the displacement fields of the conventional bilinear isoparametric element are employed in the new models. Finally, from the stationary condition, the stress parameters can be expressed in terms of the displacement parameters, and thus the new element stiffness matrices can be obtained. Since the required number of stress variables in the Hamilton variational principle is less than that in the Hellinger-Reissner variational principle, and no additional incompatible displacement modes are considered, the new hybrid-stress element is simpler than the traditional ones. Furthermore, in order to improve the accuracy of the stress solutions, two enhanced post-processing schemes are also proposed for element HH4-3β. Numerical examples show that the proposed model exhibits great improvements in both displacement and stress solutions, implying that the proposed technique is an effective way for developing simple finite element models with high performance.