摘要
自钱伟长建立了功率型变分原理以来,功率型变分原理和功能型变分原理在理论方面和应用方面有什么区别和联系,成为学术界关注的课题.应用变积方法,根据Jourdain原理和d’Alembert原理,建立了不可压缩黏性流体力学的功率型变分原理和功能型拟变分原理,推导了不可压缩黏性流体力学的功率型变分原理的驻值条件和功能型拟变分原理的拟驻值条件.研究了不可压缩黏性流体力学的功率型变分原理在有限元素法中的应用.研究表明,功率型变分原理与Jourdain原理相吻合,功能型变分原理与d’Alembert原理相吻合.功率型变分原理直接在状态空间中研究问题,不仅在建立变分原理的过程中可以省略在时域空间中的一些变换,而且给动力学问题有限元素法的数值建模带来方便.
Since the power type variational principle was established by CHIEN Wei-zang, the differences and relations between the power type variational principles and the work-energy type quasi-variational pri_nciples in theory and practice have been a hot topic in the academic circle. According to the Jourdain principle and the d＇ Alembert principle, the power type varia- tional principles and the work-energy type quasi-variational principles were established for the incompressible viscous flow in liquid-filled systems with the variational integral operation method, so as to deduce their stationary condition and quasi-stationary condition, respectively. The applications of the power type variational principles and the work-energy type quasi-variational principles in the finite element method were studied. It shows that the work-energy type quasi- variational principles coincide with the d＇ Alembert principle and the power type variational principles do with the Jourdain principle. The power type variational principles directly work in the state space so that they not only omit some transforms in the time space during the building of the related variational principles, but also make it convenient to build numerical models for dynamic problems.
出处
《应用数学和力学》
CSCD
北大核心
2015年第11期1178-1190,共13页
Applied Mathematics and Mechanics
基金
国家自然科学基金(10272034)~~
关键词
不可压缩流体
Jourdain原理
d’Alembert原理
功率型变分原理
功能型拟变分原理
变积方法
incompressible viscous fluid
Jourdain principle
d＇ Alembert principle
power type variational principle
work-energy type quasi-variational principle
variational integral operation
作者简介
冯晓九（1964-），男，吉林人，教授，博士，硕士生导师（E—mail：fengxiaojiu999@126．com）
梁立孚（1939-），男，河北人，教授，博士生导师（通讯作者．E-mail：lianglifu@hrbeu．edu．cn）．
