基于Newmark精细积分结合法的弹塑性结构地震碰撞反应分析  

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

作　　者：张瑞杰 闫磊 ZHANG Ruijie;YAN Lei(State Key Laboratory of Mountain Bridge and Tunnel Engineering,Chongqing Jiaotong University,Chongqing 400074,China;School of Civil Engineering,Chongqing Three Gorges University,Chongqing 404100,China)

机构地区：[1]重庆交通大学,省部共建山区桥梁及隧道工程国家重点试验室,重庆400074 [2]重庆三峡学院土木工程学院,重庆404100

出　　处：《振动与冲击》2020年第24期247-253,共7页Journal of Vibration and Shock

基　　金：中国博士后科学基金项目(2019M663442);重庆市博士后特别资助项目(020919014);重庆市科委项目(cstc2018jscx-msybX0167);重庆市教委项目(KJQN201901219,KJQN202001216);三峡水库岸坡与工程结构灾变防控工程技术研究中心开放基金(SXAPGC19ZDI01)。

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。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.

关 键 词：动力平衡方程 精细积分法 Newmark精细积分结合法 弹塑性 地震碰撞 

分 类 号：TU311.1[建筑科学—结构工程]