结构动力问题的高精度组合差分时程积分法  

A high accurate combination-difference time-integration scheme for problems in structural dynamics

作　　者：张立红[1] 刘天云[1] 李庆斌[1] 管俊峰[2] 

机构地区：[1]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 [2]华北水利水电学院土木与交通学院,郑州450011

出　　处：《计算力学学报》2013年第4期491-495,513,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(90715041);十一五支撑计划(2008BAB29B05)资助项目

摘　　要：基于Taylor级数展开得到位移和加速度的中心差分格式,并结合速度的后差分格式,构造了一种求解结构动力问题的组合差分格式的时程积分算法,该算法为自起步的两步高精度算法。通过求解递推格式的传递矩阵及其特征值,对该算法的稳定性和精度进行了理论分析,结果表明,本文提出的算法虽属条件稳定,但其精度极高,具有周期延长率小、没有振幅衰减等优点。数值分析结果也证明本文提出的算法具有较高精度。A two-step self-starting algorithm for solving structural dynamic problems called Combination- Difference Time-Integration algorithm （CDTI for short） which combines the backward difference scheme of velocity with the central difference scheme of displacement and acceleration based on Taylor series expansion is proposed. The stability and accuracy of CDTI are thoroughly analyzoy the amplification matrix and the associated eigenvalues and the results indicated that although it is conditionally stable, CDTI has high-order accuracy with no amplitude decay as well as little period elongation rate. The high accuracy of CDTI was also validated by numerical analysis.

关 键 词：结构动力问题 时程积分法 组合差分 高精度 稳定性 

分 类 号：O343[理学—固体力学]