论文部分内容阅读
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 Qian Weicheng established the power variational principle, the power variational principle and the functional variational principle are different in theory and application, which has become a topic of concern in the academic field.According to Jourdain Principle and d’Alembert principle, the power-type variational principle and the functional-type quasi-variational principle for incompressible viscous fluid dynamics are established. The conditions of the power-dependent variational principle of incompressible viscous fluid dynamics and the functional type Quasi-stationary principle of quasi-variational principle is studied.The application of incompressible viscous fluid dynamics power variational principle in finite element method is studied.The results show that the power variational principle is consistent with the Jourdain principle and the functional variational The principle is consistent with d’Alembert’s principle.The power-based variational principle studies the problem directly in the state space, not only some transforms in the time-domain space can be omitted in the process of establishing the variational principle, but also the finite element method Numerical modeling brings convenience.