The TDNNS method for Reissner-Mindlin plates.

Area of Science:

• Solid Mechanics
• Computational Mechanics
• Structural Engineering

Background:

• Reissner-Mindlin plate theory is crucial for analyzing shear deformation in thin and moderately thick plates.
• Traditional finite elements often suffer from shear locking, requiring complex modifications like reduced integration.
• Developing robust and accurate elements is essential for reliable structural analysis.

Purpose of the Study:

• To present a new family of locking-free finite elements for shear deformable Reissner-Mindlin plates.
• To introduce a formulation based on "tangential-displacement normal-normal-stress" elasticity.
• To demonstrate the elimination of shear locking without special numerical treatments.

Main Methods:

• The study employs a "tangential-displacement normal-normal-stress" formulation.
• Bending moments are treated as independent unknowns within the formulation.
• Degrees of freedom include deflection, tangential rotations, and normal-normal bending strains.

Main Results:

• The proposed finite elements are locking-free for shear deformable plates.
• No special shear treatment, such as reduced integration, is required.
• The elements achieve an optimal order of convergence.

Conclusions:

• The new finite element family offers an efficient and accurate solution for Reissner-Mindlin plate analysis.
• This formulation simplifies the implementation by avoiding shear locking remedies.
• The elements provide a robust alternative for computational structural mechanics applications.