隔震结构的地震响应时程分析

建筑物在地震作用下的动力响应时程分析一直是非常复杂和计算量很大的问题。对于隔震结构,由于隔震层参数与上部结构参数相差较大,容易导致数值病态。为了准确计算隔震结构的地震响应,本文放弃了传统求解动力方程常用的差分格式,而是把二阶结构动力方程通过增维、降阶转化为一阶微分方程组,然后利用精细积分法对其求解;对杜哈梅尔积分项采用牛顿-柯特斯公式及相应的复化公式进行数值计算;考虑建筑物地震作用力—等效惯性力的特点,实现其简化计算,节约计算时间;插值点间隔为地震波的取样时间,确保地震作用大小无插值误差。本文算法避免矩阵求逆,提高了计算效率,数值算例显示了算法的有效性和效率。

On the Time-history of Seismic Response of Base-isolated Structure

The time-history of seismic response of a building is always a complex and large-scale problem. Because the great difference between parameters of base-isolation story and super structure, numerical morbidity arises easily, In this paper, using the increment-dimensional and diminishment-order method, second-order differential dynamical equations is converted into first-order ones; a numerical algorithm of the precise integration method based on Newton-Cotes formula is used to calculate the time-history of seismic response of the base-isolation structure. The new algorithm avoids calculations of the inverse matrix and improves the computing efficiency. Numerical examples were given to demonstrate the validity and efficiency of the algorithm.