框剪结构动力时程分析的精细积分法
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摘要
从框剪结构的总势能出发,根据结构的并联铁摩辛柯梁模型求得框剪结构协同分析的哈密顿对偶体系,由两端边值问题精细积分法中的区段混合能矩阵推导出结构的层单元刚度矩阵,然后利用有限元刚度集成法形成总刚矩阵,利用初值问题的精细积分法对框剪结构进行动力时程分析,并以Matlab编制相应程序。以某19层框剪结构为例,进行多遇地震作用下的动力时程分析,结果表明该结构的最大层间位移角为1/1 329,且结构没有出现明显的薄弱层,说明整个结构是处在弹性工作的状态,从而验证了该方法的可行性与可靠性。
Proceeding from the total potential energy of frame-shear wall structure,the Hamiltonian dual system of coordination analysis is established according to the parallel Timoshenko beam beam model.The layer element stiffness matrix is deduced according to interval mixed energy matrix which is based on the precise integration method of the double end boundary value problems,and then the global stiffness matrix of structure can be set up by according to the finite element stiffness integration method.The dynamic time history analysis is eventually processed on the frame-shear wall structures based on the precise integration method of initial value problems,and the relevant program is programmed with the Matlab software.The reliability and feasibility of this method is tested by a 19-floor frame-shear building,and the result shows that the most story drift angle of the building is 1/1 329 under frequent earthquake action,which indicates the whole building is in the elastic working state.
Proceeding from the total potential energy of frame-shear wall structure,the Hamiltonian dual system of coordination analysis is established according to the parallel Timoshenko beam beam model.The layer element stiffness matrix is deduced according to interval mixed energy matrix which is based on the precise integration method of the double end boundary value problems,and then the global stiffness matrix of structure can be set up by according to the finite element stiffness integration method.The dynamic time history analysis is eventually processed on the frame-shear wall structures based on the precise integration method of initial value problems,and the relevant program is programmed with the Matlab software.The reliability and feasibility of this method is tested by a 19-floor frame-shear building,and the result shows that the most story drift angle of the building is 1/1 329 under frequent earthquake action,which indicates the whole building is in the elastic working state.
引文
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[2]汪梦浦,沈蒲生.钢筋混凝土高层结构非线性地震反应分析现状[J].世界地震工程,1998,14(2):1-8.
[3]沈小璞,肖卓.高层建筑结构动力时程响应的状态空间迭代法[J].建筑结构学报,1998,26(2):67-69.
[4]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-136.
[5]汪梦浦,周锡元.结构动力方程的更新精细积分法[J].力学学报,2004,36(2):191-195.
[6]钟万勰.应用力学对偶体系[M].北京:科学出版社,2002.
[7]侯瑞珀.基于并联剪弯梁模型的高层建筑结构协同分析[D].邯郸:河北工程大学,2006.
[8]高洪俊,王羡农,闫亚光.框剪结构协同分析的状态空间法[J].西安科技大学学报,2007,27(4):573-574.
[9]钟万勰.应用力学的辛数学方法[M].北京:高等教育出版社,2006.
[10]胡启平,李张苗,侯瑞珀.铁摩辛柯梁弯曲问题的对偶求解体系[J].河北工程大学学报(自然科学版),2006,23(3):1-4.
[11]包世华.高层建筑结构计算[M].北京:高等教育出版社,1991.
[12]汪梦浦,周锡元.结构动力方程的高斯精细时程积分法[J].工程力学,2004,21(4):13-16.
[13]胡启平,刘鹏,吕铭.考虑部分楼板变形时框-剪结构的协同分析[J].河北工程大学学报(自然科学版),2009,26(3):4-7.
[14]胡启平,孙良鑫,高洪俊.铁摩辛柯梁弯曲问题的精细积分法[J].工业建筑,2007,37(s1):268-270.
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