An Asymptotic Numerical Method for non-linear transient dynamics

Abstract

ABSTRACT The main objective of this presentation is to show that a perburbation method can be very effective for solving a large class of transient non-linear dynamic problems. We describe an algorithm which has three part: apply a perturbation technique to transform a non-linear problem into a series of linear ones, use an FEM and a time stepping scheme to solve the linear problems, perform the summation of the series to get the solution. Usually, the perturbation series has a finite radius of convergence, and the algorithm has to be restarted several times to get the solution on the whole time interval. However, as compared to a classical conbination of time stepping and Newton-Raphson method, the present algorithm requires much less stiffness matrix evaluations and triangulations. The performances of the proposed algorithm will be demonstrated with an example.