In this paper, a novel implicit family of composite two sub-step algorithms with controllable dissipations is developed to effectively solve nonlinear structural dynamic problems. The primary superiority of the present method over other existing integration methods lies that it is truly self-starting and so the computation of initial acceleration vector is avoided, but the second-order accurate acceleration responses can be provided. Besides, the present method also achieves other desired numerical characteristics, such as the second-order accuracy of three primary variables, unconditional stability and no overshoots. Particularly, the novel method achieves adjustable numerical dissipations in the low and high frequency by controlling its two algorithmic parameters (\( \gamma \) and \( \rho _{\infty }\)). The classical dissipative parameter \( \rho _{\infty }\) determines numerical dissipations in the high-frequency while \( \gamma \) adjusts numerical dissipations in the low-frequency. Linear and nonlinear numerical examples are given to show the superiority of the novel method over existing integration methods with respect to accuracy and overshoot.

为了有效地解决非线性结构动力问题，本文提出了一种新颖的具有可控耗散的复合两步法隐式族。与其他现有的积分方法相比，本方法的主要优势在于它确实是自启动的，因此可以避免计算初始加速度矢量，但是可以提供二阶准确的加速度响应。此外，本方法还实现了其他期望的数值特性，例如三个主要变量的二阶精度，无条件稳定性和无超调。特别是，该新方法通过控制其两个算法参数（\（\ gamma \）和\（\ rho _ {\ infty} \））。经典的耗散参数\（\ rho _ {\ infty} \）确定高频中的数值耗散，而\（\ gamma \）调整低频中的数值耗散。给出了线性和非线性数值示例，以显示该方法在精度和超调方面优于现有积分方法。