基于哈密顿理论的束筒结构剪力滞后分析
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摘要
根据连续化原理,将超高层建筑束筒等效连续化为由各向异形板和角柱围成的等效实腹薄壁筒。计及剪切变形与纵向翘曲,引入纵向位移的分段线性插值函数,得到弯扭作用下高层建筑束筒结构的总势能,并由此得出相应的拉格朗日函数。引入对偶变量,建立考虑剪力滞后影响的束筒结构弯扭分析的哈密顿对偶求解体系,导出束筒结构弯扭作用下的哈密顿正则方程。用两端边值问题的半离散半精细积分法求该体系的高精度数值解。计算结果表明,模型的简化合理可行,具有较高的精度和实用性,为超高层建筑结构计算分析提供了一种可行的方法。
According to the continuous principle,super tall building bundled-tube structure is made equal to equivalent solid thin-walled tube which is enclosed with orthotropic plates and corner column. Function of the length travel and the shear lag impact is introduced. The total potential energy of tall building bundled-tube structure with bending-torsion effect and its corresponding Lagrange function are obtained. By introducing dual variables, a Hamiltonian dual system for the static analysis of bundled-tube structure is constituted, then Hamiltonian canonical equations are derived for the analysis of bending-torsion effect. High accuracy numerical solutions are obtained using a half discrete precise integration method of two and boundaries. The numerical results show that analytical model and the method are effective and reasonable. This method is of higher precision and applicability,it is easy to accept with a simple and clear mathematic derivation as well as efficient numerical algorithms. And it provides a feasible method for super tall building bundled-tube structures.
According to the continuous principle,super tall building bundled-tube structure is made equal to equivalent solid thin-walled tube which is enclosed with orthotropic plates and corner column. Function of the length travel and the shear lag impact is introduced. The total potential energy of tall building bundled-tube structure with bending-torsion effect and its corresponding Lagrange function are obtained. By introducing dual variables, a Hamiltonian dual system for the static analysis of bundled-tube structure is constituted, then Hamiltonian canonical equations are derived for the analysis of bending-torsion effect. High accuracy numerical solutions are obtained using a half discrete precise integration method of two and boundaries. The numerical results show that analytical model and the method are effective and reasonable. This method is of higher precision and applicability,it is easy to accept with a simple and clear mathematic derivation as well as efficient numerical algorithms. And it provides a feasible method for super tall building bundled-tube structures.
引文
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[2]包世华.新编高层建筑结构[M](第二版).北京:中国水利水电出版社,2005Bao Shihua.New edition of tall building structures[M](Second edition).Beijing:China Water Conservancy and Hydropower Press,2005(in Chinese)
[3]Lee Kangkun,Loo Yewchaye,and Guan Hong,Simple Analysis of Framed-tube Structures with Multiple Internal Tubes[J].Journal of Structural Engineering,ASCE,2001,127(4):450-460
[4]胡启平,涂佳黄,梁经群.组合断面薄壁杆件弯扭耦合分析[J].工程力学,2010,27(7):52-55Hu Qiping,Tu Jiahuang,Liang Jingqun.Coupling Analysis of Cross Section Thin-walled Bar Bending and Twisting[J].Engineering Mechanics,2010,27(7):52-55(in Chinese)
[5]胡启平,董宝锋,吕铭.基于哈密顿理论的薄壁杆件稳定性分析[J].四川建筑科学研究,2011,37(4):26-29Hu Qiping,Dong Baofeng,Lv Ming.Based on the Theory of Hamiltonian Thin-walled Bar Stability Analysis[J].Sichuan Building Science,2011,37(4):26-29(in Chinese)
[6]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(增刊):268-270Hu Qiping,Sun Liangxin,Gao Hongjun.Timoshenko Beam the Precise Integration Method of Bending Problem[J].Industrial Construction,2007,37(Sup):268-270(in Chinese)
[7]刘开国.结构简化计算原理及应用[M].北京:科学技术出版社,1996Liu Kaiguo.The Simplified Principle and Application of Structure[M].Beijing:Science and Technology Press,1996(in Chinese)
[8]钟万勰.应用力学对偶体系[M].北京:科学出版社,2002Zhong Wanxie.Applied Mechanics Dual System[M].Beijing:Science and Technology Press,2002(in Chinese)
[9]钟万勰.应用力学的辛数学方法[M].北京:高等教育出版社,2006Zhong Wanxie.Applied Mechanics of Symplectic Mathematics Method[M].Beijing:Higher Education Press,2006(in Chinese)
[10]包世华,张铜生.高层建筑结构设计和计算[M].北京:清华大学出版社,2007Bao Shihua,Zhang Tongsheng.High-rise Building Structural Design and Calculation[M].Beijing:Tsinghua University Press,2007(in Chinese)