一类变截面刚架结构的临界载荷算法研究

Research of critical load algorithm for a class of rigid frame structures with variable cross-section

本文提出了一类变截面刚架结构非对称临界载荷的数值算法。本文算法以临界载荷、节点内力与挠度为设计变量,根据屈曲状态下满足的挠曲线微分方程组、结构离散化的思想和差分原理构建了目标函数模型。通过VB语言结合多维Powell优化方法编制了变截面刚架结构的临界载荷求解程序,并计算了典型工程算例的临界载荷。运用ANSYS有限元软件对算例结果进行了仿真对比分析,发现了随着离散点数量的增加,本文算法计算的临界载荷与仿真计算的结果之间的相对误差呈减小趋势并最终满足精度要求,证实了本文算法的正确性和有效性,为工程中刚架结构稳定性问题的研究提供了参考。

In this paper, a numerical algorithm of asymmetric critical load for a class of rigid frames with variablecross-section is proposed. Taking the critical load, internal force of nodes and deflection of each node as designvariables , the objective function model is established by the deflection curve differential equations in the bendingstage , the idea of structural discretization , and the difference principle. Then the critical load solution program of rigid frame structure with variable section is compiled by VB language which combining multi-dimensional Powell optimization method , and the critical load of a typical engineering example is analyzed and calculated. ApplyingANSYS to simulate the results of numerical example , the relative error of the critical load between the algorithm ofauthor and the simulation show a reduced trend with the increase of discrete points , and the final calculated resultsmeet the precision requirement , which verify the correctness and validity of the algorithm , providing a reference forthe research on the stability of rigid frame structure in engineering.