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Some new elements for the Reissner-Mindlin plate model. (English) Zbl 0817.73058
Lions, Jacques-Louis (ed.) et al., Boundary value problems for partial differential equations and applications. Dedicated to Enrico Magenes on the occasion of his 70th birthday. Paris: Masson. Res. Notes Appl. Math. 29, 287-292 (1993).
We report on a new approach to obtaining stable locking-free discretizations of the Reissner-Mindlin plate model. We present also some choices of elements with continuous piecewise linear approximation of the shear stress. The choice of these elements uses the velocity and pressure interpolations from the MINI Stokes element for the transverse displacement and the shear stress, respectively, and for the rotations uses a space which contains the space used for the shear stress. Using other Stokes elements, in a similar way we can derive other stable Reissner-Mindlin elements, all with continuous piecewise polynomial approximation of the shear stress.
MSC:
74S05Finite element methods in solid mechanics
74K20Plates (solid mechanics)