A technique for time integration analysis with steps larger than the excitation steps

Abstract

SUMMARYThe integration step size is the main algorithmic parameter in time integration analysis. Nowadays, for time integration with the complete records of digitized excitations, the integration steps cannot be set larger than the excitation steps. Considering the practical importance of this restriction, and with the aim of structural dynamic analysis with less computational cost, this paper intends to extend conventional time integration analyses to analyses, if needed, carried out with steps larger than the excitations steps. In view of few simplifying assumptions, and presenting a new theorem on responses convergence, a technique is developed and a computational procedure is set. Being based on convergence-oriented redefinition of digitized excitations, the implementation of the new procedure is simple and, though, sacrificing some accuracy, can considerably reduce the total computational cost.

More Versatility for an Integration-Step-Size-Enlargement Technique in Time Integration Analysis

“…Convergence is both the first essentiality in general numerical computation [17][18][19], and also the key basis in the recently proposed technique [16]. In numerical investigation of convergence and order of accuracy, for problems subjected to digitized excitations, e.g.…”

“…In view of this idea, we can convert an earthquake record digitized at steps equal to t  , to a record digitized at smaller steps, by linear interpolation, and expect no loss of accuracy in time integration analysis (compared to the exact responses); though in the price of more computational cost. Considering the new record, as an original record, we can implement the recent technique [16], to arrive at a record with the larger steps to be used in time integration, with reduced computational cost. Since in view of the existing experiences, the recent technique is successful [16,[22][23][24][25][26][27][28][29][30][31][32][33], the loss of accuracy is trivial.…”

“…Considering the new record, as an original record, we can implement the recent technique [16], to arrive at a record with the larger steps to be used in time integration, with reduced computational cost. Since in view of the existing experiences, the recent technique is successful [16,[22][23][24][25][26][27][28][29][30][31][32][33], the loss of accuracy is trivial. In other words, by linear interpolation, the original excitation (with digitization steps equal to…”

“…, by the recent technique [16]. In consequence, while in implementation of the recent technique, the integration steps can be enlarged by a positive integer greater than one, the integration steps can now be enlarged by a positive rational number (ratio of two positive numbers) greater than one ( q p  ; see also Figure 1), and the reductions of computational cost, i.e.…”

“…(3) (4) results in additional computational cost. Recently a technique is proposed to reduce this additional cost, by replacing the excitation with an excitation, with n times larger digitization steps, where, n is a positive integer, greater than one [16]. The corresponding reduction of computational cost, c A , is not more than…”