Document Type : Research Paper


1 Oil and Natural Gas Directorate, Ministry of Energy and Mineral Resources, Amman, Jordan. Department of Mechanical Engineering, Faculty of Engineering, University of Jordan, Jordan.

2 Department of Mechanical Engineering, Faculty of Engineering, University of Jordan, Jordan.


In this paper, layerwise finite element analysis for the free vibration behavior of two-dimensional functionally graded sandwich plates with different boundary conditions is presented. The plates consist of three layers; a functionally graded layer embedded between ceramic and metal isotropic layers. The layerwise approach is based on the third order shear deformation theory for the middle layer, while the first order shear deformation theory is used to model both the upper and lower isotropic layers. Quadrilateral 8-noded element with 13-degrees of freedom per node is used for this purpose. The present results show very good agreements with the published analytical results of plates consist of a single functionally graded layer. Furthermore, for sandwich plates good agreements were obtained when the present results are compared with similar problems solved by other methods in literature. Parametric studies were investigated for various plate parameters including applied boundary conditions, volume fraction exponents and plate side to thickness ratio.


Main Subjects

  1. Sharma, A., & Sinha, A. K. (2018). Ultrasonic testing for mechanical engineering domain: present and future perspective. International journal of research in industrial engineering7(2), 243-253.
  2. Koizumi, M. F. G. M. (1997). FGM activities in Japan. Composites part B: engineering28(1-2), 1-4.
  3. Satapathy, P. K., Sahoo, B., Panda, L. N., & Das, S. (2018, March). Finite element analysis of functionally graded bone plate at femur bone fracture site. IOP conference series: materials science and engineering(Vol. 330, No. 1, p. 012027). IOP Publishing. DOI: 1088/1757-899X/330/1/012027
  4. Ashwinkumar, A. K. (2017). Review on functionally graded materials and various theories. International research journal of engineering and technology (IRJET), 4(9), 890-893.
  5. Medeiros, M. S., Parente, E., & Melo, A. M. C. D. (2019). Influence of the micromechanics models and volume fraction distribution on the overall behavior of SiC/Al functionally graded pressurized cylinders. Latin American journal of solids and structures16(4).
  6. Thai, H. T., & Choi, D. H. (2013). Finite element formulation of various four unknown shear deformation theories for functionally graded plates. Finite elements in analysis and design75, 50-61.
  7. Jha, D. K., Kant, T., & Singh, R. K. (2013). A critical review of recent research on functionally graded plates. Composite structures96, 833-849.
  8. Zare Jouneghani, F., Dimitri, R., Bacciocchi, M., & Tornabene, F. (2017). Free vibration analysis of functionally graded porous doubly-curved shells based on the first-order shear deformation theory. Applied sciences7(12), 1252.
  9. Hosseini-Hashemi, S., Taher, H. R. D., Akhavan, H., & Omidi, M. (2010). Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Applied mathematical modelling34(5), 1276-1291.
  10. Van Long, N., Quoc, T. H., & Tu, T. M. (2016). Bending and free vibration analysis of functionally graded plates using new eight-unknown shear deformation theory by finite-element method. International journal of advanced structural engineering8(4), 391-399.
  11. Natarajan, S., & Manickam, G. (2012). Bending and vibration of functionally graded material sandwich plates using an accurate theory. Finite elements in analysis and design57, 32-42.
  12. Karamanli, A., & Aydogdu, M. (2021). Vibration behaviors of two-directional carbon nanotube reinforced functionally graded composite plates. Composite structures262, 113639.
  13. Abrate, S. (2008). Functionally graded plates behave like homogeneous plates. Composites part B: engineering39(1), 151-158.
  14. Liu, B., Ferreira, A. J. M., Xing, Y. F., & Neves, A. M. A. (2016). Analysis of functionally graded sandwich and laminated shells using a layerwise theory and a differential quadrature finite element method. Composite structures136, 546-553.
  15. Moleiro, F., Correia, V. F., Araújo, A. L., Soares, C. M., Ferreira, A. J. M., & Reddy, J. N. (2019). Deformations and stresses of multilayered plates with embedded functionally graded material layers using a layerwise mixed model. Composites part B: engineering156, 274-291.
  16. Belarbi, M. O., Tati, A., & Khechai, A. (2015). Efficient layerwise finite element model for multilayer sandwich plates analysis. In Design and modeling of mechanical systems-II(pp. 305-314). Springer, Cham.
  17. Belarbi, M. O., Tati, A., Ounis, H., & Khechai, A. (2017). On the free vibration analysis of laminated composite and sandwich plates: a layerwise finite element formulation. Latin American journal of solids and structures14, 2265-2290.
  18. Belarbi, M. O., Zenkour, A. M., Tati, A., Salami, S. J., Khechai, A., & Houari, M. S. A. (2021). An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates. International journal for numerical methods in engineering122(9), 2360-2387.
  19. Hirane, H., Belarbi, M. O., Houari, M. S. A., & Tounsi, A. (2021). On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Engineering with computers, 1-29.
  20. Burlayenko, V. N., & Sadowski, T. (2020). Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements. Meccanica55(4), 815-832.
  21. Uysal, M. U. (2013). Investigation of thermal and mechanical loading on functional graded material plates. International journal of aerospace and mechanical engineering7(11), 2283-2289.
  22. Tabatabaei, S. S., & Fattahi, A. M. (2016). Finite element method for modal analysis of FGM. International journal of mechanical and mechatronics engineering10(2), 352-356.
  23. Benslimane, A., Bouzidi, S., & Methia, M. (2018). Displacements and stresses in pressurized thick-walled FGM cylinders: Exact and numerical solutions. International journal of pressure vessels and piping168, 219-224.
  24. Asgari, M., & Akhlaghi, M. (2011). Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations. European journal of mechanics-a/solids30(2), 72-81.
  25. Zafarmand, H., Salehi, M., & Asemi, K. (2015). Three-dimensional free vibration and transient analysis of two directional functionally graded thick cylindrical panels under impact loading. Latin American journal of solids and structures12, 205-225.
  26. Van Do, T., Nguyen, D. K., Duc, N. D., Doan, D. H., & Bui, T. Q. (2017). Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory. Thin-Walled structures119, 687-699.
  27. Al-Hawamdeh, O., Abu-Alshaikh, I., & Al-Huniti, N. (2017). Finite element coding of functionally graded beams under various boundary and loading conditions. Journal of applied research on industrial engineering4(4), 279-290.
  28. Karamanlı, A. (2017). Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory. Composite structures174, 70-86.
  29. Mazahreh, L. O., & Abu-Alshaikh, I. M. (2021). Layerwise finite element approach for the bending analysis of bi-directional functionally graded layered plates. Journal of applied research on industrial engineering8(2), 176-194.
  30. Asemi, K., Salehi, M., & Akhlaghi, M. (2013). Three-dimensional static analysis of two dimensional functionally graded plates. IJMECH2(2), 21-32.
  31. Thai, H. T., & Kim, S. E. (2013). A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Composite structures96, 165-173.
  32. Li, Q., Iu, V. P., & Kou, K. P. (2008). Three-dimensional vibration analysis of functionally graded material sandwich plates. Journal of sound and vibration311(1-2), 498-515.
  33. Pandey, S., & Pradyumna, S. (2018). Analysis of functionally graded sandwich plates using a higher-order layerwise theory. Composites part B: engineering153, 325-336.