CONSIDERATIONS ON THE CONVERGENCE OF STRUCTURAL ANALYSIS RESULTS PERFORMED BY FINITE ELEMENT METHOD

The article contains some considerations on possible convergence concepts in structural analysis. Meaning these notions of convergence is explained using the example of analysis of a very simple structure. We have introduced tools that facilitate the study of convergence in broad sense used by structures engineers (estimators of convergence, graphs, statistics estimators).Article highlights certain phenomena (on convergence), which are caused by the meshing of the structural model. It shows that, the trajectory of meshing (points having as coordinates number of items or the maximum size of a finite element side), in a meshing multiparametric space, has important consequences for the investigative work of convergence. To expand the notion of convergence in structural analysis, are given in the first part, two analytical solutions of the same problem. Although these solutions are not accurate, they can contribute to greater confidence in the results of structural analysis. These solutions are alternative models to the structural model and exemplifies together, what we call convergence in models. Basically, two types of convergence are proposed, which, considering the notion of convergence from mathematics, should be called pseudo-convergence. The third type is actually, the convergence in the mathematical sense, which can be applied at the analytical solutions (approximate solutions given by developments in series or series of functions), but not to the numerical solutions given by method of finite element, or by finite difference schemes, etc. A few general remarks are made in the closing of the article.

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