On the accuracy of direct integration methods for structural dynamics

Abstract

This paper presents a method of eigen analysis to evaluate the accuracy of the time integration method in the structural dynamic analysis of both transient and steady state responses. Accuracy measure for transient response is evaluated by period elongation and amplitude decay after a complete cycle of response of an undamped system. The proposed method is a unique measure, independent of the initial conditions. Accuracy measure for steady state response is evaluated by the amplitude decay and phase angle of a frequency response. The accuracy measure proposed by this method can be applied to all ranges of Δt/T. The significance of the large range Δt/T is discussed. The proposed method is used to evaluate the accuracy of three commonly used time integration methods: the Wilson method, the Newmark method and the Houbolt method. ffimmtimmtpmmMftmzmmftVx £^l*ft#T^K«B8lfIK«S 5SM£ Mmmw±m±*JLmm&