基于组合时间积分算法的碰撞问题振荡现象修正  

CORRECTION OF OSCILLATION PHENOMENON IN IMPACT PROBLEM BASED ON COMBINED TIME INTEGRATION ALGORITHM

作　　者：张立红 李庆斌[2] 张艳红[1] 罗丹旎 高建勇[1] ZHANG Li-hong;LI Qing-bin;ZHANG Yan-hong;LUO Dan-ni;GAO Jian-yong(State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research,Beijing 100048,China;State Key Laboratory of Hydroscience and Engineering,Tsinghua University,Beijing 100084,China;School of Civil Engineering and Architecture,Guangxi Univerisity,Nanning,Guangxi 530004,China)

机构地区：[1]中国水利水电科学研究院流域水循环模拟与调控国家重点实验室,北京100048 [2]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [3]广西大学土木建筑工程学院,广西南宁530004

出　　处：《工程力学》2023年第S01期1-5,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(52179125);中国水利水电科学研究院基本科研业务费专项项目(HTEB0145B01202100000)。

摘　　要：该文提出了一种能够有效改善碰撞问题振荡现象的修正方法。基于有限元方法,采用Lagrange乘子法施加接触约束条件,并与一种无条件稳定的隐式组合时间积分算法相结合对无摩擦动接触问题进行求解。通过引入附加Lagrange乘子对组合时间积分算法得到的速度和加速度进行修正,使其能够满足速度和加速度形式的接触约束的一致性条件。数值算例结果表明:该文提出的修正方法能够有效地改善碰撞问题中初始接触时速度、接触力等的振荡现象,进一步提高了碰撞问题的求解精度。A correction method is presented which can effectively improve the spurious oscillation phenomenon in impact problems.Based on the finite element method,the Lagrange multiplier method is introduced to impose contact constraints,and an unconditionally stable implicit combined time integration algorithm is combined to solve the frictionless dynamic contact problem.By introducing additional Lagrange multipliers,the velocity and acceleration obtained by the combined time integration algorithm are modified to meet the persistency conditions of the contact constraints in the form of velocity and acceleration.Numerical example results show that the correction method can effectively improve the spurious oscillation of velocity,contact force,etc.at the time of initial contact,and improve the solution accuracy of impact problems.

关 键 词：碰撞问题 组合时间积分算法 LAGRANGE乘子法 一致性条件 振荡现象 

分 类 号：TB115[理学—数学]