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.
出处
《计算力学学报》
CAS
CSCD
北大核心
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
关键词
结构动力问题
时程积分法
组合差分
高精度
稳定性
structural dynamic problems
time integration method
combination difference
high accuracy stability
