斜冲击动荷系数的能量法推导

Derivation of Dynamic Factor for Oblique Impact Using Energy Method

冲击问题是工程中常见的问题,也是材料力学授课的重要组成部分。然而一般授课中只讲竖直冲击和水平冲击问题,对于工程中可能遇到的斜冲击问题暂无涉及。该文针对斜冲击问题,采用能量方法对动荷系数进行了推导。结果表明:对于斜冲击动荷系数,水平杆的水平冲击问题取极大值,竖直梁的水平冲击问题取极小值,得到的斜冲击动荷系数可以退化到水平冲击和竖直冲击。并用有限元数值模拟进行了验证,数值解与理论解相对差不超过1.5%。该结果有助于深入了解冲击问题,对材料力学的教学和工程应用问题的分析具有重要意义。

Impact problem is a common problem in engineering,and it is also an important part of mechanics of material.In general teaching process of mechanics of material teaching,only vertical impact and horizontal impact problems are taught.However,oblique impact problems are not involved.In this paper,the dynamic load coefficient is derived by energy method for oblique impact problem.The results show that for the dynamic load coefficient of oblique impact,the horizontal impact problem of horizontal bar is the maximum,and the horizontal impact problem of vertical beam is the minimum.The obtained oblique impact dynamic load coefficient can be degenerated to horizontal and vertical impact.It is verified by finite element numerical simulation,and the relative difference between numerical solution and theoretical solution is not more than 1.5%.This result helps to understand the impact problem in depth,which is of great significance for materials mechanics teaching and analysis of engineering application problems.