变截面压杆稳定非线性微分方程边值问题的最优化算法研究

针对任意约束类型的变截面受压杆件的稳定临界载荷计算问题,结合非线性微分方程数值算法和最优化方法,以起点边界的初始条件、待求临界荷载和附加约束力为设计变量;以终点边值条件满足的函数关系与位型条件构建目标函数,提出变截面压杆临界载荷和稳定位型的优化求解算法。应用VB编制通用的优化计算程序,分析了典型算例;通过对比发现,本文以较少设计变量实现了临界载荷的高精度计算,为工程应用提供参考。

Optimization algorithm of boundary value problem of stable nonlinear differential equation for variable cross-section compression bar

For computation of critical load of variable cross-section compression bar under all types of constraints, numerical algorithms for nonlinear differential equation are combined with optimization methods. Taking initial condition of the starting point boundary, unknown critical load and additional constraint force as design variables, terminal boundary value condition and buckling position condition as objective function, an optimization algorithm for critical load and stable buckling deformation of variable cross-section compression bar is proposed. Visual Basic is used to develop a universal computing program. Typical examples are analyzed. Comparison shows that critical load is computed with high precision and the method can be applied in engineering.