We consider a family of shell finite elements with quadratic displacementsacross the thickness. These elements are very attractive, but compared to standard general shell elements they face another sourceof numerical locking in addition to shear and membrane locking. Thisadditional locking phenomenon – that we call “pinching locking” – is thesubject of this paper and we analyse a numerical strategy designed to overcomethis difficulty. Using a model problem in which only this specific sourceof locking is present, we are able to obtain error estimatesindependent of the thickness parameter, which shows that pinching lockingis effectively treated. This is also confirmed by some numerical experimentsof which we give an account.
