Abstract: Based on the Newmark's implicit integration algorithm which is well known and widely used in the domain of structural dynamic analyses,an explicit scheme, called the Newmark's Explicit Scheme, is constructed in this paper. Unlike existing explicit algorithms, the integration process of this scheme is extremely simple. No matter what form the damping matrix is, this scheme no longer need to solve high order algebraic linear equations in each integration step as long as the mass matrix is diagonal. Therefore, it is very convenient for this explicit method to analyse large nonlinear dynamic systems discretized by finite element methods. The computer-time efficiency will be much more enhanced.In this paper, the numerical stability and accuracy of the new scheme is discussed. Some linear and nonlinear numerical examples are used to compare this scheme with currently popular methods. Two problems of railway engineering are analysed at the end of the paper.

Key words: structural dynamics, computational structural mechanics, numerical integration, explicit scheme

摘要： 本文基于结构动力分析中广泛采用的Newmark(隐式)积分方法,构造了一类显式积分格式,称之为"Newmark显式算法"。与一般的显式法(如中心差分法)不同,该方法积分过程甚为简捷,只要其质量阵是对角阵或经对角化而不论阻尼阵如何复杂,积分中都无须求解线性代数方程组。这就大大节省了计算内存与时间,因而用于分析工程中大型非线性结构动力问题可以显著地提高计算效率与经济性。文中讨论了方法的精度与稳定性,给出了若干数值算例,并具体分析了二个工程应用实例。

关键词: 结构动力学, 计算结构力学, 数值积分, 显式法