Abstract
A new family of locking-free finite elements for shear deformable Reissner–Mindlin plates is presented. The elements are based on the “tangential-displacement normal-normal-stress” formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the rotations and normal–normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence.
Highlights
In this paper we are concerned with finite elements for shear deformable plates based on the Reissner–Mindlin model [34,42]
Brezzi and Marini [18] developed a nonconforming element in the framework of discontinuous Galerkin methods
The plate elements proposed in the current paper are based on the “tangentialdisplacement normal-normal-stress” (TDNNS) formulation of elasticity introduced by the authors in [38]
Summary
In this paper we are concerned with finite elements for shear deformable plates based on the Reissner–Mindlin model [34,42]. Brezzi and Marini [18] developed a nonconforming element in the framework of discontinuous Galerkin methods In both works, the shear strain is projected into a lower-order finite element space to alleviate the Kirchhoff constraint. The plate elements proposed in the current paper are based on the “tangentialdisplacement normal-normal-stress” (TDNNS) formulation of elasticity introduced by the authors in [38] This leads to a formulation containing deflection, rotations and bending moments as separate unknowns. The main benefit of this choice is that the gradient of the deflection space is a subset of the rotation space both for the infinite dimensional and for the finite element problem, and the Kirchhoff constraint of vanishing shear strain does not lead to locking.
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