理想粘塑性流体润滑问题的参变量变分原理

本文给出了理想粘塑性流体润滑问题的参变量变分原理.在膜厚方向压力为常数的假设下,塑性剪切滑移面将发生在固液交界面上,因而可以选择边界速度滑移量为参变量(控制变量).文中讨论了采用有限元求解时的实施过程,原问题最后可化为求解带约束条件的参数二次规划问题.该方法简单可靠,具有良好的工程应用前景.

Parametric Variational Principle for Lubrication Problem of Perfectly Viscous-Plastic Fluids

In the past there has not been an effective mathematic method to deal with the lubrication problem of perfectly viscous-plastic fluid. As a result there has been a little progress in the study related to this topic. The parametric variational principle for this kind lubrication problem is presented in this paper. The plastic slippage would occur at the two lubricated surfaces if the fluid film pressure were assumed to be constant through the film thickness, so that the boundary tangential slippage velocity can be ingeniously taken as the parametric vector (in other words, the control vector). The solution process of finite element method is discussed. The studied problem can be, at last, reduced to a parametric quadratic programming with the constraint conditions. The present method, which is simple and reliable, shows us a good prospect in the engineering application.