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