应力符号规定的差异与注释

Differences and Annotations of Stress Symbols Convention

为避免材料力学、弹性力学及土力学中应力符号规定的差异导致初学者理解上的混乱,系统阐释了应力符号差异的原因,采用了比较的方法对三种力学中单元体任意方位面上的应力公式及主应力的大小和方向进行了推导。首先,三种力学在剪应力符号规定上存在较大差异:材料力学中将引起单元体顺时针方向转动的剪应力规定为正值,反之为负值;弹性力学中将正(负)面上的剪应力指向正(负)的坐标方向的规定为正,这和材料力学的规定不一致;土力学中和弹性力学的规定完全相反,推导了土力学的主应力表达式,得到斜截面上的主应力表达式与弹性力学的相同,土力学与材料力学主应力方向的表达方式差一个负号。其次,采用张量的形式对材料力学、弹性力学和土力学的应力状态进行描述,避免了应力符号规定差异带来的描述形式和理解上的不一致问题。最后,对一点的应力状态的表达和理解建议使用张量形式,而对二向应力状态主应力和主方向的具体求解采用莫尔圆法更直观。

To avoid confusion for beginners,this paper is aimed at systematically explaining and practically analyzing the differences of stress symbols convention in material mechanics,elastic mechanics,and soil mechanics.A comparative method is used to deduce the size and direction of the main stress and the stress formula of a single unit on any azimuth in these three mechanics.Firstly,the definition of shear stress symbol varies in above-mentioned mechanics,which can be summarized as follows:(1)In the mechanics of materials,the shear stress that makes a single unit rotate in a clockwise direction is defined as positive stress,and vice versa.(2)In elastic mechanics,the direction that the shear stress on the positive(negative)plane points to the positive(negative)coordinate is defined as positive stress,which is inconsistent with the provisions of material mechanics.(3)The stipulations of stress symbol in soil mechanics are contrary to those in elastic mechanics.We deduce the main stress formula in soil mechanics,which is the same as that in elastic mechanics on sloping section,and the difference between the formula of main stress direction in soil mechanics and material mechanics is a negative sign.Secondly,the stress states of material mechanics,elastic mechanics and soil mechanics are described as tensor to avoid the inconsistency of description form and confusion,which is caused by the differences of stress symbol convention.Finally,it is suggested to use tensor to express and understand the stress state at one point,while the Mohr’s circle is more intuitive to obtain the main stress and main direction of the two-way stress state.