考虑恒载效应对梁静力反应影响的有限元分析  

The finite element analysis for effect of dead load on static responses of beam

作　　者：张家玮[1,2] 刘生纬[1,2] 吴亚平[1,2] 杨治国[1,2] 刘廷滨[1,2] 赵建昌[1,2] 

机构地区：[1]兰州交通大学甘肃省道路桥梁与地下工程重点实验室,兰州730070 [2]兰州交通大学土木工程学院,兰州730070

出　　处：《应用力学学报》2013年第5期762-767,807,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51368035);长江学者和创新团队发展计划资助(IRT1139)

摘　　要：从非线性弹性理论出发,应用Hamilton原理,采用三次多项式作为位移函数给出了考虑恒载效应影响的一般形式的单元刚度矩阵,建立了考虑恒载效应影响时梁静力分析的有限元方法,为解决各种不同构造、荷载类型、刚度变化、边界条件下的实际结构考虑初始恒载影响提供了有效的工具。讨论了在分布和集中两种恒载类型条件下恒载大小、结构自身刚度(惯性矩、惯性半径、跨度)等因素对各类梁(简支梁、两端固支梁、悬臂梁)静力反应的影响,结果表明:梁自身的刚度会对恒载效应造成影响,结构越柔(约束越弱、或惯性矩越小、或跨度越大、或回转半径越小),这种影响越大。验证了初始恒载的存在减小了梁在活载作用下的静力反应,并且这种影响与恒载的大小及结构自身的刚度有关。Based on nonlinear elastic theory and Hamilton's principle,a more generalized element stiffness matrix,the effect of dead load on the stiffness being considered,is given with a cubic polynomial being taken as the displacement function.A finite element method for static analysis considering the effect of dead load is presented,with corresponding computer programs being coded,which facilitates the analysis of real structures with various conformations,stiffness distribution features,loading and boundary conditions.Through a discussion of various beams(simply-supported beam,beam fixed at the two ends,and cantilever beam),the effects of key physical parameters,including the magnitude of initial load,sectional inertia moment and inertia radius,span,and restraint conditions,on the initial load influence factor are discussed and the corresponding static and dynamic characteristics are presented.The results validate that with the dead load in existence,the static responses induced by later-applied loads would become reduced and extent of this reduction relates to the magnitude of dead load,stiffness and restraining conditions of the beam.

关 键 词：恒载效应 静力反应 有限元法 载荷影响刚度矩阵 

分 类 号：TU31[建筑科学—结构工程]