Asymptotic study of the solution for pinched cylindrical shells

We consider the displacement problem of a cylindrical roof under a pointwise Dirac load acting in the normal direction, and recognize two classes of possible responses in dependence of the boundary conditions: the bending dominated and the “intermediate” case. We theoretically analyze the local form of the solution around the load application point in both cases; the latter (which is equivalent to the classical pinched cylinder benchmark) shows a layer of characteristic length t1/4 in the angular direction, while the first one shows a smoother solution. Finally we exploit the results obtained in order to derive some good numerical strategies for the problem. In the last section, we show the perfect correspondence between the theoretical results and the solution obtained through numerical means.