This paper proposes a novel composite two sub-step implicit method to effectively solve structural dynamic problems. The main highlight of the new method lies that it is truly self-starting and so avoids computing the initial acceleration vector, but the second-order accurate acceleration output can be still provided. Besides, the new method does not sacrifice other desired numerical characteristics, such as the identical second-order accuracy, unconditional stability (L-stability) and no overshoots. As with the existing Bathe algorithm, the new method also includes a unique algorithmic parameter [Formula: see text] to adjust numerical dissipation imposed in the low-frequency range. Numerical spectral analysis and examples show that the new method with [Formula: see text] is highly recommended solving various dynamical problems.

中文翻译：

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一种简单的真正自启动和 L 稳定的结构动力学积分算法

本文提出了一种新颖的复合二分步隐式方法来有效解决结构动力问题。新方法的主要亮点在于它是真正的自启动，因此避免了计算初始加速度矢量，但仍然可以提供二阶精确的加速度输出。此外，新方法不会牺牲其他所需的数值特性，例如相同的二阶精度、无条件稳定性（L-稳定性）和无超调。与现有的 Bathe 算法一样，新方法还包括一个独特的算法参数 [公式：见正文]，以调整施加在低频范围内的数值耗散。数值谱分析和实例表明，强烈推荐使用[公式：见正文]的新方法解决各种动力学问题。