Resolution of the transient dynamic problem with arbitrary loading using the asymptotic method

Analysis of dynamic systems is more time consuming than of static ones due to the presence of inertia forces which vary in time. Equations of a dynami c system excited by arbitrary loads result in partial differential equation s. The spatial part is discretized by the finite element method and the tem poral part by implicit or explicit integration scheme. The time integration methods have already proved their effectiveness. However, in order to impr ove computing time for the resolution and quality of results, we present in this paper, a semi-analytical method based on an asymptotic method which a llows to obtain a continuous solution for all time. In this method, the dis placement field is expressed in power series. From this series, velocity an d acceleration are easily computed. The load must be expressed also in seri es in the same manner as displacement. To do so, we use the Fourier integra l to obtain an analytical function of an arbitrary load and then, we develo p this function in power series using Taylor series. The dynamic asymptotic method (DAM) belongs to the conditionally stable-explicit methods. We appl y this method in modal space in order to eliminate higher modes which influ ence the critical time (time segment length). Through numerical examples, w e show better effectiveness of the asymptotic method compared to the Newmar k method when we applied those schemes in the modal space. (C) 2001 Academic Press.