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Acta Mechanica
Published in: Acta Mechanica 4/2020

25-01-2020 | Original Paper

New finite element model for the stability analysis of a functionally graded material thin plate under compressive loadings

Authors: Oussama Bourihane, Khadija Mhada, Yassir Sitli

Published in: Acta Mechanica | Issue 4/2020

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Abstract

The main objective of this work is to present a finite element model for the stability analysis of functionally graded material thin plates subjected to uniaxial and biaxial loads. This model is developed using the classic thin plate’s kinematics of von Kármán. Static equilibrium equations are established by means of the principle of stationary potential energy. The formulation is made without any homogenization technique or rule of mixtures; thus, the stress and strain vectors are split into two parts: a membrane part and a second bending part. For the elastic behavior matrix, it is written in dimensionless form. The finite element discretization is done using a four-node quadrilateral element with five degrees of freedom per node. Lagrange bilinear shape function are adopted for the membrane components, and Hermite’s high-degree shape function are adopted for the flexural component. The critical buckling loads are established by solving the eigenvalue problem. The efficiency of the model is tested on several examples of buckling plates under different types of loading. In the present study, specimens of rectangular and perforated plates were tested in three different loading conditions: uniaxial compression, biaxial compression, and compression–traction.
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Metadata
Title
New finite element model for the stability analysis of a functionally graded material thin plate under compressive loadings
Authors
Oussama Bourihane
Khadija Mhada
Yassir Sitli
Publication date
25-01-2020
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 4/2020
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-019-02609-2

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