对偶变量块体混合元及其位移元的收敛性和精度分析

卿光辉; 刘艳红

doi:10.21656/1000-0887.370089

对偶变量块体混合元及其位移元的收敛性和精度分析

doi: 10.21656/1000-0887.370089

中国民航大学航空工程学院, 天津 300300

基金项目: 国家自然科学基金青年科学基金(11502286)

详细信息

作者简介:
卿光辉（1968—），男，教授，博士，硕士生导师(通讯作者. E-mail: qingluke@126.com).

中图分类号: O342; O343
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- 被引次数: 0
出版历程
- 收稿日期: 2016-03-28
- 修回日期: 2016-10-19
- 刊出日期: 2017-02-15

Convergence and Precision of the Dual-Variable Brick Mixed Element and Its Displacement Element

College of Aeronautical Engineering, Civil Aviation University of China,Tianjin 300300, P.R.China

Funds: The National Science Fund for Young Scholars of China(11502286)

摘要

摘要: 弹性力学Hamilton正则方程和Hamilton混合元的等效刚度系数矩阵，均具有直观的辛特性.基于HR变分原理和弹性力学保辛理论建立的对偶变量块体混合元，其等效刚度系数矩阵同样具有直观的辛特性.根据对偶变量块体混合元列式，可直接建立问题的控制方程，进行混合法求解.同时，通过对偶变量块体混合元列式可以导出对偶变量块体位移元列式，建立问题的控制方程后，可先求位移的解.数值实例表明：线性8结点对偶变量块体位移减缩积分元的各力学量的收敛速度均衡、收敛过程稳定、结果精度高，其应力变量的收敛速度与传统的20结点位移协调减缩积分元接近.对偶变量块体位移元具有普适性.
- 对偶变量 /
- H-R变分原理 /
- 对偶变量块体混合元 /
- 对偶变量块体位移元
Abstract: The symplectic characteristics of the equivalent stiffness coefficient matrix for the Hamiltonian canonical equations of elasticity and the Hamiltonian mixed element were intuitive, and the symplectic characteristics of the equivalent stiffness coefficient matrix for the dual-variable brick mixed element (DVBME), which was derived based on the Hellinger-Reissner (H-R) variational principle and the symplectic-conservative theory of elasticity, were similarly intuitive. The governing equations of elasticity were established immediately through the DVBME formulation, and the solution of the governing equations was obtained with the mixed method. Meanwhile, the dual-variable brick displacement element (DVBDE) formulation was deduced from the DVBME formulation, which was only related to displacement variables. The solution of the governing equations based on the DVBDE formulation was got with the displacement method. The numerical examples show that the convergence rates of displacement and stress variables of the 8-node DVBDE with reduced integration are balanced and stable with high precision. The convergence rate of stress of the DVBDE is almost equal to that of the translational 20-node displacement element with reduced integration. The DVBDE is universal.
- dual variable /
- Hellinger-Reissner variational principle /
- dual-variable brick mixed element /
- dual-variable brick displacement element

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参考文献(15)

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