悬臂梁固定端不同位移边界条件下解的对比  

Comparison of solutions from different displacement boundary conditions at fixed end of cantilever beams

作　　者：杨连枝[1,2] 张亮亮[2,3] 余莲英[2] 尚兰歌 高阳[2] 王敏中[4] 

机构地区：[1]北京科技大学土木与环境工程学院,北京100083 [2]中国农业大学理学院,北京100083 [3]中国农业大学工学院,北京100083 [4]北京大学力学与空天技术系,北京100871

出　　处：《浙江大学学报（工学版）》2014年第11期1955-1961,共7页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(11472299;11172319);中央高校基本科研业务费专项资金资助项目(2011JS046;2013BH008);教育部新世纪优秀人才支持计划项目(NCET-13-0552);非线性力学国家重点实验室开放基金;国家大学生科研创新项目

摘　　要：为了获得不同的悬臂梁固定端位移边界处理方式对结果的影响,针对悬臂梁承受3种载荷的情况:自由端受切向力,上表面受均布载荷和线性分布载荷,给出悬臂梁固定端利用传统边界条件和最小二乘法处理边界时,Timoshenko梁理论、Levinson梁理论和弹性力学理论的解析解,与有限元计算结果对比.结果表明,Timoshenko梁理论采用传统位移边界和最小二乘法处理边界的结果一致,采用最小二乘法处理边界获得的Levinson梁理论和弹性力学理论的解明显优于传统位移确定方法,且这种优势随着载荷阶次的增加而越加明显.To obtain the influence of different displacement boundary conditions for the fixed end on analyt- ical solutions of a cantilever beam, three load cases for a cantilever beam were investigated, which were a transverse shear force at the free end, a uniformly distributed load at the top surface, and a linearly dis- tributed load at the top surface, respectively. Analytical solutions were given for Levinson theory, Timo- shenko theory, and the elastic theory by using the conventional displacement boundary condition and the boundary condition through least squares method at the fixed end of the beam, and were compared with the solutions by finite element method. It is shown that the solutions from Timoshenko theory by using both the conventional displacement boundary condition and the condition through least squares method are the same; Levinson theory and the elastic theory by using the boundary condition through least squares meth- od provide better results than those by using the conventional boundary condition. With an increase in the order of the load, the superiority becomes more and more obvious.

关 键 词：悬臂梁 边界条件 TIMOSHENKO梁理论 Levinson梁理论 最小二乘法 

分 类 号：TU391[建筑科学—结构工程] TU392