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Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation

Author

Listed:
  • Fatima Zohra Zaoui

    (Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology, Ibn Badis University, Mostaganem 27000, Algeria)

  • Djamel Ouinas

    (Laboratory of Science and Technology Environment and Valorization, Faculty of Sciences and Technology, Ibn Badis University, Mostaganem 27000, Algeria)

  • Belkacem Achour

    (Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia)

  • Mabrouk Touahmia

    (Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia)

  • Mustapha Boukendakdji

    (Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia)

  • Enamur R. Latifee

    (Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia)

  • Ahmed A. Alawi Al-Naghi

    (Civil Engineering Department, University of Ha’il, Ha’il 55476, Saudi Arabia)

  • Jaime Aurelio Viña Olay

    (Department of Materials Science and Metallurgical Engineering, University of Oviedo, Viesques Campus, 33203 Gijón, Spain)

Abstract

This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures.

Suggested Citation

  • Fatima Zohra Zaoui & Djamel Ouinas & Belkacem Achour & Mabrouk Touahmia & Mustapha Boukendakdji & Enamur R. Latifee & Ahmed A. Alawi Al-Naghi & Jaime Aurelio Viña Olay, 2022. "Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation," Mathematics, MDPI, vol. 10(24), pages 1-29, December.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4764-:d:1004244
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    References listed on IDEAS

    as
    1. Ashraf M. Zenkour & Zahra S. Hafed & Ahmed F. Radwan, 2020. "Bending Analysis of Functionally Graded Nanoscale Plates by Using Nonlocal Mixed Variational Formula," Mathematics, MDPI, vol. 8(7), pages 1-14, July.
    2. Qadeer Raza & M. Zubair Akbar Qureshi & Behzad Ali Khan & Ahmed Kadhim Hussein & Bagh Ali & Nehad Ali Shah & Jae Dong Chung, 2022. "Insight into Dynamic of Mono and Hybrid Nanofluids Subject to Binary Chemical Reaction, Activation Energy, and Magnetic Field through the Porous Surfaces," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
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    Cited by:

    1. Mahmure Avey & Francesco Tornabene & Nigar Mahar Aslanova & Abdullah H. Sofiyev, 2024. "The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations," Mathematics, MDPI, vol. 12(5), pages 1-22, March.

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