结构动力问题的高精度组合差分时程积分法

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

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 analyzed by 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.