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<p>This paper introduces an enriched four-node quadrilateral finite element, referred to as Q4γ, specifically developed for investigating the free vibration response of graphene platelet–reinforced (GPL) nanocomposite plates. A salient feature of the proposed element is using a discrete shear projection technique to address the shear-locking issue and develop a novel projection framework for consistent mass matrix construction. An advancement not implemented in conventional quadrilateral plate formulations. The proposed technique amplifies the transverse inertial contribution by refining the displacement-based inertia representation. This improvement accelerates the convergence of the modal solution without requiring fine mesh discretization, differentiating the present Q4γ formulation from prior techniques that enhance stiffness matrices in isolation or rely on simplified lumped mass approaches. The methodology preserves theoretical consistency by embedding kinematic-inertial coupling in a projection-compatible finite element structure. The element’s performance is validated through numerical benchmarks and convergence studies, including tests under significant mesh distortion. The results demonstrate close agreement with reference solutions derived from higher-order and isogeometric formulations. Ultimately, the results confirm that the enriched Q4γ element provides an efficient and accurate platform for vibration modeling advanced nanocomposite structures, particularly where bending-membrane coupling is significant.</p>

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Shear-locking-free finite element formulation for vibrating functionally graded graphene nanocomposites using an enriched quadrilateral plate element

  • 期刊论文

  • 发表日期：

    2025年9月23日

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  • Zakaria Belabed,
  • M. A. Kenanda,
  • Fodil Hammadi,
  • Hamid M. Sedighi

摘要

This paper introduces an enriched four-node quadrilateral finite element, referred to as Q4γ, specifically developed for investigating the free vibration response of graphene platelet–reinforced (GPL) nanocomposite plates. A salient feature of the proposed element is using a discrete shear projection technique to address the shear-locking issue and develop a novel projection framework for consistent mass matrix construction. An advancement not implemented in conventional quadrilateral plate formulations. The proposed technique amplifies the transverse inertial contribution by refining the displacement-based inertia representation. This improvement accelerates the convergence of the modal solution without requiring fine mesh discretization, differentiating the present Q4γ formulation from prior techniques that enhance stiffness matrices in isolation or rely on simplified lumped mass approaches. The methodology preserves theoretical consistency by embedding kinematic-inertial coupling in a projection-compatible finite element structure. The element’s performance is validated through numerical benchmarks and convergence studies, including tests under significant mesh distortion. The results demonstrate close agreement with reference solutions derived from higher-order and isogeometric formulations. Ultimately, the results confirm that the enriched Q4γ element provides an efficient and accurate platform for vibration modeling advanced nanocomposite structures, particularly where bending-membrane coupling is significant.