简支梁大挠度弹性后屈曲载荷与变形的优化算法

An optimization algorithm for calculating the post-buckling load and deformation of simply supported beams with large deflection

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。

In this paper, an optimization algorithm for calculating the post-buckling load and deformation of simply supported beams with large deflection is presented. Firstly, the supported beam is divided into finite sub-sections under large deflection buckling equilibrium state. Then, the post-buckling load is taken as the design variable, and other coordinates of each node are calculated by coordinates of the starting point and formula of bending deformation. After that, the objective function model is constructed by the endpoint coordinates that satisfy boundary conditions. On this basis, two typical examples are analyzed by MATLAB programming, and the theoretical results are compared with the calculation results of finite element analysis software, then the algorithm correctness is confirmed. The solving process of the algorithm in this paper is simple, fast and practical, which provides a reference for the study of large deflection elastic buckling stability of structures with variable cross-section.