A faster and accurate explicit algorithm for quasi-harmonic dynamic problems

It is known that the explicit time integration is conditionally stable. The very small time step leads to increase of computational time dramatically. In this paper, a mass-redistributed method is formulated in different numerical schemes to simulate transient quasi-harmonic problems. The essential idea of the mass-redistributed method is to shift the integration points away from the Gauss locations in the computation of mass matrix for achieving a much larger stable time increment in the explicit method. For the first time, it is found that the stability of explicit method in transient quasi-harmonic problems is proportional to the softened effect of discretized model with mass-redistributed method. With adjustment of integration points in the mass matrix, the stability of transient models is improved significantly. Numerical experiments including 1D, 2D and 3D problems with regular and irregular mesh have demonstrated the superior performance of the proposed mass-redistributed method with the combination of smoothed finite element method in terms of accuracy as well as stability.