雙對稱薄壁梁在軸力與不均勻彎矩作用下的側向-扭轉挫屈分析

Abstract

本研究的主要目的是探討雙對稱薄壁梁在軸向力及不均勻彎矩同時作用下的非線性側向-扭轉挫屈分析。 本研究採用文獻[1]的梁元素，在文獻[1]中利用共旋轉法，虛功原理及非線性梁理論之二階一致線性化來推導梁元素。 本文解非線性平衡方程式的數值計算方法是基於牛頓-拉福森(Newton-Raphson)法配合弧長控制(arc length control)法的增量迭代法。本研究中以系統切線剛度矩陣之行列式值為零當作挫屈準則，利用弧長的二分法求得挫屈負荷。 本研究中探討了不同斷面、長度、邊界條件的梁在軸力及各種不均勻彎矩作用下的側向-扭轉挫屈彎矩及挫屈後行為，並驗證文獻上線性挫屈分析結果的正確性。

In the study, the nonlinear lateral-torsional buckling analysis of bisymmetric thin-walled beam under axial force and nonuniform bending moment is investigated. The beam element developed in reference [1] is employed here. In reference [1], the co-rotational formulation, the virtual displacement method and the consistent second order linearization of geometric beam theory are used. An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A bisection method of the arc length is used to find the buckling load. The nonlinear lateral-torsional buckling moment and post buckling behavior of beams with different sections, lengths, and boundary conditions under axial force and nonuniform bending momen is investigated. The accuracy of results of the linear buckling analysis given in the literature is examined.