Energy Behavior of Two Classical Benchmark Shell Problems

In the classification of shells, among the two classical families known as membrane dominated and bending dominated, there is a third class which is surely less known. For such family, theoretical results about the energy norm behavior and percentage of bending energy have been proved rather recently. Such results allow a rigorous study of the asymptotic behavior of some \"famous\" shell benchmarks (in other words, problems which are classical tests for shell finite elements in the engineering literature). In the first part of the talk I will therefore introduce briefly the classical theory of shells and follow with a survey of the recent aforementioned results. In the second part I will show the theoretical results obtained for the classical shell benchmarks known as \"pinched roof\" and \"Scordelis-Lo roof\", and compare them with those obtained through numerical techniques.