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Membrane locking in the finite element computation of very thin elastic shells. (English) Zbl 0905.73066
The locking phenomenon is described in terms of lack of robustness (i.e. lack of uniformity of the finite element convergence \(h\searrow 0\) with respect to the thickness of the shell \(2\varepsilon\)). We prove that any finite element scheme consisting of piecewise polynomial functions necessarily exhibits locking for certain shells (and probably for almost any shell admiting pure bendings). Numerical experiments are done for a hyperbolic paraboloid. The superiority of schemes involving high-order polynomials (Ganev-Argyris, in particular) is shown. It is also seen that reduced integration has very little influence on membrane locking.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K15 Membranes
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References:
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