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<p>This paper presents a strain-based finite element formulation for the static, free vibration, and buckling analyses of laminated cross-ply plates within the framework of the High-Order Shear Deformation Theory (HSDT). The existing strain-based formulations are predominantly limited to First-Order Shear Deformation Theory (FSDT) or restricted analyses (mainly static or vibration), without a unified framework for complete mechanical behavior assessment of laminated plates. The novelty of the proposed approach lies in the integration of HSDT into a strain-based formulation, together with a new hyperbolic shear deformation function specifically developed in this work, which accurately captures transverse shear effects, enforces zero shear stresses at the plate surfaces, and reduces the number of kinematic unknowns from six to five. Unlike existing polynomial or trigonometric shear functions commonly used in HSDT formulations, the proposed hyperbolic function provides a more physically consistent representation of shear deformation distribution, leading to improved accuracy in transverse shear response prediction. The formulation is implemented through a High-order Strain-Based Laminated Quadrilateral Plate element (HSBLQP), obtained by coupling a strain-based in-plane element with a strain-based plate bending element. The present work introduces a hyperbolic shear deformation function within a strain-based HSDT finite element formulation for a complete structural analysis including static, free vibration, and mechanical buckling of laminated composite plates. The accuracy and reliability of the proposed element are first validated through static analysis of elliptical plates and free vibration analysis of L-shape plates by comparison with benchmark solutions available in the literature. Notably, this work also introduces, for the first time in this context, validation cases involving L-shaped and elliptical plates within a strain-based HSDT framework, demonstrating the robustness of the proposed formulation for complex geometries. Subsequently, a comprehensive parametric study is carried out to investigate the influence of geometrical and material parameters on the static, free vibration, and buckling responses of laminated cross-ply plates. The numerical results demonstrate excellent agreement with reference solutions, confirming the accuracy, robustness, and computational efficiency of the proposed strain-based HSDT formulation for laminated composite plate analysis.</p>

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An advanced strain-based finite element model for laminated plates based on a novel hyperbolic shear deformation theory

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Madjda Chenafi,
  • Giovanni Castellazzi,
  • Taqiyeddine Assas,
  • Abdulrahman M. Al-Nadhari

摘要

This paper presents a strain-based finite element formulation for the static, free vibration, and buckling analyses of laminated cross-ply plates within the framework of the High-Order Shear Deformation Theory (HSDT). The existing strain-based formulations are predominantly limited to First-Order Shear Deformation Theory (FSDT) or restricted analyses (mainly static or vibration), without a unified framework for complete mechanical behavior assessment of laminated plates. The novelty of the proposed approach lies in the integration of HSDT into a strain-based formulation, together with a new hyperbolic shear deformation function specifically developed in this work, which accurately captures transverse shear effects, enforces zero shear stresses at the plate surfaces, and reduces the number of kinematic unknowns from six to five. Unlike existing polynomial or trigonometric shear functions commonly used in HSDT formulations, the proposed hyperbolic function provides a more physically consistent representation of shear deformation distribution, leading to improved accuracy in transverse shear response prediction. The formulation is implemented through a High-order Strain-Based Laminated Quadrilateral Plate element (HSBLQP), obtained by coupling a strain-based in-plane element with a strain-based plate bending element. The present work introduces a hyperbolic shear deformation function within a strain-based HSDT finite element formulation for a complete structural analysis including static, free vibration, and mechanical buckling of laminated composite plates. The accuracy and reliability of the proposed element are first validated through static analysis of elliptical plates and free vibration analysis of L-shape plates by comparison with benchmark solutions available in the literature. Notably, this work also introduces, for the first time in this context, validation cases involving L-shaped and elliptical plates within a strain-based HSDT framework, demonstrating the robustness of the proposed formulation for complex geometries. Subsequently, a comprehensive parametric study is carried out to investigate the influence of geometrical and material parameters on the static, free vibration, and buckling responses of laminated cross-ply plates. The numerical results demonstrate excellent agreement with reference solutions, confirming the accuracy, robustness, and computational efficiency of the proposed strain-based HSDT formulation for laminated composite plate analysis.