三向应力Mohr圆的真实构成及剪应力作用方向的确定

三向应力Mohr圆的构成在传统上是借助公式推证而得，并以平面图形来表示，缺乏三维的真实感和直观性。在应力应变分析中，对于平面应力问题，可以通过平面应力摩尔圆确定过一点不同斜面上的应力分量及其作用方向。对于三维问题，利用摩尔圆图解法可以确定某一斜面上的正应力和剪应力的数值，但不能表示剪应力的作用方向。剪应力的作用方向需要通过另外的图解方法来确定。本文分别从坐标系旋转和数值计算的角度解释了三向应力Mohr圆的构成过程，形象地说明了Mohr圆的物理本质。针对三向应力Mohr圆不能表示剪应力作用方向的问题，通过矢量运算，给出了剪应力作用方向的确定公式。

Construction of Mohr Stress Circle for Three-Dimensional Stress and Determination of Shear Stress Direction

The Mohr stress circle for three-dimensional stress is usually determined by formulas and illustrated in plane, which is lack of intuitional meanings. In stress analysis, a single Mohr circle is often used to illustrate two-dimensional stress tensors or as a practical method of stress determination. As for three-dimensional states, the Mohr circle diagram does not provide the direction of shear stress, and a secondary construction is required to obtain the shear stress direction. In this paper, the axis-rota ting method and numerical method were used to interpret the construction of Mohr stress circle for three-dimensional stress. Regarding the shortcoming of Mohr stress circle in describing the direction of shear stress, a ma thematic formula was given to determine the direction of shear stress meanwhile.