## The problem of membrane locking in finite element analysis of cylindrical shells.(English)Zbl 0768.73079

Membrane (or shear-membrane) locking may arise in a thin shell problem if the deformation state of the shell is such that bending deformations carry the dominating part of the total deformation energy. In this paper finite element schemes are studied where the displacement fields is approximated using $$C^ 0$$ finite elements of degree $$\geq 1$$ on a rectangular or quadrilateral grid. Two alternative strategies are considered: one where the energy is simply minimized as it is given, and a special implementation of selective reduced integration strategy, where the strain components that cause locking are underintegrated in a special way. The basic idea for the second strategy is due to K.-J. Bathe and E. N. Dvorkin [Int. J. Numer. Methods Eng. 22, 697-722 (1986; Zbl 0585.73123)]. The main results of the paper are error estimates for the two families of finite element schemes in relative energy norm.
Reviewer: V.Arnautu (Iaşi)

### MSC:

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

Zbl 0585.73123
Full Text:

### References:

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