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

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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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Authors and Affiliations

  1. Laboratory of Mechanical Engineering, Faculty of Sciences and Technologies Fez, Sidi Mohamed Ben Abdellah University, Imouzzer Road, BP 2202, Fez, Morocco

    Oussama Bourihane

  2. Laboratory of Engineering and Materials, Faculty of Sciences Ben M’sik, Hassan II University of Casablanca, Av Driss El Harti Sidi Othmane, B.P. 7955, Casablanca, Morocco

    Oussama Bourihane

  3. Laboratory of Innovation in Science, Technologies and Modeling, Faculty of Sciences El Jadida, Chouaïb Doukkali University, Ben Maachou Road, B.P. 20, 24000, El Jadida, Morocco

    Khadija Mhada

  4. Laboratory of Nuclear, Atomic, Molecular, Mechanical and Energetic Physics, Faculty of Sciences El Jadida, Chouaïb Doukkali University, Ben Maachou Road, B.P. 20, 24000, El Jadida, Morocco

    Yassir Sitli

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  1. Oussama Bourihane
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Correspondence to Oussama Bourihane.

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Bourihane, O., Mhada, K. & Sitli, Y. New finite element model for the stability analysis of a functionally graded material thin plate under compressive loadings. Acta Mech 231, 1587–1601 (2020). https://doi.org/10.1007/s00707-019-02609-2

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  • DOI: https://doi.org/10.1007/s00707-019-02609-2

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