基于Newmark精细积分结合法的弹塑性结构地震碰撞反应分析

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (24) : 247-253.

论文

张瑞杰1，闫磊1,2

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Seismic collision response analysis of elastic-plastic structures based on a Newmark precise integral method

ZHANG Ruijie1, YAN Lei1,2

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摘要

传统精细积分法在实现方程降阶的同时，系统矩阵的维数增加一倍，而且非齐次项的解析解需要对系统矩阵求逆，这对于刚度矩阵时变的弹塑性结构地震反应分析，不仅大大增加了存储以及计算工作量，有时还会因逆矩阵不存在而求解失败。为改进上述缺点，推导了全量动力平衡方程和增量动力平衡方程的Newmark精细积分结合法；推导了非齐次项为线性变化和常量的级数解公式。针对弹塑性结构界点转换以及时变刚度问题，给出了全量迭代修正法和增量迭代修正法。上述几种方法结合使用，研制了弹塑性结构地震碰撞反应分析程序，并进行了算例验证。研究表明：Newmark精细积分结合法可以应用于弹塑性结构地震碰撞反应分析，结果精度对积分步长敏感。

Abstract

While the traditional precise integration method reduces the order of an equation, the dimension of the system matrix doubles, and the analytical solution of the non-homogeneous term needs to be inverted.This not only greatly increases the storage and calculation workload, but also sometimes fails to solve the time-varying elastic-plastic structural seismic response analysis because the inverse matrix does not exist.In order to improve the above shortcomings, a Newmark precise integration method of the total dynamic equilibrium equation and the incremental dynamic equilibrium equation was deduced, and the series solution formulas with linear variation and constant nonhomogeneous terms were deduced.Aiming at the boundary transformation and time-varying stiffness of elastic-plastic structures, the full iteration correction method and incremental iteration correction method were presented.Combining these methods, a program for seismic impact response analysis of elastic-plastic structures was developed and verified by an example.The results show that the Newmark precise integration method can be applied to the seismic impact collision analysis of elastic-plastic structures, and the accuracy of the results is sensitive to the integration step.

Key words

dynamic equilibrium equation / precise integration method / Newmark precise integration method / elastic-plastic / seismic collision

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张瑞杰1，闫磊1,2. 基于Newmark精细积分结合法的弹塑性结构地震碰撞反应分析[J]. 振动与冲击, 2020, 39(24): 247-253

ZHANG Ruijie1, YAN Lei1,2. Seismic collision response analysis of elastic-plastic structures based on a Newmark precise integral method[J]. Journal of Vibration and Shock, 2020, 39(24): 247-253

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