MEMBRANE LOCKING IN THE FINITE-ELEMENT COMPUTATION OF VERY THIN ELASTIC SHELLS

The membrane locking phenomenon arises in cases when the middle surfac e of the shell admits ''pure bendings'' satisfying the kinematic bound ary conditions. It then appears that the discrete approximations by fi nite elements is unsuited to describe such pure bendings, which are th e limit configuration of solutions as the thickness tends to zero. Thi s phenomenon is described in terms of lack of robustness (i.e. lack of uniformity of the finite element convergence h \ O with respect to th e thickness of the shell 2 epsilon). We prove that any finite element scheme consisting of in piecewise polynomial functions necessarily exh ibits locking for certain shells (and probably for almost any shell ad miting pure bendings). Numerical experiments are done for a hyperbolic paraboloid. The superiority of schemes involving high order polynomia ls (Ganev-Argyris in particular) is shown. It is also seen that reduce d integration have very little influence on membrane locking.