基于内力图和几何条件求解梁位移方程的方法  

A Method for Solving Displacement Equation of Beam Based on Internal Force Diagram and Geometric Conditions

作　　者：张宏学 Zhang Hongxue(School of Mechanics and Optoelectronics 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》2021年第5期16-20,共5页Journal of Huanghe S&T College

基　　金：安徽省教学研究项目(2019jyxm0175);2017年度校级教学改革研究项目资助(2017jyxm056)。

摘　　要：挠度和转角是衡量梁弯曲变形程度的两个参数,为了确定梁的挠曲线方程和转角方程,基于梁的弯矩图建立了挠曲线方程和转角方程的表达式,然后基于挠曲线近似微分方程建立了梁的挠度、剪力、载荷集度三者之间的微分关系。最后结合算例说明如何利用内力图、力的边界条件和位移边界条件求解挠曲线方程和转角方程中的待定系数。与积分法相比,利用该方法求解挠曲线方程和转角方程不需要列弯矩方程,其本质是求解代数方程,工程技术人员易于理解和掌握。Deflection and angle are two parameters to measure the degree of beam bending deformation.In order to determine the equation of deflection line and rotation angle of the beam,the equation of deflection line and rotation angle are established based on the moment diagram of the beam.The differential relationship among the deflection,shear force and load concentration of the beam are established based on the approximate differential equation of the deflection line.Finally,an example is given to show how to use internal force,force boundary conditions and displacement boundary conditions to solve the undetermined coefficients in the equations of deflection and rotation.Compared with the integral method,the bending moment equation is not required to solve the equation of deflection line and angle by means of this method.To solve algebraic equations is the essence of the method.It is easy to understand and master for engineering technicians and students.

关 键 词：力的边界条件 位移边界条件 平面弯曲梁 挠曲线方程 转角方程 

分 类 号：O341[理学—固体力学]