基于位移置换法的超静定梁变形解析计算  

Analytical calculation of deformation of statically indeterminate beam based on displacement replacement method

作　　者：李银山[1] 刘灿昌[2] 王新筑[3] 李欣业[1] Li Yinshan;Liu Canchang;Wang Xinzhu;Li Xinye

机构地区：[1]河北工业大学机械工程学院,天津300401 [2]山东理工大学交通与车辆工程学院,淄博255000 [3]重庆大学航空航天学院,重庆400044

出　　处：《起重运输机械》2022年第11期74-79,共6页Hoisting and Conveying Machinery

基　　金：国家自然科学基金(11972145);山东省自然科学基金(ZR2020ME122);重庆市研究生教学改革研究基金(yjg193010)。

摘　　要：文中利用位移互等定理给出了单位载荷作用下的位移置换函数,通过变形叠加方法计算超静定梁任意一点变形。首先推导在单位力作用下各种边界梁的位移置换函数,然后通过外载与位移置换函数互乘的积分求解超静定梁变形解析解,再利用Maple程序计算任意节点位移数值,得到超静定梁变形曲线。计算实例表明,位移置换法计算梁的位移程式化,公式简单且概念清楚,编程方便且计算速度快,易于得到解析解。In this paper,the displacement replacement function under unit load is given based on the displacement reciprocity theorem,and the deformation of any point of statically indeterminate beam was calculated by deformation superposition method.Firstly,the displacement replacement functions of various boundary beams under the action of unit force were derived.Then,the analytical solution of statically indeterminate beam deformation was solved by the integration of external load and displacement replacement functions.Then,the displacement value of any node was calculated by Maple program,and the deformation curve of statically indeterminate beam was obtained.The calculation example shows that the displacement replacement method is stylized,the formula is simple,the concept is clear,the programming is convenient,the calculation speed is fast,and the analytical solution is easy to obtain.

关 键 词：位移置换法 位移置换函数 超静定 计算 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]