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简略回顾了柱子和平板的弹塑性分支屈曲问题。由于薄壁组合结构内力分布的不均匀性和结构本身的复杂性,本文提出了一种计算薄壁组合结构弹塑性分支屈曲荷载的有限元混合解法。利用切线刚度增量法和修正的Newton-Raphson法计算屈曲前的弹塑性内力分布,然后和用Stowell形变理论和逆幂叠代法求弹塑性屈曲荷载。此算法已在微型计算机上实现。程序要求材料是应变强化的,并接受三种强化的应力-应变关系:(1)Ramberg-Osgood应力-应变关系,(2)双线性应力-应变关系,(3)以离散点数值输入的任意凸强化的应力-应变关系。 用本文的方法计算了梁、框架、矩形板和加筋板壳在各种边界条件和不同荷载工况下的弹塑性屈曲荷载。计算结果与解析解及有关作者的数值和实验结果很好符合。
The elasto-plastic branch buckling problems of columns and plates are briefly reviewed. Due to the inhomogeneity of the internal force distribution and the complexity of the structure of the thin-walled composite structure, this paper presents a finite element hybrid solution method to calculate the elastoplastic bifurcation buckling loads of thin-walled composite structures. The tangential stiffness increment method and the modified Newton-Raphson method are used to calculate the elastic-plastic internal force distribution before buckling, and then the elastic-plastic buckling load is obtained by using the Stowell deformation theory and the inverse power iteration method. This algorithm has been implemented on a microcomputer. The procedure requires the material to be strain-strengthened and accepts three kinds of reinforced stress-strain relations: (1) Ramberg-Osgood stress-strain relationship, (2) bilinear stress-strain relationship, (3) numerical input with discrete points Arbitrary convex reinforced stress-strain relationship. In this paper, the elasto-plastic buckling loads of beams, frames, rectangular plates and stiffened plate shells under various boundary conditions and different load conditions are calculated. The calculation results are in good agreement with the analytical solution and the author’s numerical and experimental results.