Examples of Non-inhibited Shell Problems (Non-geometrically Rigid Problems)

In this chapter, we shall see how the numerical anisotropic adaptive procedure of remeshing reacts when the shell is not inhibited. In that case, the middle surface naturally deforms with inextensional displacements, and the Koiter model tends to a pure bending problem when e tends to zero (see section 2.3.5 of chapter 2). Indeed, in order to minimize elastic energy, the natural trend of the shell (for small e) is to deform by “pure bendings”: it avoids the (large) membrane energy, and only uses the (small) bending energy. In these very particular deformations, involving inextensional displacements, the asymptotic lines of the surface play a peculiar role, leading to an anisotropic behavior.