高阶能量一致积分方法及其在结构动力分析中的应用  

High-order energy consistent integration method and its application in structural dynamic analysis

作　　者：潘天林 张文迪 韩炎涛 徐小洁 曾聪[1] PAN Tianlin;ZHANG Wendi;HAN Yantao;XU Xiaojie;ZENG Cong(School of Civil Engineering and Architecture,Northeast Electric Power University,Jilin 132000,China)

机构地区：[1]东北电力大学建筑工程学院,吉林吉林132000

出　　处：《振动与冲击》2023年第9期247-252,292,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51808101,52078398,51908106)。

摘　　要：能量一致积分方法是一种二阶精度、无条件稳定的逐步积分方法。为提高计算精度,将辛Runge-Kutta方法进行改进,构造出高阶能量一致积分方法一般形式。这种方法既保持了四阶精度,又具有能量一致属性。通过非线性弹性算例验证了方法的精度和数值稳定属性。将方法应用到桁架单元,推导了具体计算格式,并完成对应的非线性计算程序。程序集成了二阶与四阶能量一致积分方法、平均加速度方法(average acceleration method,AAM)以及由AAM构造的四阶方法。通过弹性摆与平面桁架结构非线性动力分析,对比4种逐步积分方法。分析结果表明,四阶能量一致积分方法在精度、稳定性与计算效率上优于其他3种方法。The energy consistent integration method is a stepwise integration one with second-order accuracy and unconditional stability.Here,to increase calculation accuracy,the symplectic Runge-Kutta method was improved to construct the general form of high-order energy consistent integration method.The new method could not only maintain fourth-order accuracy,but also have the property of energy consistency.The accuracy and numerical stability of this method were verified with nonlinear elastic examples.This method was applied in truss element,the specific calculation format was derived,and the corresponding nonlinear calculation program was completed.The program integrated 4 step-by-step integration methods including the 2nd order and 4th order energy consistent integration methods,the average acceleration method(AAM)and the fourth order method constructed with AAM.Through nonlinear dynamic analyses of an elastic pendulum and a plane truss structure,these 4 step-by-step integration methods were compared.The analyses results showed that the 4th order energy consistent integration method is superior to the other 3 methods in accuracy,stability and computational efficiency.

关 键 词：逐步积分方法 能量一致 非线性 数值稳定 平均加速度方法(AAM) 辛方法 

分 类 号：TU311.4[建筑科学—结构工程]