基于Hamilton原理分析柱脚铰接弹性刚架的静力屈曲  

The static buckling of elastic portal frame with hinged-hinged support based on the Hamilton principle

作　　者：韩志军[1] 王倩颖 张善元[1] 路国运[1] 王景超 

机构地区：[1]太原理工大学应用力学与生物医学工程研究所,山西太原030024 [2]赛鼎工程有限公司(化学工业第二设计院),山西太原030006

出　　处：《西安建筑科技大学学报（自然科学版）》2010年第4期480-486,共7页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10772129;10702047);山西省自然科学基金资助项目(2010011005)

摘　　要：基于Hamilton原理导出刚架屈曲的控制方程,求解控制方程,得出了有侧移和无侧移刚架屈曲的计算长度系数μ的解析表达式,给出了刚架屈曲时梁柱的模态方程,画出了不同梁柱线刚度比G下的屈曲模态图.用MATLAB编程计算得到刚架屈曲时的计算长度系数μ的范围,进一步得到了弹性刚架的静力屈曲荷载.结果表明:刚架的计算长度系数随着梁柱线刚度比的增大而减小;有侧移刚架的计算长度系数高于无侧移的,其最小倍数约为2.7,有侧移刚架计算长度系数的范围为2～+∞,无侧移为0.7～1;柱的屈曲模态随着梁柱线刚度比的增大而逐渐明显,梁的屈曲模态与梁柱线刚度比无关.用ANSYS对其进行计算机模拟,其模拟结果和理论值基本吻合,其误差不超过0.4%.The buckling governing equation of the portal frame is derived based on the Hamilton principle. The calculating length of factors μ of no-sway and lateral sway portal frame is acquired by solving the governing equation. The mode equations on different stiffness of beam and column G are given,and the buckling modes are drawn. The scope of the calculating length of factors μ is obtained using MATLAB,and the static buckling load of elastic portal frame is also obtained. The calculating results are as follows. The effective length factor decrease as G increased,the factor of the lateral sway portal frame is larger than that of the no-sway,the smallest multiple is about 2.7,and the scopes of the factor are 2～＋∞,0.7～1 respectively. The mode of column change clearly as G increase,the mode of beam has nothing with G. The static buckling of portal frame is simulated by using ANSYS,and the results remain nearly the same as those from the theoretical ones,the error is less than 0.4%.

关 键 词：HAMILTON原理 有侧移 计算长度系数 梁柱线刚度 

分 类 号：O343.9[理学—固体力学]