A spectral consistent starting procedure is proposed for the first‐order‐type A‐stable linear two‐step (LTS) time integration methods in structural dynamics analysis. The accuracy analysis for the LTS methods in structural dynamics is presented based on the first‐order model, which enables the algorithms in first‐order transient systems to be extended to structural dynamics under the umbrella of a consistent framework. It is indicated that the approximation of the loads plays an essential role in the equivalence between the LTS methods and some single‐step methods. An algorithmic equivalence feature, which is stricter than the spectral equivalence, is revealed between the two‐leg generalized‐α methods in first‐order systems and the A‐stable LTS methods. The measures of the error constant in the LTS methods and the ultimate spectral radius are extended to optimize a class of single‐step methods of a given convergence order. The spectral consistent starting procedure for the A‐stable LTS methods is developed by utilizing the algorithmic equivalence of the single‐step methods, which results in an optimal A‐stable LTS (OALTS) method possessing a consistent spectral radius with controllable numerical dissipation in the starting step and the steps thereafter. Comparing with the equivalent single‐step methods, the present OALTS method does not need the auxiliary variables, and its displacement, velocity and acceleration can achieve second‐order accuracy simultaneously. The performance of the present OALTS method is verified by numerical examples including physical damping, external loads, and/or nonlinearity.

中文翻译：

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稳定一致的线性平稳两步时间积分方法及其等效单步方法，用于结构动力学分析

针对结构动力学分析中的一阶A稳定线性两步（LTS）时间积分方法，提出了一种频谱一致的起始程序。基于一阶模型对结构动力学中的LTS方法进行了精度分析，这使得一阶瞬态系统中的算法可以在一致框架的框架下扩展到结构动力学。结果表明，载荷的近似在LTS方法和某些单步方法之间的等效性中起着至关重要的作用。一阶系统的双腿广义α方法与A稳定LTS方法之间揭示了一种算法等效功能，它比频谱等效严格。扩展了LTS方法中误差常数和最终光谱半径的量度，以优化给定收敛阶的一类单步方法。利用单步法的算法等效性开发了A稳定LTS方法的光谱一致的起始程序，这导致了最优A稳定LTS（OALTS）方法具有一致的光谱半径，并且可控的数值耗散可控。开始步骤及其后的步骤。与等效的单步方法相比，本发明的OALTS方法不需要辅助变量，并且其位移，速度和加速度可以同时达到二阶精度。现有的OALTS方法的性能已通过数值示例得到了验证，这些示例包括物理阻尼，外部载荷，