On Computational Asymptotic Analysis of General Sensitive Shells of Revolution

Recent advances in drug delivery technology have led to renewed interest in shell structures with mixed kinematical constraints, one end clamped, another one free, the so-called sensitive shells. It is known that elliptic sensitive shell problems may not always satisfy the Shapiro–Lopatinsky conditions and hence are not necessarily well-posed. The new observation is that for shells of revolution if the profile function has regions of elliptic Gaussian curvature, that region will dictate the overall response of the structure under concentrated loading. Despite the monotonically increasing total energy as the thickness tends asymptotically to zero, these shells are not in a pure bending state. The numerical results have been verified using equivalent lower-dimensional solutions.