应力应矩平衡微分方程、斜截面上的应力应矩及边界条件
New Equilibrium Differential Equations and Boundary Conditions
本文由应力、应矩共同作用下的单元的平衡,推导出含有应力和应矩的6个平衡微分方程及6个综合平衡微分方程。新平衡微分方程把9个应力分量和9个应矩分量联系在一起;完全不同于现行弹性理论把扭矩和弯矩化成剪应力和正应力。新平衡微分方程得出不是任何变形形式下都存在剪应力互等定理;只有纯拉伸和纯剪切存在剪应力互等定理;扭转和弯曲不存在剪应力互等定理。推导出物体内任一点任意方向上的应力和应矩。在此基础上出推导出三个应力边界条件和三个应矩边界条件。
In this paper, from the balance of a unit body under the action of the stress and MPUA, 6 new equilibrium differential equations and 6 comprehensive equilibrium differential equations are deduced. The new equilibrium differential equations connect 9 stress quantities with 9 MPUA quantities, which is not like the now-used elastics mechanics that transform the torsion and bending moment into shear stress and normal stress. The new equilibrium differential equations pointed out that the shear stress reciprocal theorem works only on the conditions of pure pulling and pure shearing. The stress state of a unit body is developed. 3 boundary conditions of stress and 3 boundary conditions of MPUA are developed.
韩晓东、蔡冰倩、韩文坝
力学
单位面积上力矩的极限(应矩) 平衡微分方程 边界条件 剪应力互等定理
MPUA (Moment per Unit Area)Equilibrium Differential EquationsBoundary conditionsShear Stress Reciprocal Theorem
韩晓东,蔡冰倩,韩文坝.应力应矩平衡微分方程、斜截面上的应力应矩及边界条件[EB/OL].(2006-08-08)[2025-08-04].http://www.paper.edu.cn/releasepaper/content/200608-91.点此复制
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