Principles of Mechanics
Principles of Mechanics
复制标题
力学原理
DOI：
10.1007/978-1-4471-0397-4_2
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发表时间：
1993
影响因子：
5.6
通讯作者：
Tongxi Yu
中科院分区：
文献类型：
--
作者：
W. Stronge;Tongxi Yu
物体对缓慢变化的载荷的反应是静态或准静态的。对于缓慢变化的载荷，作用在物体任何一段上的所有力的总和是平衡的，因为没有加速度；即对于物体的任何一段，作用在该段表面的牵引力在大小上是相等的，但在方向上与作用在该段上的任何外力相反。另一方面，载荷的快速变化导致物体加速；在这种情况下，作用于身体任何部位的应力的结果都与加速度和惯性的乘积有关，这与运动定律有关。对于这两大类载荷，可从平衡方程或运动定律得到物体任意部分的应力(或应力合成)变化的微分方程式。这些定律构成了几个有用的原则的基础。在本章中，这些原理的特殊形式将应用于细长物体平面位移的小挠度理论。
The response of bodies to slowly varying loads is static or quasistatic. For slowly varying loads, the sum of all forces acting on any segment of a body are in balance since there are no accelerations; i.e. for any segment of the body, the resultant of tractions on the surface of the segment is equal in magnitude but opposite in direction to any external force acting on the segment. On the other hand, rapid changes in load cause the body to accelerate; in this case the resultants of stresses acting on any part of the body are related to the product of acceleration and inertia by the laws of motion. For these two broad classes of loading the differential equations for variations in stress (or stress resultant) across an arbitrary segment of the body are obtained from either equilibrium equations or the laws of motion. These laws form the basis of several useful principles. In this chapter special forms of these principles will be developed that apply to small deflection theory for planar displacements of slender bodies.