Most newly proposed explicit time integration methods may have one or more of such problems as unexpected stability limits, accuracy order loss for damped systems and unsatisfactory computational accuracy for the case of zero initial conditions and initial external load. For addressing these problems, a three-stage explicit time integration method is proposed in this paper. The proposed method is second-order accurate for linear systems with and without damping, and it is completely explicit if the mass matrix is diagonal, even when the damping matrix is not diagonal in linear analysis or the internal force is a function of velocity in nonlinear analysis. The stability limit and numerical dissipation are exactly controlled by the parameter ρ_b, the spectral radius at the bifurcation point. For undamped systems, the stability limit of the proposed method ranges from 5.5608 to 6 with the increase in ρ_b from 0 to 1 and its degree of numerical dissipation is exactly controlled by ρ_b. The recommended values of ρ_b for different types of dynamics systems are determined by analyzing the algorithmic eigenvalue properties and the dynamics system properties. Numerical experiments show that the new method has advantages in accuracy and stability over most up-to-date explicit methods.

大多数新提出的显式时间积分方法可能存在一个或多个问题，例如意外的稳定性极限、阻尼系统的精度阶数损失以及在零初始条件和初始外部载荷的情况下的计算精度不令人满意。针对这些问题，本文提出了一种三阶段显式时间积分方法。所提出的方法对于有阻尼和无阻尼的线性系统都是二阶精度的，如果质量矩阵是对角的，即使在线性分析中阻尼矩阵不是对角的，或者内力是非线性的速度的函数时，该方法也是完全明确的分析。稳定极限和数值耗散由参数ρ _b精确控制，分岔点处的光谱半径。对于无阻尼系统，随着ρ _b从0增加到1，该方法的稳定性极限范围为5.5608至6，其数值耗散程度由ρ _b精确控制。通过分析算法特征值性质和动力学系统性质，确定不同类型动力学系统的ρ _b推荐值。数值实验表明，与大多数最新的显式方法相比，新方法在准确性和稳定性方面具有优势。