Singular perturbations generating complexification phenomena for elliptic shells

摘要

This paper deals with elliptic shell problems using the Koiter shell model. When the shell is well-inhibited, the limit membrane problem satisfies the Shapiro-Lopatinskii condition and we have a classical singular perturbation problem. In a previous paper, the existence of two kinds of singularities was put in a prominent position for this kind of problem. Conversely, for ill-inhibited shells (when a part of the boundary is free), the limit problem does not satisfy the Shapiro-Lopatinskii condition. Complexification phenomenon appears when the thickness approaches zero, leading to large oscillations corresponding to a new kind of instability on the free boundary. To complete the theoretical analysis, numerical simulations are performed with a finite element software coupled with an anisotropic adaptive mesh generator. This enables us to visualize precisely the singularities and the instabilities predicted by the theory with only a small number of elements.