标签 材料力学 下的文章

一、位移分量与应变分量1、位移与变形设物体变形前占据区域 $D$，变形后占据区域 $D_1$。同一质点变形前的位置为 $P(x,y,z)$，变形后的位置为 $P_1(\xi,\eta,\zeta)$。记两位置的矢量分别为 $\boldsymbol{r}$ 和 $\boldsymbol{\rho}$，则位移矢量定义为$$ \boldsymbol{u}=\boldsymbol{\rho}-\boldsymbol{r} =u\boldsymbol{e}_x+v\boldsymbol{e}_y+w\boldsymbol{e}_z $$位移分量为$$ \begin…

一、体力和面力确定弹性体的受力状态和变形，需要用到三类基本关系：平衡关系（力之间的平衡，即牛顿力学）几何关系（变形与运动）物理关系（力与变形之间的相互联系）外力在其中作为已知量进入平衡关系，是求解的出发点。作用于弹性体上的外力分为体力和面力两类。体力（body force）是作用在物体微粒体上的力，以单位体积的力即体力集度度量。在物体内取包含点 $O$、体积为 $\Delta V$ 的微元体，作用其上的体力合力为 $\Delta\boldsymbol{P}$，定义：$$ \boldsymbol{p}=\lim_{\Delta V\to0}\frac{\D…

[!NOTE]约定主应力按代数值排序 $\sigma_1 \ge \sigma_2 \ge \sigma_3$；拉应力为正，压应力为负。一、应力状态1、应力是位置的函数材料中不同点处的应力一般不同：$$ \sigma=\sigma(x) $$更一般地，三维连续体中某点的应力状态可由应力张量表示：$$ \boldsymbol{\sigma} = \begin{bmatrix} \sigma_x & \tau_{xy} & \tau_{xz}\\ \tau_{yx} & \sigma_y & \tau_{yz}\\ \tau_…

I. Concepts and ExamplesThe bars is subjected to a pair of longitudinal forces with equal magnitude and opposite directions, and the line of action forces coincides with the axis of the bar.II. Internal Forces and Stress1. Internal forceBecause the action line of the external for…

I. StressThe internal force of a member is not uniformly distributed in most cases, so the definition of internal force concentration is not only accurate but also important, because failure or damage often starts from the place where the internal force concentration is the great…

I. Introduction1. An Overview of Mechanics of MaterialsMechanics of materials mainly studies the deformation of deformable body under external forces,, the additional internal forces caused by the deformation, the failure caused by the internal forces, and the criteria to avoid/c…