<p>The novelty of the present work lies in the development of a new four-node rectangular finite element using strain-based and Reissner–Mindlin theory. This paper is the first to apply this innovative approach to study the static, free vibration, and buckling responses of functionally graded materials (FGMs) plates. The mechanical properties of the FGM plate are considered to vary along the thickness direction by the power-law distributions. The notion of a neutral surface has been used to prevent the stretching–bending effect. The developed element has six degrees of freedom (DOFs) per node, obtained by combining two strain-based elements. The first one is a membrane which has three DOFs per node, and the second one is a Reissner–Mindlin plate which has three DOFs per node. The displacement fields of these components are represented by higher-order expressions based on the strain approach, which satisfy both rigid body modes and compatibility equations. The performance of the proposed element is evaluated through various numerical problems, and the results are compared with those published in the literature, showing good agreement. The impact of the gradient index, side-to-thickness ratio, aspect ratio, and loading types on the stresses, transverse displacements, frequency response, and critical buckling load of FGM plates is also investigated and discussed.</p>

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Static, free vibration, and buckling analysis of functionally graded plates using strain approach and Reissner–Mindlin elements

  • Taqiyeddine Assas,
  • Messaoud Bourezane,
  • Madjda Chenafi

摘要

The novelty of the present work lies in the development of a new four-node rectangular finite element using strain-based and Reissner–Mindlin theory. This paper is the first to apply this innovative approach to study the static, free vibration, and buckling responses of functionally graded materials (FGMs) plates. The mechanical properties of the FGM plate are considered to vary along the thickness direction by the power-law distributions. The notion of a neutral surface has been used to prevent the stretching–bending effect. The developed element has six degrees of freedom (DOFs) per node, obtained by combining two strain-based elements. The first one is a membrane which has three DOFs per node, and the second one is a Reissner–Mindlin plate which has three DOFs per node. The displacement fields of these components are represented by higher-order expressions based on the strain approach, which satisfy both rigid body modes and compatibility equations. The performance of the proposed element is evaluated through various numerical problems, and the results are compared with those published in the literature, showing good agreement. The impact of the gradient index, side-to-thickness ratio, aspect ratio, and loading types on the stresses, transverse displacements, frequency response, and critical buckling load of FGM plates is also investigated and discussed.