中文摘要：

针对大型复杂结构的动力学问题,为了得到高效的计算方法,以泰勒公式为基础,通过调整参数改善算法的稳定性,得到了一类具有非耗散特性且以加速度为基本变量的显式数值积分方法。对提出的方法进行了稳定性和精度分析,并通过多个算例对提出的方法、蛙跳式中心差分法、Newmark-β法和精确解进行比较。结果表明,无阻尼情况下,所提出的方法的稳定性条件与中心差分法相同;提出的方法的振幅衰减率为0,具有非耗散特性,其周期误差约为隐式Newmark-β法的一半;所提出的方法给出了蛙跳式中心差分法和无耗散特性的翟方法的统一格式,并可以衍生出更多的显式时间积分方法。

英文摘要：

In order to obtain efficient calculation methods for dynamical problems of large and complex structures. A class of non-dissipitive explicit numerical integration methods is proposed through adjusting parameters to improve the stability of algorithms. Accelerations are used as the basic variables in the proposed methods which are on the basis of the Taylor＇s formula. The analyses of stability and accuracy are performed for the proposed methods. Finally, some numerical examples are given for the comparison between the proposed methods, and some current methods including the leapfrog central difference method （LCDM）, the Newmark-β method and the exact solution. The results show that the proposed methods have the same stability condition as the LCDM under undamped condition. The amplitude attenuation of the proposed methods is 0, which means they are non-dissipative. The periodic error is about half of that of the implicit Newmark-β method. The proposed methods provide a unified format of the LCDM and the Zhai method without dissipation, and more explicit integration algorithms can be derived directly.