Static Analysis of Simply Supported Functionally Graded Sandwich Plates by Using Four Variable Plate Theory

Year 2019, Volume: 30 Issue: 2, 8987 - 9007, 01.03.2019

Pınar Aydan Demirhan , Vedat Taskın

https://doi.org/10.18400/tekderg.396672

Cited By: 6

Abstract

In this study, the static analysis of a simply
supported square functionally graded sandwich plate is performed. The core of
the sandwich plate is assumed isotropic and the face sheets are functionally
graded. The variations in the effective properties of functionally graded face
sheets along the thickness are obtained by using Mori-Tanaka Micromechanical
Model. Four variable plate theory is used for the displacement fields. The
equation of sandwich plate under sinusoidal load is obtained by using the virtual
displacement principle. Closed form solution is obtained with Navier’s
approach. Parametric values are obtained for the core and face sheet thickness
ratios. The numerical results are compared with the literature and a good
agreement between the obtained results and the other theories in the literature
is seen.

Keywords

Sandwich Plate, Functionally Graded Plate, Navier’s Solution, Bending Stress, Shear Stress

Static Analysis of Simply Supported Functionally Graded Sandwich Plates by Using Four Variable Plate Theory

Abstract

In this study, the static analysis of a simply supported square functionally graded sandwich plate is performed. The core of the sandwich plate is assumed isotropic and the face sheets are functionally graded. The variations in the effective properties of functionally graded face sheets along the thickness are obtained by using Mori-Tanaka Micromechanical Model. Four variable plate theory is used for the displacement fields. The equation of sandwich plate under sinusoidal load is obtained by using the virtual displacement principle. Closed form solution is obtained with Navier’s approach. Parametric values are obtained for the core and face sheet thickness ratios. The numerical results are compared with the literature and a good agreement between the obtained results and the other theories in the literature is seen.

Keywords

Sandwich plate, functionally graded plate, navier’s solution, bending stress, shear stress

References

• [1] Reddy, J.N., Wang, C.M., An overview of the relationships between solutions of the classical and shear deformation plate theories. Composites Science and Technology, 60, 2327-2335, 2000.
• [2] Thai, H.T., Kim, S.E., A review of theories for the modeling and analysis of functionally graded plates and shells. Composite Structures. 128, 70-86, 2015.
• [3] Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses. International Journal of Solids and Structures, 42, 5224-5242, 2005.
• [4] Zenkour, A.M., Alghamdi, N.A., Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads. Mechanics of Advanced Materials and Structures, 17, 419–432, 2010.
• [5] Thai, H.T., Choi, D.H., A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates. Composite Structures, 101, 332-340, 2013.
• [6] Thai, H.T., Nguyen, T.K., Vo, T.P., Lee, J., Analysis of functionally graded sandwich plates using a new first-order shear deformation theory. European Journal of Mechanics A/Solids, 45, 211-225, 2014.
• [7] Kim, J., Reddy, J.N., Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory. Composite Structures, 103, 86-98, 2013.
• [8] Tounsi, A., Houari, M.S.A., Benyoucef, S., Bedia, E.A.A., A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates. Aerospace Science and Technology, 24, 209-220, 2013.
• [9] Reddy, J.N., Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47, 663-684, 2000.
• [10] Mantari, J.L., Oktem, A.S., Soares, C.G., Static and dynamic analysis of laminated composite and sandwich plates and shells by using a new higher-order shear deformation theory. Composite Structures, 94, 37-49, 2011.
• [11] Abdelaziz, H.H., Atmane, H.A., Mechab, I., Boumia, L., Tounsi, A., Abbas, A.B.E., Static analysis of functionally graded sandwich plates using an efficient and simple refined theory. Chinese Journal of Aeronautics, 24, 434-448, 2011.
• [12] Mantari, J.L., Granados, E.V., Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns. Composites: Part B, 69, 317-334, 2014.
• [13] Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T., Kröplin, B., Thermo-mechanical bending of functionally graded plates. Journal of Thermal Stresses, 31, 286-308, 2008.
• [14] Nguyen, V.H., Nguyen, T.K., Thai, H.T., Vo, T.P., A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates. Composites: Part B, 66, 233-246, 2014.
• [15] Li, X.F., Wang, B.L., Han, J.C., A higher-order theory for static and dynamic analyses of functionally graded beams. Archive of Applied Mechanics, 80, 1197-1212, 2010.
• [16] Shimpi, R.P., Refined Plate Theory and Its Variants. AIAA JOURNAL, 40, 137-146, 2002.
• [17] Mechab, I., Atmane, H.A., Tounsi, A., Belhadj, H.A., Bedia, E.A.A., A two variable refined plate theory for the bending analysis of functionally graded plates. Acta Mechanica Sinica, 26, 941-949, 2010.
• [18] Houari, M.S.A., Benyoucef, S., Mechab, I., Tounsi, A., Bedia, E.A.A., Two-variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates. Journal of Thermal Stresses, 34(4), 315-334, 2011.
• [19] Benachour, A., Tahar, H.D., Atmane, H.A., Tounsi, A., Ahmed, M.S., A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient. Composites Part B-Engineering, 42(6), 1386-1394, 2011.
• [20] Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I., Bedia, E.A., Free vibration of functionally graded sandwich plates using four-variable refined plate theory. Applied Mathematics and Mechanics, 32(7), 925-942, 2011.
• [21] Bouiadjra, M.B., Houari, A.M.S., Tounsi, A., Thermal buckling of functionally graded plates according to a four-variable refined plate theory. Journal of Thermal Stresses, 35(8), 677-694, 2012.
• [22] Demirhan, P.A., Taskin, V., Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory. Composite Structures, 177, 80-95, 2017. https://doi.org/10.1016/j.compstruct.2017.06.048.
• [23] Thai, H.T., Choi, D.H., A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation. Composites Part B-Engineering, 43(5), 2335-2347, 2012.
• [24] Thai, H.T., Uy, B., Levy solution for buckling analysis of functionally graded plates based on a refined plate theory. Proceedings of The Institution of Mechanical Engineers Part C-journal of Mechanical Engineering Science, 227(12), 2649-2664, 2013.
• [25] Thai, H.T., Choi, D.H., Improved refined plate theory accounting for effect of thickness stretching in functionally graded plates. Composites: Part B, 56, 705–716, 2014.
• [26] Thai, H.T., Choi, D.H., Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory. KSCE Journal of Civil Engineering 18(6), 1813-1824, 2014.
• [27] Rouzegar, J., Abad, F., Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory. Thin-Walled Structures, 89, 76-83, 2015.
• [28] Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Bedia, E.A.A., A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets. Journal of Sandwich Structures and Materials, 15(6), 671–703, 2013.
• [29] Thai, C.H., Zenkour, A.M., Wahab, M.A., Nguyen-Xuan, H., A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis. Composite Structures, 139, 77–95, 2016.
• [30] Akavci, S.S., Tanrikulu, A.H., Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories. Composites Part B, 83, 203-215, 2015.