考虑材料非线性的两端固支柱后屈曲载荷优化算法

针对满足Ramberg-Osgood本构关系的6082-T6铝合金固支柱的后屈曲问题进行了研究。利用泰勒展开式得到了用于计算横截面上弯矩的应力显式表达式，并通过弯矩-曲率关系导出了用剪力表示的控制方程。由于同时考虑材料非线性和几何非线性，此时控制方程为二阶非线性微分方程，本文提出了求解包含屈曲载荷的控制方程的优化算法。以屈曲载荷和固支端处的曲率为设计变量，以固支柱中点处的转角和挠度形成目标函数。利用进退法和黄金分割法改变设计变量的值，通过程序中包含的R-K法输出不同的结果，然后将输出的结果代入到目标函数中进行比较，获得包含目标函数极小值的最小区间，最终实现了对满足计算精度的设计变量值的确定。相较于打靶法复杂的分析过程，该优化算法优化过程简单，计算速度较快。为了验证本文算法的正确性，与两端固支6082-T6铝合金柱后屈曲时的数值解进行了对比。

Optimization algorithm for post-buckling load of clamped-clamped column considering material nonlinearity

The post-buckling of 6082-T6 aluminum alloy columns with a clamped-clamped boundary condition and satisfying Ramberg-Osgood constitutive relationship is investigated.An explicit stress expression for calculating the bending moment on the cross section is obtained by using the Taylor expansion, and the governing equation for shear stress is derived in terms of the bending moment-curvature relationship.Since both material nonlinearity and geometric nonlinearity are considered, the governing equation is a second-order nonlinear differential equation, and an optimization algorithm for solving the governing equation containing buckling load is proposed in this paper.The buckling load and curvature at the fixed end are taken as design variables.The objective function is formed by the rotation angle and deflection at the midpoint of the clamped-clamped column.The values of design variables are changed by using advance and retreat method and golden section method, and different results are outputted by the R-K method included in the program.Then the results are substituted into the objective function for comparison, and the minimum interval containing the minimum value of the objective function is obtained.Finally, the values of the design variables satisfying the calculation accuracy are determined.Compared with the complex analysis process of shooting method, the optimization algorithm has a simple optimization process and high calculation speed.In order to verify the correctness of the algorithm, the numerical results of a post-buckling of 6082-T6 aluminum alloy clamped-clamped column are compared.