功率型变分原理和功能型拟变分原理及其应用

自从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.

Power Type Variational Principles and Work-Energy Type Quasi-Variational Principles and Their Applications

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 principles 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 variational 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.