Matlab数值积分法求解悬臂梁弯曲变形问题  

Application of Matlab Software in Bending Problem of a Cantilever Beam

作　　者：李亮 Li Liang(School of Mechanics and Optoelectronic Physics,Anhui University of Science and Technology,Huainan City,Anhui Province 232001)

机构地区：[1]安徽理工大学力学与光电物理学院,安徽淮南232001

出　　处：《黄河科技学院学报》2023年第8期50-55,共6页Journal of Huanghe S&T College

基　　金：国家自然科学基金项目(11902002);安徽省质量工程项目(2020xsxxkc149,S202110361198,S202210361197)。

摘　　要：提出使用Matlab数值积分法求解悬臂梁弯曲变形问题。首先根据载荷作用形式将梁分段,由载荷集度、剪力、弯矩之间的微分关系,以及梁弯曲近似微分方程,得到使用载荷集度表示的挠曲线微分方程,将该方程转化为4个变量函数的线性常微分方程组,通过确定常微分方程组的初值条件,利用Matlab ODE45命令求解微分方程组,得到4个变量函数,进而得到剪力、弯矩、转角和挠度,并绘制出内力图和变形图,并确定出内力和变形的最大值。通过计算实例,验证了方法的有效性。A numerical integration method based on Matlab software is introduced to solve the bending deformation problem of a cantilever beam.The beam is segmented according to the form of load action firstly.The ordinary differential equation between deflection of the beam and density of load is obtained by considering the differential relationship among the density of load,shear force and bending moment and the approximate differential equation of deflection.This equation is transformed into a set of linear ordinary differential equations with four variable functions.By determining the initial value conditions of the ordinary differential equations,the Matlab ODE45 command is used to solve differential equations and obtain four variable functions.Shear force,bending moment,rotation angle and deflection of the beam is derived based on four variable functions.Internal force diagrams and deformation diagrams are drawn and the maximum values are obtained.The effectiveness of the method is verified by taking a calculation example.

关 键 词：悬臂梁 弯曲 剪力 弯矩 挠度 转角 MATLAB 

分 类 号：O341[理学—固体力学]