Richardson Error Estimator and Convergence Error Estimator applied in a buckling analysis by Finite Difference Method (FDM)

Resumo

In order to reduce the numerical error caused by discretization errors, the Richardson Extrapolation and
Convergence Error Estimator were used. The main goal relies on estimating and reducing the numerical error in
the analysis of a simply-supported stepped column. The estimate of the discretization error followed the
approach proposed by Marchi and Silva [1-2]. The variable of interest was the critical buckling load obtained
through the Finite Difference Method (FDM). The main concern regards the verification of the order of
convergence for a buckling problem of continuous and stepped columns. The equivalent moment of inertia is
determined at the node where the sudden cross-section variation occurs. Different ratios between moments of
inertia of the cross-sections were considered. The use of the equivalent moment of inertia in the modeling
reached the order of convergence 2 for Richardson Error Estimator and the convergence order 4 using
Convergence Error Estimator.