基于哈密顿理论求结构单元刚度矩阵的新方法

A New Method for Solving the Element Stiffness Matrix of the Structure Based on the Hamiltonian Theory

选用并联Timoshenko梁模型,将构成筒中筒结构的外框筒和内筒抗侧力结构单元看成竖立的并联悬臂梁.根据哈密顿理论体系,首先求出结构的总势能,推导出拉格朗日函数,继而求出结构协同工作分析的哈密顿正则方程,然后根据基本区段的混合能矩阵求出筒中筒结构以层为单元的刚度矩阵,利用位移法原理,将层刚矩阵整合成总刚度矩阵,并编制Matlab计算程序.最后通过算例验证本方法的可靠性与精度要求.本方法也适用于框剪等高层建筑结构单元刚度矩阵的求解.

By using the parallel Timoshenko beam model,two inner and outer cylinder anti-lateral force units which are composed of the tube-in-tube structure are regarded as parallel cantilever beam.According to the Hamiltonian theory system,the total potential energy of the structure is obtained first,the Lagrangian function is deduced,and then the Hamiltonian regular equation of structural synergy analysis is obtained.The element stiffness matrix is introduced according to interval mixed energy matrix.The global stiffness matrix of structure is established according to the finite element displacement method,and the relevant Matlab calculation program is compiled.Finally,the reliability and precision requirements of this method are verified by an example,and this method can also be applied to the element stiffness matrix of other tall buildings,such as frame-shear wall structures and so on.