Newmark-精细积分方法的选择及稳定性

英文篇名：Integration formula selection and stability for Newmark-precision direct integral method
中文刊名：世界地震工程
英文刊名：World Earthquake Engineering
作者：郭泽英 ; 李青宁
英文作者：GUO Zeying1 ; 2 ; LI Qingning1(1.School of Civil Engineering ; Xi'an University of Architecture and Technology ; Xi'an 710055 ; China ; 2.School of Engineering ; Shanxi Normal University ; Linfen 041000 ; China)
中文关键词：Newmark-精细直接积分法 ; 直接积分 ; 稳定性分析
英文关键词：Newmark-precision direct integral method ; direct integration ; stability analysis
出版日期：2008-09-15
机构：西安建筑科技大学土木工程学院;
年：2008
期：03
出版单位：世界地震工程

摘要

针对Newmark-精细直接积分法,对其非齐次项的积分方法进行了讨论,并分析了该逐步积分方法的稳定性。通过理论推导和数值验证,此方法的非齐次项采用高斯积分公式,其计算误差均比采用柯特斯积分公式和辛浦生积分公式的误差小,且其计算工作量比原方法的少,因此Newmark-精细直接积分法得到了改进。通过稳定性的分析得知,改进的Newmark-精细直接积分法虽是条件稳定的,但是其稳定性条件极易满足。综合分析,此方法可推广应用于实际结构的动力反应分析中。
In view of the Newmark-precision direct integral method,integration formulas of the non-homogeneous vector are discussed and the stability of this method is analyzed.Theoretical analysis and numerical results show that the computation accuracy of Gauss formula applied is higher than that of Cotes and Simpson,and the computa-tional effort is smaller than that of the conventional method.Therefore,the Newmark-precision direct integral method is improved.Although the improved scheme is conditionally stable,the conditions are very easy to be satisfied from the stability analysis.Comprehensive analysis demonstrates the proposed method can be applied to the dynamic analysis of actual large systems.

引文

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