虚功原理在结构杆件内力计算中的应用  

Application of principle of virtual work to computation of internal forces of structural bars

作　　者：周欣竹[1,2] 林佳辉 胡哲文 郑建军 ZHOU Xinzhu;LIN Jiahui;HU Zhewen;ZHENG Jianjun(College of Civil Engineering and Architecture,Zhejiang University of Technology,Hangzhou 310023,China;Zhejiang Key Laboratory of Civil Engineering Structures&Disaster Prevention and Mitigation Technology,Hangzhou 310023,China)

机构地区：[1]浙江工业大学建筑工程学院,浙江杭州310023 [2]浙江省工程结构与防灾减灾技术研究重点实验室,浙江杭州310023

出　　处：《浙江工业大学学报》2020年第2期212-216,共5页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(51878615,51779227);浙江工业大学研究生核心课程项目(GZ17571060001);本科核心课程建设项目(PX-48181685)的资助.

摘　　要：提出了应用虚功原理计算静定结构杆件内力的方法。首先,对于刚体平面运动的7种情形:给定两点虚位移方向和其中一点虚位移大小、两点虚位移大小和其中一点虚位移方向、两点虚位移大小和另外一点虚位移方向、两点虚位移方向和另外一点虚位移大小、瞬心位置和一点虚位移大小、瞬心位置和一点虚位移投影、虚位移在两个方向的投影,归纳出刚体中任意一点虚位移的计算公式;然后,应用虚功原理提出静定结构杆件内力的计算方法;最后,给出了一个组合结构和两个平面桁架的实例说明该方法的有效性。与传统的静力分析方法相比,该方法不必事先求解约束反力,对于计算结构中某一特定杆件的内力特别有效。A method was proposed for computing the internal forces of structural bars by use of the principle of virtual work.First,for seven cases of plane motion of a rigid body,given the virtual displacement directions at two points and the magnitude at one of them,the virtual displacement magnitudes at two points and the direction at one of them,the virtual displacement magnitudes at two points and the direction at the third point,the virtual displacement directions at two points and the magnitude at the third point,the position of the instantaneous center and the virtual displacement magnitude at one point,the position of the instantaneous center and the virtual displacement projection at one point,and the virtual displacement projections along two directions,the computational formula of the virtual displacement at any point in the rigid body was summarized.A computational method was then presented for the internal forces of the bars in a statically determinate structure.Finally,examples of a composite structure and two plane trusses were worked out to verify the validity of the method.Compared with traditional static analysis methods,this one does not need to compute the constraint forces of structures and is particularly efficient for computing the internal force of a specific structural bar.

关 键 词：虚功原理 虚位移 结构 杆件内力 

分 类 号：O342[理学—固体力学]