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In this work, we present a finite element approach for numerical modeling of functionally graded plates buckling under to mechanical loads. The theoretical modeling framework is built upon Reddy’s Third-Order Shear Deformation Theory (TSDT). Subsequently, the principle of minimum total potential energy to formulate the mathematical model for the stability equation of the plate. A quadrilateral isoparametric Lagrangian and Hermitian finite elements are developed to derive the finite element system that corresponds to the buckling problem, then the determination of the critical buckling loads is reduced to the resolution of the eigenvalue problem associated to the finite element model. The developed approach is validated by comparison with the analytical results.

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Hermite and Lagrange Finite Elements for Analysis of Buckling FGM Plates Under Mechanical Loading

  • 会议论文

  • 发表日期：

    2025年

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  • Khadija Zahari,
  • Youssef Hilali,
  • Said Mesmoudi,
  • Rachid El Khaoulani,
  • Oussama Bourihane

摘要

In this work, we present a finite element approach for numerical modeling of functionally graded plates buckling under to mechanical loads. The theoretical modeling framework is built upon Reddy’s Third-Order Shear Deformation Theory (TSDT). Subsequently, the principle of minimum total potential energy to formulate the mathematical model for the stability equation of the plate. A quadrilateral isoparametric Lagrangian and Hermitian finite elements are developed to derive the finite element system that corresponds to the buckling problem, then the determination of the critical buckling loads is reduced to the resolution of the eigenvalue problem associated to the finite element model. The developed approach is validated by comparison with the analytical results.