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<p>In this study, the buckling and post-buckling behavior of Functionally Graded Material (FGM) plates is numerically investigated using a combination of the Hermite Radial Point Interpolation Method (HRPIM) and the Asymptotic Numerical Method (ANM). The Third-Order Shear Deformation Theory (TSDT) is employed to derive the nonlinear deformation equations. The HRPIM is then used to discretize the differential equations, while the ANM is applied to transform the resulting nonlinear equations into a sequence of linearized equations with the same tangent operator. Using ANM, an arc-length path-following technique is implemented to conduct the geometrically nonlinear stability analysis and to capture the buckling and post-buckling paths. Notably, the key phenomenon in this nonlinear analysis is the occurrence of buckling, whose critical load results from the accumulation of incremental steps. The reliability of the mesh-free-ANM approach is validated by comparing the results with available solutions from the literature. Following this, a comprehensive analysis is conducted, considering various geometric and mechanical parameters-such as material volume fraction, boundary conditions, length-to-thickness ratio, and more-that influence the buckling and post-buckling behavior of FGM plates.</p>

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High-order Hermite mesh-free continuation for buckling analysis of FGM sandwich thin plates

  • 期刊论文

  • 发表日期：

    2026年1月14日

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  • Sokayna Baid,
  • Omar Askour,
  • Youssef Hilali,
  • Said Mesmoudi,
  • Oussama Bourihane

摘要

In this study, the buckling and post-buckling behavior of Functionally Graded Material (FGM) plates is numerically investigated using a combination of the Hermite Radial Point Interpolation Method (HRPIM) and the Asymptotic Numerical Method (ANM). The Third-Order Shear Deformation Theory (TSDT) is employed to derive the nonlinear deformation equations. The HRPIM is then used to discretize the differential equations, while the ANM is applied to transform the resulting nonlinear equations into a sequence of linearized equations with the same tangent operator. Using ANM, an arc-length path-following technique is implemented to conduct the geometrically nonlinear stability analysis and to capture the buckling and post-buckling paths. Notably, the key phenomenon in this nonlinear analysis is the occurrence of buckling, whose critical load results from the accumulation of incremental steps. The reliability of the mesh-free-ANM approach is validated by comparing the results with available solutions from the literature. Following this, a comprehensive analysis is conducted, considering various geometric and mechanical parameters-such as material volume fraction, boundary conditions, length-to-thickness ratio, and more-that influence the buckling and post-buckling behavior of FGM plates.