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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>1</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Reduced order shear projection virtual element method for Mindlin plates

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月18日

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  • Luke Wyatt,
  • Zahra Sharif Khodaei,
  • M. H. Ferri Aliabadi

摘要

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 \(L^2\) L 2 norm and \(H^1\) 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.