Journal of Applied and Computational Mechanics
Bending of Functionally Graded Sandwich Nanoplates Resting on Pasternak Foundation under Different Boundary Conditions
Document Type : Research Paper
Authors
1 Laboratoire d'Etude des Structures et de Mécanique des Matériaux, Department of Civil Engineering, Mascara, Algeria
2 Mechanics of Structures and Solids Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Algeria
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
4 Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt
Abstract
This article proposes a refined higher order nonlocal strain gradient theory for stresses and deflections of new model of functionally graded (FG) sandwich nanoplates resting on Pasternak elastic foundation. Material properties of the FG layers are supposed to vary continuously through-the-thickness according to a power function or a sigmoid function in terms of the volume fractions of the constituents. The face layers are made of FG material while the core layer is homogeneous and made of ceramic. In this study, an analytical approach is proposed using the higher-order shear deformation plate theory and nonlocal strain gradient theory with combination of various boundary conditions. Numerical outcomes are reported to display the impact of the material distribution, boundary conditions, elastic foundation parameters and the sandwich nanoplate geometry on the deflections and stresses of FG sandwich nanoplates. The exactness of this theory is determined by comparing it to other published outcomes.
Keywords
Main Subjects
[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.
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