论文标题
夫妇的性格和夫妇压力在连续力学中
Character of couple and couple-stress in continuum mechanics
论文作者
论文摘要
在本文中，从基本的角度研究了力矩和夫妻在机械上的概念。事实证明，尽管一对夫妇的力矩向量在刚体的机械和材料的强度中非常有用，但在连续力学中它一直具有误导性。为了指定一对在连续力学中的集中夫妇的效果，不仅必须指定夫妻时刻，而且还必须指定其组成平行的相反力的作用线。然而，在连续的平衡或运动方程式中，只有身体夫妇的瞬间，夫妇的束缚和夫妇压力的力矩出现，而没有指定任何夫妇密度力量的作用线。这导致连续体的应力状态和变形的状态不唯一，这表明了夫妻压力张量的不确定性。然而，连续体中压力和变形的物理状态是独特而确定的。因此，这对身体夫妇的形式，夫妇牵引力和夫妇应力施加了一些限制。在这里，使用连续体中相互作用的唯一性用于确定连续体不支持身体夫妇的分布，以及与正常矩的表面扭曲夫妇牵引分布的分布。由此，还建立了夫妇牵引力作为双层剪切力的双层牵引力的作用机理，以及连续力力学中夫妇压力矩张量的偏斜对称特征。
In this paper, the concept of moment and couple in mechanics is examined from a fundamental perspective. It turns out that although representing a couple by its moment vector is very useful in rigid body mechanics and strength of materials, it has been very misleading in continuum mechanics. To specify the effect of a concentrated couple in continuum mechanics, not only the couple moment, but also the line of action of its constituent parallel opposite forces must be specified. However, in the governing equations of equilibrium or motion of a continuum, only moment of body couple, moment of couple-tractions, and moment of couple-stresses appear without specifying the line of action of any couple density forces. This results in non-uniqueness of the state of stresses and deformation in the continuum, which has shown itself in the indeterminacy of the couple-stress tensor. Nevertheless, the physical state of stress and deformation in the continuum is unique and determinate. Therefore, this imposes some restrictions on the form of body couple, couple-traction and couple-stresses. Here, the uniqueness of interactions in the continuum is used to establish that the continuum does not support a distribution of body couple, and a distribution of surface twisting couple-traction with normal moment. From this the mechanism of action of the couple-traction as a double layer of shear force-tractions, and the skew-symmetric character of the couple-stress moment tensor in continuum mechanics are also established.
