Bending of Functionally Graded Sandwich Nanoplates Resting on ‎Pasternak Foundation under Different Boundary Conditions

[1] Miyamoto, Y., Kaysser, W., Rabin, B., Kawasaki, A., Ford, R.G., Functionally graded materials: design, processing and applications, Springer Science & Business Media, 1999.

[2] Finot, M., Suresh, S., Bull, C., Sampath, S., Curvature changes during thermal cycling of a compositionally graded Ni/A12O3 multi-layered material, Materials Science and Engineering: A, 205 1996, 59-71.

[3] Zenkour, A.M., A comprehensive analysis of functionally graded sandwich plates: Part 1—Deflection and stresses, International Journal of Solids and Structures, 42, 2005, 5224-5242.

[4] Zenkour, A.M., The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates, International Journal of Applied Mechanics, 1, 2009, 667-707.

[5] Wang, Z.X., Shen, H.S., Nonlinear analysis of sandwich plates with FGM face sheets resting on elastic foundations, Composite Structures, 93, 2011, 2521-2532.

[6] Zenkour, A.M., Alghamdi, N., Thermoelastic bending analysis of functionally graded sandwich plates, Journal of Materials Science, 43, 2008, 2574-2589.

[7] Zenkour, A.M., Alghamdi, N., Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads, Mechanics of Advanced Materials and Structures, 17, 2010, 419-432.

[8] Zenkour, A.M., Alghamdi, N., Thermomechanical bending response of functionally graded nonsymmetric sandwich plates, Journal of Sandwich Structures & Materials, 12, 2010, 7-46.

[9] Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H., Benyoucef, S., Two new refined shear displacement models for functionally graded sandwich plates, Archive of Applied Mechanics, 51, 2011, 1507-1522.

[10] Natarajan, S., Manickam, G., Bending and vibration of functionally graded material sandwich plates using an accurate theory, Finite Elements in Analysis and Design, 57, 2012, 32-42.

[11] Iurlaro, L., Gherlone, M., Di Sciuva, M., Bending and free vibration analysis of functionally graded sandwich plates using the refined zigzag theory, Journal of Sandwich Structures & Materials, 16, 2014, 669-699.

[12] 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, 2014, 211-225.

[13] Mahi, A., El Abbas, A.B., Tounsi, A., A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates, Applied Mathmatical Modelling, 39, 2015, 2489-2508.

[14] Mantari, J., Granados, E., A refined FSDT for the static analysis of functionally graded sandwich plates, Thin-Walled Structures, 90, 2015, 150-158.

[15] Nguyen, T-K., Nguyen, V-H., Chau-Dinh, T., Vo, T. P., Nguyen-Xuan, H., Static and vibration analysis of isotropic and functionally graded sandwich plates using an edge-based MITC3 finite elements, Composites Part B: Engineering, 107, 2016, 162-173.

[16] Mantari, J., Monge, J., Free vibration and bending analysis of functionally graded sandwich plates based on an optimized hyperbolic unified formulation, International Journal of Mechanical Sciences, 119, 2016, 170-186.

[17] Xiang, S., Liu, Y.Q., An nth-order shear deformation theory for static analysis of functionally graded sandwich plates, Journal of Sandwich Structures & Materials, 18, 2016,579-596.

[18] Kashtalyan, M., Menshykova, M., Three-dimensional elasticity solution for sandwich panels with a functionally graded core, Composite Structures, 87, 2009, 36-43.

[19] Woodward, B., Kashtalyan, M., Bending response of sandwich panels with graded core: 3D elasticity analysis, Mechanics of Advanced Materials and Structures, 17, 2010, 586-594.

[20] Abdelaziz, H.H., Atmane, H.A., Mechab, I., Boumia, L., Tounsi, A., Adda Bedia, E.A., Static analysis of functionally graded sandwich plates using an efficient and simple refined theory, Chinese Journal of Aeronautics, 24, 2011, 434-448.

[21] Li, D., Deng, Z., Xiao, H., Zhu, L., Thermomechanical bending analysis of functionally graded sandwich plates with both functionally graded face sheets and functionally graded cores, Mechanics of Advanced Materials and Structures, 25, 2018, 179-191.

[22] Thanh, C-L., Ferreira, A.J.M., Abdel Wahab, M., A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis, Thin–Walled Structures, 145, 2019, 106427

[23] Phung-Van, P., Tran, L.V., Ferreira, A.J.M., Nguyen-Xuan, H., Abdel-Wahab, M., Nonlinear transient isogeometric analysis of smart piezoelectric functionally graded material plates based on generalized shear deformation theory under thermo-electro-mechanical loads, Nonlinear Dynamics, 87, 879–894.

[24] Phung-Van, P., Thai, C-H., Nguyen-Xuan, H., Abdel-Wahab, M., An isogeometric approach of static and free vibration analyses for porous FG nanoplates, European Journal of Mechanics / A Solids, 78, 2019, 103851.

[25] Phung-Van, P., Thai, C-H., Nguyen-Xuan, H., Abdel-Wahab, M., Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis, Composites Part B, 164, 2019, 215-225.

[26] Thai, C-H., Ferreira, A.J.M., Rabczuk, T., Nguyen-Xuan, H., Size-dependent analysis of FG-CNTRC microplates based on modified strain gradient elasticity theory, European Journal of Mechanics / A Solids, 72, 2018, 521-538.

[27] Thanh C-L., Phung-Van, P., Thai, C-H., Nguyen-Xuan, H., Abdel-Wahab, M., Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory, Composite Structures, 184, 2018, 633-649.

[28] Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N., Soares, C.M.M., Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique, Composites Part B: Engineering, 44, 2013, 657-674.

[29] Demirhan, P.A., Taskin, V., Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory, Composite Structures, 177, 2017, 80-95.

[30] Moradi-Dastjerdi, R., Aghadavoudi, F., Static analysis of functionally graded nanocomposite sandwich plates reinforced by defected CNT, Composite Structures, 200, 2018, 839-848.

[31] Li, D., Deng, Z., Xiao, H., Jin, P., Bending analysis of sandwich plates with different face sheet materials and functionally graded soft core, Thin-Walled Structures, 122, 2018, 8-16.

[32] Thai, C-H., Ferreira, A.J.M., Nguyen-Xuan, H., Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory, Composite Structures, 192, 2018, 274-288.

[33] Phung-Van, P., Thanh, C-L., Nguyen-Xuan, H., Abdel-Wahab, M., Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments, Composite Structures, 201, 2018, 882-892.

[34] Thanh, C-L., Tran, L-V., Bui, T.Q., Nguyen, H.X., Abdel-Wahab, M., Isogeometric analysis for size-dependent nonlinear thermal stability of porous FG microplates, Composite Structures, 221, 2019, 110838.

[35] Daikh, A.A., Zenkour, A.M., Effect of porosity on the bending analysis of various functionally graded sandwich plates, Materials Research Express, 6, 2019, 065703.

[36] Cao, Z-Y., Tang, S-G., Cheng, G-H., 3D analysis of functionally graded material plates with complex shapes and various holes, Applied Mathematics and Mechanics: English Edition, 30(1), 2009, 13–18.

[37] Rezaei, R., Shaterzadeh, A.R., Abolghasemi, S., Buckling analysis of rectangular functionally graded plates with an elliptic hole under thermal loads, Journal of Solid Mechanics, 7(1), 2015, 41–57.

[38] Yang, B., Chen, W.Q., Ding, H.J., 3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holes, Acta Mechanica,226, 2015, 1571–1590.

[39] Yang, B., Chen, W.Q., Ding, H.J., Equilibrium of transversely isotropic FGM plates with an elliptical hole: 3D elasticity solutions, Archive of Applied Mechanics,I86, 2016, 1391–1414.

[40] Ansari, R., Faghih Shojaei, M., Shahabodini, A., Bazdid-Vahdati, M., Three-dimensional bending and vibration analysis of functionally graded nanoplates by a novel differential quadrature-based approach, Composite Structures, 131, 2015, 753-764.

[41] Ansari, R., Torabi, J., Norouzzadeh, A., Bending analysis of embedded nanoplates based on the integral formulation of Eringen's nonlocal theory using the finite element method, Physica B: Condensed Matter, 534, 2018, 90–97.

[42] Sobhy, M., A comprehensive study on FGM nanoplates embedded in an elastic medium, Composite Structures, 134, 2015, 966-980.

[43] Salehipour, H., Nahvi, H., Shahidi, A.R., Mirdamadi, H.R., 3D elasticity analytical solution for bending of FG micro/nanoplates resting on elastic foundation using modified couple stress theory, Applied Mathematical Modelling, 47, 2017, 174-188.

[44] Kolahchi, R., Moniri Bidgoli, A.M., Heydari, M.M., Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium, Structural Engineering and Mechanics, 55(5), 2015, 1001-1014.

[45] Arefi, M., Zenkour, A.M., Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates, The European Physical Journal Plus, 132(423), 2017, 1-13.

[46] Lim, C., Zhang, G., Reddy, J.N., A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 2015, 298-313.

[47] Eringen, A.C., On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 1983, 4703-4710.

[48] Ebrahimi, F., Barati, M.R., Dabbagh, A., A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates, International Journal of Engineering Science, 107, 2016, 169-182.

[49] Reddy, J.N., A general non-linear third order theory of plates with moderate thickness, International Journal of Non-linear Mechanics, 25, 1990, 677-686.

[50] Touratier, M., An efficient standard plate theory, International Journal of Engineering Science, 29, 1991, 901-916.

[51] Senthilnathan, N.R., Lim, S.P., Lee, K.H., Chow, S.T., Buckling of shear-deformable plates, AIAA Journal, 25, 1987, 1268-1271.

[52] Thai, H.T., Nguyen, T.K., Vo, T.P., Lee, J., Analysis of functionally graded sandwich platesusing a new first-order shear deformation theory, European Journal of Mechanics-A/Solids, 45, 2014, 211-225.

[53] Zenkour, A. M., A comprehensive analysis of functionally graded sandwich plates: Part 2―Buckling and free vibration, International Journal of Solids and Structures, 42, 2005, 5243-5258.

[54] Daikh, A.A., Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation, Materials Research Express, 6, 2019, 065702.

[55] Nguyen-Xuan, H., Thai, C.H., Nguyen-Thoi, T., Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory, Composites Part B: Engineering, 55, 2013, 558-74.

[56] Nguyen, T.N., Thai, C.H., Nguyen-Xuan, H., On the general framework of high-order shear deformation theories for laminated composite plate structures: A novel unified approach, International Journal of Mechanical Sciences, 110, 2016, 242-255.