Efficient Kinematic model for Stability Analysis of Imperfect Functionally Graded Sandwich Plates with Ceramic middle layer and Varied Boundary Edges

Document Type : Research Paper


1 Department of Civil Engineering, Faculty of Technology, University of Ferhat Abbas, Setif 19137, Algeria.

2 Research Unit of Emerging Materials, University of Ferhat Abbas, Setif 19137, Algeria.

3 Department of Mechanical Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela 40000, Algeria.

4 Civil Engineering Department, College of Engineering, Jazan University, Jazan 114, Saudi Arabia.

5 Department of Civil Engineering, Faculty of Science and Technology, Abbes Laghrour University, Khenchela 40000, Algeria.

6 Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, Djillali Liabes University, Sidi Bel Abbes 22000, Algeria.

7 ICOSI Lab, Faculty of Science and Technology, Abbes Laghrour University, Khenchela 40000, Algeria.


The present paper introduces an efficient higher-order theory to analyze the stability behavior of porous functionally graded sandwich plates (FGSPs) resting on various boundary conditions. The FG sandwich plate comprises two porous FG layers, face sheets, and a ceramic core. The material properties in the FGM layers are assumed to change across the thickness direction according to the power-law distribution. To satisfy the requirement of transverse shear stresses vanishing at the top and bottom surfaces of the FGSP, a trigonometric shear deformation theory containing four variables in the displacement field with indeterminate integral terms is used, and the principle of virtual work is applied to describe the governing equation than it solved by Navier solution method for simply supported boundaries. However, an analytical solution for FGSPs under different boundary conditions is obtained by employing a new shape function, and numerical results are presented. Furthermore, validation results show an excellent agreement between the proposed theory and those given in the literature. In contrast, the influence of several geometric and mechanical parameters, such as power-law index, side-to-thickness, aspect ratio, porosity distribution, various boundary conditions, loading type, and different scheme configurations on the critical buckling, is demonstrated in the details used in a parametric study.


Main Subjects

[1]          J. Jamali, M. Naei, F. Honarvar, M. Rajabi, Acoustic scattering from functionally graded cylindrical shells, Archives of Mechanics, Vol. 63, No. 1, pp. 25-56, 2011.
[2]          O. Taleb, M. Sekkal, R. B. Bouiadjra, S. Benyoucef, K. M. Khedher, M. A. Salem, A. Tounsi, On the Free Vibration Behavior of Temperature-Dependent Bidirectional Functionally Graded Curved Porous Beams, International Journal of Structural Stability and Dynamics, pp. 2450112, 2023.
[3]          H. Z. Guerroudj, R. Yeghnem, A. Kaci, F. Z. Zaoui, S. Benyoucef, A. Tounsi, Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory, Smart structures and systems, Vol. 22, No. 1, pp. 121-132, 2018.
[4]          A. Edwin, V. Anand, K. Prasanna, Sustainable development through functionally graded materials: an overview, Rasayan Journal of Chemistry, Vol. 10, No. 1, pp. 149-152, 2017.
[5]          G. Udupa, S. S. Rao, K. Gangadharan, Functionally graded composite materials: an overview, Procedia Materials Science, Vol. 5, pp. 1291-1299, 2014.
[6]          H.-T. Thai, B. Uy, M. Khan, Z. Tao, F. Mashiri, Numerical modelling of concrete-filled steel box columns incorporating high strength materials, Journal of Constructional Steel Research, Vol. 102, pp. 256-265, 2014.
[7]          S.-H. Chi, Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis, International Journal of Solids and Structures, Vol. 43, No. 13, pp. 3657-3674, 2006.
[8]          R. Javaheri, M. Eslami, Buckling of functionally graded plates under in‐plane compressive loading, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, Vol. 82, No. 4, pp. 277-283, 2002.
[9]          E. Feldman, J. Aboudi, Buckling analysis of functionally graded plates subjected to uniaxial loading, Composite Structures, Vol. 38, No. 1-4, pp. 29-36, 1997.
[10]        R. Menaa, A. Tounsi, F. Mouaici, I. Mechab, M. Zidi, E. A. A. Bedia, Analytical solutions for static shear correction factor of functionally graded rectangular beams, Mechanics of Advanced Materials and Structures, Vol. 19, No. 8, pp. 641-652, 2012.
[11]        M. Rashidi, A. Shooshtari, O. A. Bég, Homotopy perturbation study of nonlinear vibration of Von Karman rectangular plates, Computers & Structures, Vol. 106, pp. 46-55, 2012.
[12]        R. Mindlin, Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, 1951.
[13]        E. Reissner, The effect of transverse shear deformation on the bending of elastic plates, 1945.
[14]        A. Bouhadra, A. Tounsi, A. A. Bousahla, S. Benyoucef, S. R. Mahmoud, Improved HSDT accounting for effect of thickness stretching in advanced composite plates, Structural Engineering and Mechanics, An Int'l Journal, Vol. 66, No. 1, pp. 61-73, 2018.
[15]        D. Chen, J. Yang, S. Kitipornchai, Buckling and bending analyses of a novel functionally graded porous plate using Chebyshev-Ritz method, Archives of Civil and Mechanical Engineering, Vol. 19, No. 1, pp. 157-170, 2019.
[16]        J. Reddy, C. Wang, S. Kitipornchai, Axisymmetric bending of functionally graded circular and annular plates, European Journal of Mechanics-A/Solids, Vol. 18, No. 2, pp. 185-199, 1999.
[17]        M. Mekerbi, R. Bachir Bouiadjra, S. Benyoucef, M. Selim, A. Tounsi, M. Hussain, Micromechanical models for analyzing bending of porous/perfect FG plates in a hygro-thermomechanical environment by a quasi-3D theory, Mechanics of Composite Materials, Vol. 59, No. 4, pp. 693-712, 2023.
[18]        F. Achouri, S. Benyoucef, F. Bourada, R. B. Bouiadjra, A. Tounsi, Robust quasi 3D computational model for mechanical response of FG thick sandwich plate, Struct. Eng. Mech, Vol. 70, No. 5, pp. 571-589, 2019.
[19]        S. Moradi, M. H. Mansouri, Thermal buckling analysis of shear deformable laminated orthotopic plates by differential quadrature, Steel & Composite Structures, Vol. 12, No. 2, pp. 129-147, 2012.
[20]        A. Kabouche, R. Bachir Bouiadjra, A. Bachiri, M. Sekkal, S. Benyoucef, M. M. S. Saleh, A. Tounsi, M. Hussain, Study on the Mechanical Instability of Bidirectional Imperfect FG Sandwich Plates Subjected to In-Plane Loading, Arabian Journal for Science and Engineering, Vol. 47, No. 10, pp. 13655-13672, 2022.
[21]        X. Zhao, Y. Lee, K. M. Liew, Mechanical and thermal buckling analysis of functionally graded plates, Composite Structures, Vol. 90, No. 2, pp. 161-171, 2009.
[22]        M. Mekerbi, S. Benyoucef, A. Mahmoudi, F. Bourada, A. Tounsi, Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution, Structural Engineering and Mechanics, Vol. 72, No. 4, pp. 513, 2019.
[23]        A. Chikh, A. Tounsi, H. Hebali, S. Mahmoud, Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT, Smart Structures and Systems, Vol. 19, No. 3, pp. 289-297, 2017.
[24]        A. Tamrabet, B. Mamen, A. Menasria, A. Bouhadra, A. Tounsi, M. H. Ghazwani, A. Alnujaie, S. Mahmoud, Buckling behaviors of FG porous sandwich plates with metallic foam cores resting on elastic foundation, Structural Engineering and Mechanics, Vol. 85, No. 3, pp. 289, 2023.
[25]        D. Chen, J. Yang, S. Kitipornchai, Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Composites Science and Technology, Vol. 142, pp. 235-245, 2017.
[26]        D. Chen, J. Yang, S. Kitipornchai, Free and forced vibrations of shear deformable functionally graded porous beams, International journal of mechanical sciences, Vol. 108, pp. 14-22, 2016.
[27]        A. Meksi, M. Sekkal, R. B. Bouiadjra, S. Benyoucef, A. Tounsi, Assessing the effect of temperature-dependent properties on the dynamic behavior of FG porous beams rested on variable elastic foundation, Structural Engineering and Mechanics, Vol. 85, No. 6, pp. 717, 2023.
[28]        R. B. Bouiadjra, A. Mahmoudi, M. Sekkal, S. Benyoucef, M. M. Selim, A. Tounsi, M. Hussain, A quasi 3D solution for thermodynamic response of FG sandwich plates lying on variable elastic foundation with arbitrary boundary conditions, Steel and Composite Structures, An International Journal, Vol. 41, No. 6, pp. 873-886, 2021.
[29]        M. Mekerbi, S. Benyoucef, A. Mahmoudi, A. Tounsi, A. A. Bousahla, S. Mahmoud, Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions, Journal of Sandwich Structures & Materials, Vol. 23, No. 3, pp. 1028-1057, 2021.
[30]        Ö. Civalek, Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods, International Journal of Pressure Vessels and Piping, Vol. 82, No. 6, pp. 470-479, 2005.
[31]        E. Sobhani, A. Arbabian, Ö. Civalek, M. Avcar, The free vibration analysis of hybrid porous nanocomposite joined hemispherical–cylindrical–conical shells, Engineering with Computers, pp. 1-28, 2021.
[32]        S. Dastjerdi, B. Akgöz, Ö. Civalek, M. Malikan, V. A. Eremeyev, On the non-linear dynamics of torus-shaped and cylindrical shell structures, International Journal of Engineering Science, Vol. 156, pp. 103371, 2020.
[33]        M. Chitour, S. Benguediab, A. Bouhadra, F. Bourada, M. Benguediab, A. Tounsi, Effect of variable volume fraction distribution and geometrical parameters on the bending behavior of sandwich plates with FG isotropic face sheets, Mechanics Based Design of Structures and Machines, pp. 1-27, 2023.
[34]        A. A. Daikh, A. M. Zenkour, Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory, Materials Research Express, Vol. 6, No. 11, pp. 115707, 2019.
[35]        M. Chitour, A. Bouhadra, M. Benguediab, K. Mansouri, A. Menasria, A. Tounsi, A New High Order Theory for Buckling Temperature Analysis of Functionally Graded Sandwich Plates Resting on Elastic Foundations, Journal of Nano-and Electronic Physics, Vol. 14, No. 3, 2022.
[36]        H.-T. Thai, T.-K. Nguyen, T. P. Vo, J. Lee, Analysis of functionally graded sandwich plates using a new first-order shear deformation theory, European Journal of Mechanics-A/Solids, Vol. 45, pp. 211-225, 2014.
[37]        B. M. N.Himeur, S. Benguediab, A. Bouhadra, A.Menasria, B. Bouchouicha, F. Bourada, M. Benguediab and A. Tounsi, Steel Compost. Struct, Vol. 44, 339-355. , 2022.
[38]        A. Berkia, M. Benguediab, A. Bouhadra, K. Mansouri, A. Tounsi, M. Chitour, Influence of Mechanical and Geometric Characteristics on Thermal Buckling of Functionally Graded Sandwich Plates, Journal of Nano-and Electronic Physics, Vol. 14, No. 3, 2022.
[39]        A. Berkia, S. Benguediab, A. Menasria, A. Bouhadra, F. B. B. Mamen, A. Tounsi, K. H. Benrahou, M. Benguediab, M. Hussain, Static buckling analysis of bi-directional functionally graded sandwich (BFGSW) beams with two different boundary conditions, Steel and Composite Structures, Vol. 44, No. 4, pp. 503, 2022.
[40]        N. El Meiche, A. Tounsi, N. Ziane, I. Mechab, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, International Journal of Mechanical Sciences, Vol. 53, No. 4, pp. 237-247, 2011.
[41]        R. Meksi, S. Benyoucef, A. Mahmoudi, A. Tounsi, E. A. Adda Bedia, S. Mahmoud, An analytical solution for bending, buckling and vibration responses of FGM sandwich plates, Journal of Sandwich Structures & Materials, Vol. 21, No. 2, pp. 727-757, 2019.
Volume 55, Issue 2
April 2024
Pages 184-200
  • Receive Date: 21 January 2024
  • Revise Date: 09 February 2024
  • Accept Date: 09 February 2024