基于运动学的静定结构平衡问题的虚位移原理分析  

ANALYSIS OF VIRTUAL DISPLACEMENT PRINCIPLE OF STATICALLY DETERMINATE STRUCTURE EQUILIBRIUM PROBLEM BASED ON KINEMATICS

作　　者：舒开鸥 郭子涛 杨忠[1] 陈彬 郭钊 SHU Kai’ou;GUO Zitao;YANG Zhong;CHEN Bin;GUO Zhao(School of Construction Engineering and Urban Planning,Jiujiang University,Jiujiang 332005,Jiangxi,China;School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou 221116,Jiangsu,China)

机构地区：[1]九江学院建筑工程与规划学院,江西九江332005 [2]中国矿业大学力学与土木工程学院,江苏徐州221116

出　　处：《力学与实践》2021年第6期976-980,共5页Mechanics in Engineering

基　　金：国家自然科学基金(11762008);江西省教改课题(JXJG-20-17-2);九江学院教改课题(XJJGYB-19-31)资助项目。

摘　　要：与平衡方程法相比,虚位移原理分析静定结构平衡问题的优势在于,可仅用一个虚功原理方程求出目标未知力,既不用先计算支座反力等其他未知力,也不用求解由多个方程联立组成的方程组。但虚位移原理分析静定结构平衡问题的难点在于虚位移的计算。根据基点法、速度瞬心法和速度投影定理等运动学基本理论,虚铰和无穷远虚铰的运动学特征,以及虚功的换算技巧,提出了方便简化的虚位移计算,进而能简化静定结构受力分析的方法。最后,给出了两个简单静定结构和一个复杂静定结构受力分析的算例。Compared with the equilibrium equation method,the principle of virtual displacement in the statical analysis of structural equilibrium problems has the advantage that the unknown target force can be solved by only one equation from the principle of virtual work,which means neither the supporting reaction and other unknown forces need to be calculated,nor a system of equations needs to be solved.The difficulty of virtual displacement principle is the calculation of virtual displacement.According to the basic theory of kinematics,the kinematic characteristics of virtual hinge and infinite virtual hinge,and the conversion technique of virtual work,this paper develops a method to simplify the calculation of virtual displacement.It also provides examples of force analysis,two for simple statically determinate structure and one for complex statically determinate structure.

关 键 词：虚位移 静定结构 受力分析 运动学 

分 类 号：O342[理学—固体力学]