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Abstract <p>This study examines the buckling response of functionally graded material (FGM) nanoplates resting on nonlinear Kerr elastic foundations under coupled hygrothermal-mechanical loading and diverse boundary conditions. A novel computational framework is developed by integrating a simplified quasi-3D higher-order shear deformation theory (HSDT) with only five displacement variables and Eringen’s nonlocal elasticity theory, enabling the precise modelling of nanoscale effects through integral constitutive relations. The FGM nanoplate exhibits a continuous material gradation across its thickness and is subjected to nonlinear hygrothermal gradients, mechanical stresses, and foundation interactions. The governing equations are derived using the principle of virtual displacements and solved for various edge constraints, including simply supported and clamped configurations. The developed model has been verified through comparison with established benchmark results for buckling in FG nanostructures, revealing close correspondence where deviations are generally under 0.1%, thus confirming the proper execution of the nonlocal plate theory.&#xa0;Parametric analyses revealed the critical influences of the material gradation index, nonlocal parameter, Kerr foundation stiffness, and hygrothermal environmental conditions on stability thresholds. The results highlight the destabilising effects of increasing hygrothermal gradients and the stabilising role of shear-layer stiffness in the Kerr foundation.&#xa0;This study provides a computationally efficient tool for designing advanced FGM-based nanoelectromechanical systems (NEMS) operating in multifield environments, bridging the gaps between classical plate theories and full 3D nanomechanics.</p>

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Instability Behavior of FG Nanoplates Resting on Nonlinear Kerr Foundations under Hygro-Thermo-Mechanical Load Using Nonlocal Elasticity Theory

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • H. Benachi,
  • A. Menasria,
  • A. Bouhadra,
  • S. Refrafi,
  • M. Baazouzi,
  • M. Chitour,
  • N. Himeur

摘要

Abstract

This study examines the buckling response of functionally graded material (FGM) nanoplates resting on nonlinear Kerr elastic foundations under coupled hygrothermal-mechanical loading and diverse boundary conditions. A novel computational framework is developed by integrating a simplified quasi-3D higher-order shear deformation theory (HSDT) with only five displacement variables and Eringen’s nonlocal elasticity theory, enabling the precise modelling of nanoscale effects through integral constitutive relations. The FGM nanoplate exhibits a continuous material gradation across its thickness and is subjected to nonlinear hygrothermal gradients, mechanical stresses, and foundation interactions. The governing equations are derived using the principle of virtual displacements and solved for various edge constraints, including simply supported and clamped configurations. The developed model has been verified through comparison with established benchmark results for buckling in FG nanostructures, revealing close correspondence where deviations are generally under 0.1%, thus confirming the proper execution of the nonlocal plate theory. Parametric analyses revealed the critical influences of the material gradation index, nonlocal parameter, Kerr foundation stiffness, and hygrothermal environmental conditions on stability thresholds. The results highlight the destabilising effects of increasing hygrothermal gradients and the stabilising role of shear-layer stiffness in the Kerr foundation. This study provides a computationally efficient tool for designing advanced FGM-based nanoelectromechanical systems (NEMS) operating in multifield environments, bridging the gaps between classical plate theories and full 3D nanomechanics.