基于微分变换法的变截面压杆临界载荷分析  

Analysis of critical load of variable cross-section compression bars based on differential transformation method

作　　者：杨文秀 滕兆春[1] YANG Wenxiu;TENG Zhaochun(School of Science,Lanzhou University of Technology,Lanzhou Gansu 730050)

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《首都师范大学学报（自然科学版）》2021年第5期27-31,共5页Journal of Capital Normal University：Natural Science Edition

基　　金：兰州理工大学校级高等教育研究课题(GJ2019C⁃21)。

摘　　要：通过细长压杆挠曲近似微分方程理论,建立了变截面压杆失稳控制微分方程.该方程为4阶变系数常微分方程,其解析解不易得到,采用微分变换法(DTM)进行数值求解.将变截面压杆的控制微分方程和边界条件进行无量纲化,采用DTM将变截面压杆的无量纲控制微分方程和边界条件转换为包含临界载荷的代数特征方程,通过编程计算数值,给出4种不同边界条件下变截面压杆的临界载荷值与截面变化系数之间的关系曲线.结果表明:不同边界条件下变截面压杆的临界载荷均随截面变化系数的增大而增大,即变截面杆的稳定性较好;同时也表明DTM对求解此类问题过程简单且精度较高.Through the theory of approximate differential equation of deflection curve for slender compression bar,the governing differential equation is established for unstability cross⁃section compression bars.The equation is a fourth⁃order ordinary differential equation with variable coefficients.Its analytical solution is not easy to obtain and the numerical solution is gotten by utilizing a semi⁃analytical method called differential transformation method(DTM).The dimensionless form is obtained for the governing differential equation and boundary conditions of variable cross⁃section compression bars.DTM is used to convert dimensionless governing differential equation and boundary conditions ofvariable cross⁃section compression barinto algebraic characteristic equations ofcriticalloads.The relative curves between the critical load values and the variation coefficients of variable cross⁃section compression bar are obtained numerically for four different boundary conditions by using programming and computing.The results show that the critical load values of the variable cross⁃section compression bar increase with the growth of the variation coefficients of section under different boundary conditions,the stability of the variable cross⁃section compression bar is preferably,it also show that DTM has simple process and very higher accuracy in solving this problem.

关 键 词：变截面 压杆 临界载荷 数值解 微分变换法 

分 类 号：O343[理学—固体力学]