压杆稳定的能量法视角及其在碳纳米管热屈曲中的应用  

The Perspective of Energy Method on Column Buckling Teaching and Its Application in the Thermal Buckling of Carbon Nanotubes

作　　者：吴继业 黄坤 WU Jiye;HUANG Kun(Department of Mechanics,School of Physical and Mathematical Sciences,Nanjing Tech University,Nanjing 211816,Jiangsu,China;Department of Engineering Mechanics,Faculty of Civil Engineering and Mechanics,Kunming University of Science and Technology,Kunming 650500,Yunnan,China)

机构地区：[1]南京工业大学数理科学学院力学系,江苏南京211816 [2]昆明理工大学建筑工程学院工程力学系,云南昆明650500

出　　处：《力学季刊》2025年第1期211-221,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金原创探索项目(12050001);教育部产学合作协同育人项目(231105635123012);南京工业大学教学改革项目(20230224)。

摘　　要：压杆稳定是大学材料力学课程的重要组成部分,也是比较难讲述的部分.在经典材料力学理论中,临界载荷通过讨论屈曲状态下压杆的近似平衡微分方程的非零解条件得到.该方法简单但较抽象,且不便用于复杂工程稳定性问题的具体求解.为了使学生更好地理解压杆稳定问题的含义及其处理方法,本文从虚功原理和最小势能原理出发,重新梳理了经典压杆稳定问题,并基于这一思路分析了碳纳米管在纵向温度线性梯度下的热屈曲问题,希望为压杆稳定问题的教学和研究提供新的思路,帮助学生更好地理解和掌握压杆稳定的概念和处理方法.and is difficult to apply to complex engineering stability problems.To enhance students'understanding of column buckling and its analytical methods,this study revisits the classical approach through the principles of virtual work and minimum potential energy.Additionally,based on the principle of minimum potential energy,the thermal buckling behavior of carbon nanotubes under a longitudinal linear temperature gradient is examined.This work aims to provide new perspectives for the teaching and research of column buckling,helping students gain a deeper comprehension of relevant concepts and methods in handling buckling problems.

关 键 词：材料力学 压杆稳定 能量原理 线性温度梯度 热屈曲 单壁碳纳米管 

分 类 号：O341[理学—固体力学]