A three-stage explicit time integration method with controllable numerical dissipation

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 ρb, 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 ρb from 0 to 1 and its degree of numerical dissipation is exactly controlled by ρb. The recommended values of ρb 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.