APPLICATION OF AN ASYMPTOTIC METHOD TO TRANSIENT DYNAMIC PROBLEMS

A new method to solve linear dynamics problems using an asymptotic met hod is presented. Asymptotic methods have been efficiently used for ma ny decades to solve non-linear quasistatic structural problems. Genera lly, structural dynamics problems are solved using finite elements for the discretization of the space domain of the differential equations, and explicit or implicit schemes for the time domain. With the asympt otic method, time schemes are not necessary to solve the discretized ( space) equations. Using the analytical solution of a single degree of freedom (DOF) problem, it is demonstrate, that the Dynamic Asymptotic Method (DAM) converges to the exact solution when an infinite series e xpansion is used. The stability of the method has been studied. DAM is conditionally stable for a finite series expansion and unconditionall y stable for an infinite series expansion. This method is similar to t he analytical method of undetermined coefficients or to power series m ethod being used to solve ordinary differential equations. For a multi -degree-of-freedom (MDOF) problem with a lumped mass matrix, no factor ization or explicit inversion of global matrices is necessary. It is s hown that this conditionally stable method is more efficient than othe r conditionally stable explicit central difference integration techniq ues. The solution ij continuous irrespective of the time segment (step ) and the derivatives are continuous up to order N-1 where N is the or der of the series expansion. (C) 1997 Academic Press Limited.