Precise Time Integration Methods for Transient Response Analysis of Large-Scale Structures

Abstract

To remove the calculations of inverse and/or exponential of large-scale matrix in the precise time integration (PTI) method for transient response analysis of structures, new PTI methods equipped with the restarted Krylov subspace method and real Leja points interpolation method to calculate are presented in this paper. In both kinds of methods, only the multiplications of sparse matrix and vectors are involved. The theories and implementations of the improved PTI methods are introduced. The transient responses of a cantilever beam and an aeroengine bladed disk are used as numerical examples to validate the accuracy and efficiency of the proposed methods. The effects of tunable parameters of both kinds of algorithms on the numerical efficiency are also discussed. It has been demonstrated that the improved PTI methods are accurate and insensitive to integration step length and, more importantly, are highly efficient for large-scale structures subjected to high-frequency excitations, which greatly extend the applicability of PTI methods.