During inelastic analysis, actually, only estimations of the errors are made what is not sufficient. Very often, even if these estimators are very small, this does not imply that the errors i.e. the difference between the exact solution of any field (stress, strain, energy ...) and the approximated solution of the field obtained with the numerical simulation, is small!

Sometimes, Engineers will perform the numerical simulations, then they will reduce the mesh according some rules, and if the new solution is not too far from the previous one, they will take it as a good one. This is very expensive and this is not efficient. Indeed, a lot of expertise is needed during the numerical simulations with also experimental correlations.

It is practically important to have a method where, when the range of the error (that will never be known in principle) is required, it is possible to indicate a priori the minimum cost (or Number of Degrees of Freedom or number of nodes) and to draw the optimal mesh (i.e. with this minimal number) to reach this error.

We shown, with automatic learning, that it is possible to extract some useful rules.

The main difficulty is that only a few examples of EXACT INELASTIC SOLUTIONS are known (cylinder, sphere with symmetrical loadings!) and in order to perform any automatic learning, it is necessary to have a data base of representative examples which contains several elastoplastic structures, their discretizations and for each of them the known errors!!

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