哈密顿理论在推导框剪结构刚度矩阵中的应用  

Application of Hamiltonian Theory in Solving Element Stiffness Matrix of Frame-Shear Wall Structure

作　　者：王颖[1] 潘福婷[1] 高彬森 WANG Ying;PAN Fu-ting;GAO Bin-sen(School of Civil and Environmental Engineering,Anhui Xinhua College,Hefei,Anhui 230088,China)

机构地区：[1]安徽新华学院土木与环境工程学院,安徽合肥230088

出　　处：《河北北方学院学报（自然科学版）》2018年第9期22-26,29,共6页Journal of Hebei North University:Natural Science Edition

基　　金：安徽新华学院校级自然基金重点项目:"防屈曲耗能支撑与基础隔震联合作用下的不规则结构抗震性能研究"(2016zr004);河北省自然科学基金资助项目:"基于哈密顿对偶体系的复杂建筑结构计算理论研究"(E2006000630)

摘　　要：目的对框剪结构进行静动力方面的分析时,需要推导出结构的单元刚度矩阵,而一般选用近似计算的传统有限单元法来推导单刚矩阵,这种方法误差累计较多,特别是框剪高层结构,误差积累更多。通过新的模型体系进一步探讨基于哈密顿理论及精细积分法求解结构单刚矩阵的可行性和计算精度。方法基于哈密顿理论,选用通用的并联Timoshenko梁模型,将构成框剪结构的综合框架和综合剪力墙抗侧力单元看作竖立的悬臂弯剪梁,均计算剪切、弯曲变形,两个抗侧力单元间通过刚性楼板协同工作。结果求出框剪结构在连续化假定下的拉格朗日函数,结构协同工作分析的哈密顿函数,继而利用精细积分法中基本区段的混合能矩阵求解出框剪结构的单刚矩阵,采用有限元中的位移法,把单元刚度矩阵集成为整刚矩阵。结论利用MATLAB相应程序分析某框剪结构算例,结果验证了此推导方法的可行性和精度要求,避免了一般传统有限单元法误差累计的问题,同时该方法还适用于其他类型的高层建筑结构。Objective In the analysis of the static and dynamic aspects of the frame-shear structure,the element stiffness matrix is necessary to be deduced based on the traditional finite element method.But there are more the errors with this method,especially for high-rise structures.The feasibility and accuracy of the element stiffness matrix based on Hamiltonian theory and the fine integral method are further discussed by the new model system.Methods Based on the Hamiltonian theory,the generalized parallel Timoshenko beam model is used to regard the composite frame and the composite shear wall of the frame-shear wall structure as the vertical cantilever girder.Two anti-lateral force units work together through rigid floors.Results The Lagrangian function of frame-shear structure under the continuity assumption is obtained,as well as Hamiltonian function of the cooperative work analysis.Then,the element stiffness matrix is introduced based on the mixing matrix of the basic section in the precise integration method.The total stiffness matrix is established based on the finite element displacement method.Conclusion Finally,the MATLAB program is used to analyze a frame-shear structure.The results prove the feasibility and precision of the method.It avoids the problem that the traditional finite element method error accumulates,and the method is applicable to other types of high-rise building structures.

关 键 词：单元刚度矩阵 框剪结构 铁木辛柯梁 精细积分法 哈密顿理论 

分 类 号：TU31[建筑科学—结构工程]