高层建筑结构三维分析的广义坐标方法

GENERALIZED COORDINATE METHOD FOR THREE DEMENSIONAL ANALYSIS OF TALL BUILDING STRUCTURES

本文采用刚性楼面假定,把Rayleigh-Ritz法和有限单元法相结合,以多项式作为位移函数,通过二维高次完备多项式拟合楼面位移,变位移方程为广义坐标方程,建立了高层建筑结构三维分析的广义坐标方法,使未知量数目得到有效的缩聚,并与建筑物的层数无关;同时,计算精度可以通过选择位移函数的项数来调整。文中引用一个20层L形空间刚架和一个8层的空间刚架作为算例,所得结果在实用上是有足够精度的。

Based on the assumption of rigid floor, a Generalized Coordinate Method is proposed in this paper by the aid of combining the Rayleigh-Ritz Method with the Finite Element Method. The joint displacements of tall buildings can be expressed by complete polynomials and the generalized coordinates are taken as unknown parameters. By deriving the displacement transformation matrix between the generalized coordinate vector and the element displacement vector, the displacement equation of the structure can be transformed into the generalized coordinate equation. Since the order of the generalized stiffness matrix is not increased with the number of stories of the building, the number of unknowns can be significantly reduced in the analysis of tall building structures, and results with practically enough precision can be obtained.