The treatment of “pinching locking” in 3D-shell elements

• Published in: ESAIM. Mathematical modelling and numerical analysis Vol. 37; no. 1; pp. 143 - 158
• Main Authors: Chapelle, Dominique, Ferent, Anca, Le Tallec, Patrick
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 01.01.2003
• Subjects: 65N30; 74K25; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematics; mixed formulation; Numerical analysis; Numerical analysis. Scientific computation; Numerical locking; Partial differential equations, boundary value problems; Physics; Sciences and techniques of general use; shell finite elements; Solid mechanics; Structural and continuum mechanics; Structural mechanics (beam, string...); Theory and numerical methods; Three dimensional model; Numerical analysis; Error estimation; Consistent estimator; Shell finite element; Numerical locking; A priori estimation; Model study; Numerical simulation; Partial differential equation; Variational techniques; Mixed formulation
• ISSN: 0764-583X; 1290-3841
• DOI: 10.1051/m2an:2003015

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.