大跨度空间结构抗震分析反应谱理论求解的快速算法

The speedy algorithm of response spectrum theory in seismic analysis of grid structures

振型分解反应谱法已成为各国抗震规范中最为成熟的结构地震反应分析方法.当采用反应谱法进行大跨度空间结构抗震分析时,按照规范的规定,在进行反应谱计算时应首先形成相对于各阶振型的等效节点荷载右端项,然后求解相对于各阶振型的地震反应位移解.应用本文的快速算法,可以直接写出相对于各阶振型的地震反应位移解,节省计算求解时间,同时也避免了求解过程中产生的计算精度误差.本文从理论上证明了快速算法与规范方法的等价性,并用例题加以证实.

The response spectrum analysis has become the most sophisticated seismic analysis method in codes for seismic design in the world. When response spectrum method is used in the seismic analysis of long-span grid structures, according to the code, the first step in the response spectrum analysis is forming the equivalent nodal force vector. And then, computing the displacement solution in each mode shape. By the speedy algorithm adopted by this article, the displacement solution in each mode shape can be written directly. Solution time can be saved and at the same time computing errors can be avoided by this method. In this article, the equivalence of the speedy algorithm and the method in the code is verified in theory and a simple example is provided to approve it.