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.
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. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(24): 247-253.
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