A novel three sub‐step explicit time integration method for wave propagation and dynamic problems

Abstract

A novel explicit time integration method is formulated with sub‐step strategy and Cubic B‐spline interpolation method. Theoretical and numerical analysis are conducted to obtain optimized algorithm properties including algorithm accuracy, spectral stability and numerical dissipation/dispersion. A demonstrative dispersion analysis for wave propagation is presented to acquire optimal algorithm parameter value for finite element analysis of wave propagation problems. Numerical tests demonstrate that new method show desirable algorithm accuracy and convergence for dynamic problems. Especially, for highly nonlinear problems, the new method can provide very accurate and stable solutions.