结构-地基开放系统动力相互作用问题的高效解法

An efficient method for the dynamic interaction of open structure-foundation systems

应用黏弹性人工边界将结构-地基开放系统转化为近似的封闭系统,利用等效地震波动输入方法将波动散射问题化为波源问题,再采用振型叠加法对近似封闭系统进行分析,由此建立了一种结构-地基开放系统动力反应问题的高效计算方法。采用高效算法分别计算了二维弹性半空间波源问题和地震作用下结构-地基动力相互作用问题算例,并与采用常规的直接时域逐步积分法给出的计算结果进行了对比,由此讨论了高效算法的特点。与常规直接动力分析方法相比,高效算法可以在确保模拟精度的同时,有效降低计算工作量、节省计算时间,并且结构-地基动力相互作用系统的模型越大、自由度越多,高效算法的优越性就越突出,从而为大型结构-地基系统动力相互作用问题数值分析提供了一种高效而精度足够的解法。

The structure-foundation system is transformed from an original open system into an approximately closed system through a viscous-spring artificial boundary. In addition, the seismic wave scattering problem is changed to a wave source problem by employing an equivalent seismic wave input. Subsequently, the modal superposition method is adopted to solve the approximated closed system. This procedure is highly efficient in analyzing dynamic structurefoundation interaction problems in the time domain. Two numerical examples are presented to illustrate the characteristics of the proposed method： one is a wave source problem in 2-D elastic semi-infinite space, and the other a dynamic structure-foundation interaction problem under seismic excitations. Comparing with the traditional direct step-by-step integration method, the proposed method, with a sufficient number of mode shapes included, can significantly reduce the computational time with almost the same precision. The results also indicate that the proposed method is more advantageous for solving large structure-foundation systems of many degrees of freedom.