Highly precise time integration method for linear structural dynamic analysis

Abstract

SummaryTo achieve high accuracy, conventional time integration methods require small time steps, especially when applied to large‐scale finite element systems. The use of small time steps calls for a large number of computations. In this paper, a strategy is proposed to construct an efficient and highly precise time integration method for linear time‐invariant systems. Adopting the multi‐substep notion, the highly precise time integration method creates an integrated amplification matrix prior to recursive calculations by multiplying the amplification matrices of N equal substeps, where a 2m algorithm and the method of storing incremental matrix are respectively employed to reduce computational cost and rounding error. On the basis of the Newmark method, two highly precise symplectic schemes and one highly precise dissipative scheme are developed. In addition, the consistent stability of the used Newmark schemes is presented. The free vibration of a three‐dimensional truss, the impact of a particle against a rod, and the forced vibrations of a rectangular thin plate and a stiff system are investigated to validate the performance of the proposed method.