考虑轴向均布荷载的细长压杆临界荷载近似解析解  

Approximate Analytical Solutions for Critical Load of Slender Rods by Considering Axially Uniform Load

作　　者：黄开志 丁剑平 贺燕卿 郑恒伟 陈小亮 HUANG Kaizhi;DING Jianping;HE Yanqing;ZHENG Hengwei;CHEN Xiaoliang(School of Civil and Hydraulic Engineering,Chongqing University of Science and Technology,Chongqing 401331,China;No.8 Engineering Company of China Railway No.1 Engineering Group Co.,LTD,Chongqing 401121,China)

机构地区：[1]重庆科技大学土木与水利工程学院,重庆401331 [2]中铁一局集团第八工程有限公司,重庆401121

出　　处：《江苏工程职业技术学院学报》2024年第2期1-5,共5页Journal of Jiangsu College of Engineering and Technology

基　　金：重庆市科技局基础与前沿研究项目(编号:cstc2019jcyj-msxmX0317)。

摘　　要：计算细长压杆临界荷载时,若考虑轴向均布荷载,则只能求得数值解,不能得到解析解。为获得近似解析解,建立了细长压杆屈曲时的势能函数,由势能驻值原理导出稳定方程进行求解。受既有2种细长压杆的傅里叶级数型挠曲线的启发,采用数学软件Maple 18对基本三角函数或其乘积进行循环测试,逆向筛查出另外8种既满足位移边界条件又满足内力边界条件的傅里叶级数型挠曲线,求得10种细长压杆临界荷载的近似解析解。结果表明:临界荷载与轴向均布荷载成准线性关系。若在所得解答中令轴向均布荷载为零,则可得细长压杆的欧拉临界荷载;若令上端中心轴向荷载为零,则可得细长压杆的均布临界荷载。若考虑轴向均布荷载,支座位置互换后临界荷载一般会有特别显著的变化。比较所得解答与有限元数值解发现:所有细长压杆的两种解较一致,即所得解答能满足预期要求。When axially uniform load is considered in the calculation of critical loads of slender rods,numerical solutions are obtained instead of analytical solutions.To obtain approximate analytical solutions,a potential energy function was established on condition that slender rods buckle,after which the stability equation was derived from the principle of stationary potential energy.Inspired by three existing deflection curves of the Fourier series,another six satisfying both the displacement boundary and the internal force boundary were explored,and nine approximate analytical solutions for the critical loads of slender rods were obtained.The results have shown that the critical loads have linear or quasi-linear relationships with the axially uniform load.If the axially uniform load is set to zero in the solutions obtained,the Euler critical load can be obtained.If the axial load at the center of the upper end is set to zero,the uniform critical load can be obtained.When the axially uniform load is considered,the critical load will generally have a significant change after bearing positions are reversed.By comparing the obtained solutions to the finite element solutions,it has been found that these two solutions are in good agreement for most of the slender rods,indicating the obtained solutions meet the expected requirements.

关 键 词：细长压杆 均布荷载 稳定方程 临界荷载 

分 类 号：O341[理学—固体力学]