基于哈密顿理论的束筒结构剪力滞后分析

Analysis for Bundled-tube Structures Shear-lag Effect on Hamlton Theory

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.