Numerical evaluation of the asymptotic energy behavior of intermediate shells with application to two classical benchmark tests

We consider the class of shell problems which are neither purely bending neither purely membrane dominated. In such cases the asymptotic energy norm behavior (which is useful not only because it represents the structure stiffness, but also for numerical comparison purposes) is not a priori known. In this work we apply a numerical procedure in order to estimate the energy behavior of a general shell problem. In order to test its reliability, the method is applied to various problems for which the theoretical energy behavior is known and the results can be compared. Among the problems tested, we have two classical engineering shell benchmarks which are neither bending neither membrane dominated, and for which an analytical evaluation has been obtained in a recent work. All the energy behavior estimates obtained with the numerical method are in perfect agreement with the theoretical values.