基于哈密顿理论的薄壁杆件稳定性分析

从薄壁杆件弯扭耦合变形的经典理论出发,由产生变形相等的原则引入等效荷载,进而导出薄壁杆件稳定分析时的方程组;通过引入对偶变量,将问题的求解体系从拉格朗日体系导入哈密顿对偶体系,从而建立薄壁杆件稳定问题的哈密顿正则方程。然后,采用二分法和精细积分法求出临界荷载高精度的数值解,与算例结果比较吻合,验证了本方法的可靠性与可行性。本方法可方便地用于变截面薄壁杆件的计算,同时也适用于高层建筑中,可简化薄壁杆件的构件或结构。

Analysis for stability of thin-walled bar using Hamiltonian theory

Based on studying the coupled bending-torsional deformation classical theory and equal load which is introduced by principle of equal deformation,the equations of analysis for stability of thin-walled bar are got.The dual systematic methodology of Hamiltonian is got from Alagrange system by introducing the dual equations,then the Hamilton’s canonical equations which are used to analyse stability of thin-walled bar are established.Precise numerical value of critical load can be achieved according to the using of dichotomy theory and precise integration method.More consistent with the simulation results to verify the reliability and feasiblity of this method.This method is easily used in calculation of thin-walled bar with variable cross-section as well as high buildings that are simplied as thin-walled bar members or structural components.