Asymptotic energy behavior of two classical intermediate benchmark shell problems

We consider two classical problems which are widely used as benchmark tests for shell numerical methods: the Scordelis-Lo roof and the pinched roof. Due to the particular load and boundary conditions applied, neither belongs to the well known classes of purely bending or purely membrane dominated shells. Consequently 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, using space interpolation techniques and a recently developed ``intermediate'' shell theory, the asymptotic energy behavior of both problems is found analytically. The results are in agreement with the numerical estimates obtained in other papers.