Abstract
On the basis of the applied loadings simulated by piecewise interpolation polynomials, a precise integration method using the Ritz vectors and a modified Krylov precise integration method are presented. The Ritz method is used to reduce the dimension of structural dynamic equations and the Krylov subspace method is applied to reduce the dimension of the exponential matrix required in the evaluation. The Padé approximation is employed in computing the initial matrices required for the recurrence evaluations of the exponential matrices of reduced size. The new cut-off criteria proposed in this paper are used to determine the required number of the Ritz vectors and the required size of the Krylov subspace. The accuracy of the time integration schemes presented is studied and compared with those of other commonly used schemes. The time integration schemes presented have arbitrary order of accuracy, wider application and are less time-consuming. Two numerical examples are also presented to demonstrate the applicability of the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.
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