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Buckling of Coated Functionally Graded Spherical Nanoshells Rested on Orthotropic Elastic Medium

Author

Listed:
  • Gamal S. Abdelhaffez

    (Mining Engineering Department, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

  • Ahmed Amine Daikh

    (Department of Technology, University Centre of Naama, Naama 45000, Algeria
    Laboratoire d’Etude des Structures et de Mécanique des Matériaux, Département de Génie Civil, Faculté desSciences et de la Technologie, Université Mustapha Stambouli, Mascara 29000, Algeria)

  • Hussein A. Saleem

    (Mining Engineering Department, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

  • Mohamed A. Eltaher

    (Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, Jeddah P.O. Box 80204, Saudi Arabia)

Abstract

Coated functionally graded materials (FGMs) are used in several industrial structures such as turbine blades, cutting tools, and aircraft engines. Given the need for analytical and numerical analysis of these complex structures, a mathematical model of tricoated FG structures is presented for the first time in this paper. The objective of this work was to analyze analytically the buckling problem of unidirectional (1D), bidirectional (2D), and tridirectional (3D) coated FG spherical nanoshells resting on an orthotropic elastic foundation subjected to biaxial loads. Based on the generalized field of displacement, a 2D higher-order shear deformation theory was proposed by reducing the number of displacement variables from five to four variables for specific geometry cases. The nonlocal strain gradient theory was employed to capture the size-dependent and microstructure effects. The equilibrium equations were performed by applying the principle of the virtual work, and the obtained differential equations were solved by applying the Galerkin technique to cover all possible boundary conditions. The proposed elastic foundation was defined based on three parameters: one spring constant and two shear parameters referring to the orthotropy directions. A detailed parametric analysis was carried out to highlight the impact of various schemes of coated FGMs, gradient material distribution, length scale parameter (nonlocal), material scale parameter (gradient), geometry of the nanoshell, and variation in the orthotropic elastic foundation on the critical buckling loads.

Suggested Citation

  • Gamal S. Abdelhaffez & Ahmed Amine Daikh & Hussein A. Saleem & Mohamed A. Eltaher, 2023. "Buckling of Coated Functionally Graded Spherical Nanoshells Rested on Orthotropic Elastic Medium," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:409-:d:1033993
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    References listed on IDEAS

    as
    1. Ammar Melaibari & Ahmed Amine Daikh & Muhammad Basha & Ahmed Wagih & Ramzi Othman & Khalid H. Almitani & Mostafa A. Hamed & Alaa Abdelrahman & Mohamed A. Eltaher, 2022. "A Dynamic Analysis of Randomly Oriented Functionally Graded Carbon Nanotubes/Fiber-Reinforced Composite Laminated Shells with Different Geometries," Mathematics, MDPI, vol. 10(3), pages 1-24, January.
    2. Shaowu Yang & Yuxin Hao & Wei Zhang & Lingtao Liu & Wensai Ma, 2022. "Static and Dynamic Stability of Carbon Fiber Reinforced Polymer Cylindrical Shell Subject to Non-Normal Boundary Condition with One Generatrix Clamped," Mathematics, MDPI, vol. 10(9), pages 1-25, May.
    3. Emad E. Ghandourah & Ahmed A. Daikh & Abdulsalam M. Alhawsawi & Othman A. Fallatah & Mohamed A. Eltaher, 2022. "Bending and Buckling of FG-GRNC Laminated Plates via Quasi-3D Nonlocal Strain Gradient Theory," Mathematics, MDPI, vol. 10(8), pages 1-37, April.
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