有侧移对称变截面刚架屈曲临界载荷优化算法  

The Buckling Critical Load Optimization Algorithm for a Rigid Frame with a Sway Symmetric Variable Cross Section

作　　者：侯祥林 马英成 刘铁林[2] HOU Xianglin;MA Yingcheng;LIU Tielin(School of Mechanical Engineering,Shenyang Jianzhu University,Shenyang,China,110168;School of Civil Engineering,Shenyang Jianzhu University,Shenyang,China,110168)

机构地区：[1]沈阳建筑大学机械工程学院,辽宁沈阳110168 [2]沈阳建筑大学土木工程学院,辽宁沈阳110168

出　　处：《沈阳建筑大学学报（自然科学版）》2020年第1期94-99,共6页Journal of Shenyang Jianzhu University：Natural Science

基　　金：国家自然科学基金项目(11672190);辽宁省自然科学基金项目(2015020129)

摘　　要：目的针对一类具有侧移的对称变截面刚架屈曲临界载荷求解问题,探讨稳定位型下临界载荷的数值优化算法,并提出基于非线性微分方程边值问题的刚架结构临界载荷优化求解算法.方法从立柱起点条件出发,以待求临界荷载、结点弯矩为设计变量,以结点满足连续和边值条件构造目标函数,应用VB语言编制优化程序对算例进行分析计算,并通过ANSYS有限元软件进行仿真对比.结果横梁长为2 l,柱高为l的等截面刚架的临界载与仿真结果相对误差为1.99%;变截面单梁门式起重机的临界载荷与仿真结果相对误差为2.22%,算法结果与仿真结果相对误差满足精度要求,证实了笔者所提算法的正确性和有效性.结论笔者所提临界载荷优化算法实现了以较少设计变量对临界载荷的高精度计算,为工程中刚架结构稳定性问题的研究提供了参考.To solve a class of sway variable cross-section rigid frame with symmetric buckling critical load problem,the numerical optimization algorithms of critical load with the stable buckling position are discussed,and an algorithm of critical load for rigid frame structures based on the boundary values of nonlinear equations is proposed.Starting from the condition of the starting point of the column,the critical load and junction bending moment are considered as design variables,the objective function is established by the conditions of continuity and boundary values of nodes,the numerical examples are analyzed by VB program,and the results are compared by ANSYS simulation.The relative error of critical load is 1.99%between the algorithm and simulation of the constant cross-section frame with the beam length being is 2 l and the column height is l;The relative error of critical load is 2.22%for variable cross-section single-girder gantry crane,the relative error is satisfied the accuracy requirement,and confirming the correctness and effectiveness of the proposed algorithm.The proposed algorithm achieves high precision calculation of critical load with less design variables,and provides a reference for the study of the stability of rigid frame structures in engineering.

关 键 词：刚架稳定 非线性微分方程边值问题 优化算法 临界载荷 位型 

分 类 号：TU973.25[建筑科学—结构工程] O224[理学—运筹学与控制论]