基于哈密顿体系的薄壁型钢构件的整体稳定性分析

摘要

In this paper,a calculation model of Cold-formed thin-wall steel which under the axial compression load was set up by using the coupled bending-torsional deformation classical theory,and then the Lagrange function and the Lagrange equations were got; A Hamiltonian functions was constituted by introducing dual variables,the use of Hamiltonian mechanics leaded the question from the Lagrange system to the Hamilton dual system,then the Hamilton' s canonical equations which were used to analyze stability of thin-walled bar were established.The precise numerical value of critical load could be achieved according to the using of dichotomy theory and precise integration method.This method has higher precision and the calculating process is simple and clean.This method can be extended to apply to study the stability of the Variable Cross-section.%根据薄壁杆件弯扭耦合变形的经典理论,建立轴心压力作用下的薄壁型钢构件的弯扭稳定分析的计算模型,导出拉格朗日函数和拉格朗日方程；并引入对偶变量,将问题导入哈密顿对偶求解体系,建立型钢构件稳定问题的哈密顿正则方程,最后利用混合能的精细积分法及二分法求出临界荷载.本方法思路清晰,计算精度高,可推广应用于变截面构件的稳定性分析.