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A compressed solution method for the equation of isolated structure[J].计算力学学报,2020,37(5):651~654

A compressed solution method for the equation of isolated structure
A compressed solution method for the equation of isolated structure

DOI：10.7511/jslx20190714001

 作者 单位 E-mail 田志昌 内蒙古科技大学 土木工程学院, 包头 014010 孙欣欣 内蒙古科技大学 土木工程学院, 包头 014010 1668790595@qq.com 李娟 内蒙古科技大学 土木工程学院, 包头 014010 李革 内蒙古科技大学 土木工程学院, 包头 014010 杨志军 内蒙古科技大学 土木工程学院, 包头 014010 陈明 内蒙古科技大学 土木工程学院, 包头 014010

基础隔振体系中，隔震器的刚度远小于上部结构的刚度，如果未知量数目比较大，则经常导致总刚度矩阵病态。本文利用上部结构本身的振型叠加压缩未知数，然后与隔震器构建混合方程，此时形成的方程为非对称方程。大量压缩未知量后，减轻了总刚度矩阵的病态。以四层隔震框架结构分析为例，结果表明，压缩解法和正常解法的静力结果十分吻合，但用Newmark逐步积分计算时，正常直接解法累积误差引起发散，而压缩解法计算不发散。

In the vibration isolation system of a foundation,the stiffness of the isolator is very small compared with the stiffness of the upper structure.If the number of the unknowns is great,the stiff matrix often becomes ill-conditioned.In this paper,we propose to use the vibration mode superposition of the upper structure to reduce the number of unknowns,and then combine the isolator's parameters to form a set of mixed simultaneous equations,which are asymmetrical.After the large number of unknowns is reduced,the cumulative error is reduced and the ill-condition is relieved.The analysis of a four-story isolated frame is taken as an example in this paper.It shows that the static results of the reduced solution and the original solution are in good agreement,but the step by step integration by means of Newmark method shows that the normal direct solution is divergent,while the reduced solution is convergent.