A shell problem highly sensitive to thickness changes

In general, shell structural problems can be identi ed to fall into one of the categories of membranedominated, bending-dominated and mixed shell problems. The asymptotic behaviour with a well-de ned load-scaling factor shows distinctly into which category a given shell problem falls. The objective of this paper is to present a shell problem and its solution for which there is no convergence to a well-de ned load-scaling factor as the thickness of the shell decreases. Such shells are unduly sensitive in their behaviour because the ratio of membrane to bending energy stored changes signi cantly and indeed can uctuate with changes in shell thickness. We brie y review the di erent asymptotic behaviours that shell problems can display, and then present the speci c problem considered and its numerical solution using nite element analysis