流体应力方向、运动方程、广义应力公式综述

Overview about the Direction of Stress in Fluid and Equations of Motion and Generalized Stress Formulae

目前流体力学教材上,关于流体中应力分量的定义、微元六面体上应力分量方向的假设方法各不相同,与此相对应,用应力表示的流体运动微分方程及广义应力公式也必须采取不同形式。若上述对应关系搞错势必得出错误结果。这种问题可能被忽视,为解决此问题,对流体中应力分量的定义、应力方向假设方法、用应力表示的流体运动微分方程及广义应力公式进行了分析和归纳总结,用具体例子加以说明。并给出如何根据应力计算结果的正负判断应力方向的方法。

Now in a variety of fluid mechanics textbooks, the definitions of pij in viscous fluid are not identical, the hypothesis method about the directions of p which act on micro hexahedron in viscous fluid are also not identical. Corresponding to these, the differential equations of fluid motion, which are expressed in the form of stress, must take the different forms. Generalized stress formula must also take different forms. If the correspondence between the definitions of Pij and hypothesis method about the directions of pij and the differential equations of fluid motion and the generalized stress formula are mistaken, erroneous results will certainly be given. This problem may be neglected. In order to solve this problem, the definitions of Plj in a variety of fluid mechanics textbooks were analyzed, these definitions could be classified into two forms. The difference between the first form and the second forms were pointed out. Under the conditions of plj being defined in the first form and in the second form, the hypothesis method about directions of pij which act on micro hexahedron in viscous fluid were analyzed and summarized respectively. Corresponding to every hypothesis method the different forms of differential equations of fluid motion, which were expressed in the form of stress, were listed and the different forms of generalized stress formula were also listed. Specific examples were given to illustrate. The methods of determining real direction of pij according to the positive and negative of calculating results were provided.