平面应力状态下主应力方向的快速判定方法探讨

Discussion on Rapid Determination Method of Principal Stress Direction Under Plane Stress State

在实际工程问题中,关于受力构件最大主应力大小和方向的判定是十分重要的。目前相关的力学教材中关于平面应力状态主应力方向还没有十分明确和全面的论证,本文补充了教材中关于平面应力状态主应力方向判定规定的理论证明,并提出了一种直观判定主应力方向的方法,即仅利用单元体上的切应力快速判定出主方向,并引用实例进行了验证,解决了平面应力状态下主应力方向快捷确定的应力状态分析问题,研究结果对本科生和研究生理论教学和工程实践都有十分重要的意义。

In engineering practice, it is very important to determine the magnitude and direction of the maximum principal stress of the bearing member. At present, there is no clear and comprehensive demonstration of the principal stress direction of the plane stress state in the relevant mechanics textbooks. This paper supplements the theoretical proof of the determination of the principal stress direction of the plane stress state in the textbook,and proposes an intuitive method to determine the direction of the principal stress, that is, only the shear stress on the unit body is used to quickly determine the main direction, and examples are cited for verification, which solves the problem of stress state analysis that the principal stress direction is quickly determined under the plane stress state. The research results are of great significance to the theoretical teaching and engineering practice of undergraduates and postgraduates.