An effective parametrization for asymptotic extrapolations

When considering the range of validity of asymptotic expansions, the choice of the expansion parameter plays an essential role. In effect, with the exception of a posteriori adjustments of the expansion components, the definition of this parameter is the only way of improving the approximation at a finite distance from the initial point. Good parametrization equations are usually obtained by norms that involve all variables of the problem or based on the nature of the mechanical phenomena. Here this equation is constructed following the criteria of reducing the residual error and at the same time exactly reproducing solutions that admit a polynomial second degree representation. That choice is automatic in the analysis and improves the domain of accurate approximations. An appropriate predictor-corrector scheme was implemented to compare extrapolations obtained by this and several standard parametrizations. The solution scheme was used to analyse geometrically nonlinear plane Frame structures. (C) 2000 Elsevier Science S.A. All rights reserved.