Padé approximants applied to a non-linear finite element solution strategy

Abstract

The present work deals with an asymptotic numerical method, based on Padé approximants. The expected advantage of this method is twofold. Firstly, it reduces the computational costs. Secondly, the automatization of the continuation process becomes easier, since the step-length can be determined a posteriori. So far, this method has only been applied to DKT elements. Here it is applied to other types of elements, namely truss elements and finite rotation non-linear shell elements. It will be shown that difficulties arise when this method is applied to finite rotation shell elements. © 1997 by John Wiley & Sons, Ltd.