Reduced order shear projection virtual element method for Mindlin plates

This paper presents a virtual element method (VEM) for the Mindlin plate problem, employing uncoupled first order approximation for the rotations and transverse displacement. The key novelty of the proposed approach is the elimination of shear locking within the element by projecting the shear strain onto a constant space, in a manner analogous to selective reduced integration techniques in finite element methods (FEM), while retaining the flexibility to accommodate arbitrary polygonal element shapes. The proposed element is validated on benchmark problems, where it is found to perform equivalently to a previous VEM formulations, while requiring fewer degrees of freedom, and out performs the equivalent finite element on unstructured meshes. The formulation converges optimally in the L² L 2 norm and H¹ H 1 semi-norm with respect to the number of degrees of freedom and the element diameter for elements with greater than 3 sides. The VEM formulation was tested against a selective reduced integration FEM and shows very similar results for structured meshes, but performs better than the FEM on unstructured meshes in the test case chosen.