Size-Dependent Buckling Analysis of Three-Layered Nano-plate on Orthotropic Foundation Using Surface Theory

Subject Areas : Mechanics of Solids

Amir Hossein Soltan Arani ¹ (Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran)
A Ghorbanpour Arani ² (Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran--- Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran)
Z Khoddami Maraghi ³ (Faculty of Engineering, Mahallat Institute of Higher Education, Mahallat, Iran)

Received: 2023-09-11 Accepted : 2024-06-24 Published : 2024-08-15

Keywords: Bi-axial buckling load, Neutral surface, Nonlocal strain gradient theory, Stretching effect, Surface effects,

Abstract :

In this paper, a refined plate theory including the stretching effect is extended for analysis of functionally graded nano-plate integrated with piezoelectric face-sheets resting on orthotropic foundation. According to this theory, the size-dependent buckling behavior of a simply supported rectangular nano-plate is studied using surface piezoelasticity theory in the framework of the nonlocal strain gradient theory. The properties of functionally graded nano-plate are assumed to be varied in the thickness direction based on a simple power-law distribution in terms of volume fraction. The governing equations are derived by employing the principle of minimum potential energy based on the neutral surface concept. Navier-type solution is used to obtain the analytical results of nano-plate subjected to an electric field. In order to check the accuracy and efficiency of the current model, a validation study is carried out based on the obtained results and available results in the previous literature. Numerical results show that the residual surface stress and neutral surface position have an undeniable influence on the critical buckling load of the nano-plate. It is expected that the results of current study to be utilized in designing micro/nano-electro-mechanical systems components based on smart nanostructures.

References:

[1] Feri M., Krommer M., Alibeigloo A., 2021, Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers, Mechanics Based Design of Structures and Machines 51(7): 3843-3867.
[2] Marzavan S., Nastasescu V., 2023, Free vibration analysis of a functionally graded plate by finite element method, Ain Shams Engineering Journal 14(8): 102024.
[3] Frahlia H., Bennai R., Nebab M., Ait Atmane H., Tounsi A., 2022, Assessing effects of parameters of viscoelastic foundation on the dynamic response of functionally graded plates using a novel HSDT theory, Mechanics of Advanced Materials and Structures 30(13): 2765-2779.
[4] Zargar Ershadi M., Faraji Oskouie M., Ansari R., 2022, Nonlinear vibration analysis of functionally graded porous circular plates under hygro-thermal loading, Mechanics Based Design of Structures and Machines 52(2): 1042-1059.
[5] Xie K., Chen H., Wang Y., Li L., Jin F., 2024, Nonlinear dynamic analysis of a geometrically imperfect sandwich beam with functionally graded material facets and auxetic honeycomb core in thermal environment, Aerospace Science and Technology 144: 108794.
[6] Arefi M., Soltan Arani A.H., 2018, Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments, Mechanics Based Design of Structures and Machines 46(6): 669-692.
[7] Ghorbanpour Arani A., Kolahdouzan F., Abdollahian M., 2018, Nonlocal buckling of embedded magnetoelectroelastic sandwich nanoplate using refined zigzag theory, Applied Mathematics and Mechanics 39(4): 529-546
[8] Singh A.K., Koley S, Negi A., 2022. Remarks on the scattering phenomena of love-type wave propagation in a layered porous piezoelectric structure containing surface irregularity, Mechanics of Advanced Materials and Structures 30(12): 2398-2429.
[9] Dhua S., Mondal S., Maji A., 2024, Surface effects on wave propagation in piezoelectric–piezomagnetic loosely bonded bilayer system using nonlocal theory of elasticity, thin wall structure 197: 111612.
[10] Biswas M., Sahu S.A., 2022, Surface wave dispersion in imperfectly bonded flexoelectric-piezoelectric/FGPM bi-composite in contact of Newtonian liquid, Mechanics of Advanced Materials and Structures 30(14): 2995-3012.
[11] Mirzaei M., 2022, Vibration characteristics of sandwich plates with GPLRC core and piezoelectric face sheets with various electrical and mechanical boundary conditions, Mechanics Based Design of Structures and Machines 52(2): 990-1013.
[12] Hai T., Al-Masoudy M.M., Alsulamy S., El Ouni M.H., Ayvazyan A., Kumar A., 2023, Size-dependent free vibration analysis of honeycomb sandwich microplates integrated with piezoelectric actuators based on the modified strain gradient theory, Composite Structures 305: p.116555.
[13] Ghorbanpour Arani A., Jamali M., Mosayyebi M., Kolahchi R., 2016, Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory, Composites Part B: Engineering 95: 209-224.
[14] Cao T.N.T., Reddy J.N., Lieu Q.X., Nguyen X.V., Luong V.H., 2021, A multi-layer moving plate method for dynamic analysis of viscoelastically connected double-plate systems subjected to moving loads, advanced structural engineering 24(9): 1798-1813.
[15] Ragb O., Matbulyb M.S., 2021, Nonlinear vibration analysis of elastically supported multi-layer composite plates using efficient quadrature techniques, International Journal for Computational Methods in Engineering Science and Mechanics 23(2): 129-146.
[16] Taghizadeh S.A., Naghdinasab M., Madadi H., Farrokhabadi A., 2021, Investigation of novel multi-layer sandwich panels under quasi-static indentation loading using experimental and numerical analyses, Thin wall structure 160: 107326.
[17] Amoozgar M., Fazelzadeh S.A., Ghavanloo E., Ajaj R.M., 2022, Free vibration analysis of curved lattice sandwich beams, Mechanics of Advanced Materials and Structures 31(2): 343-355
[18] Sahoo B., Sharma N., Sahoo B., Ramteke P.M., Panda S.K., Mahmoud S.R., 2022, Nonlinear vibration analysis of FGM sandwich structure under thermal loadings, Structures 44: 1392-1402.
[19] Derikvand M., Farhatnia F., Hodges H., 2021, Functionally graded thick sandwich beams with porous core: buckling analysis via differential transform method, Mechanics Based Design of Structures and Machines 51(7): 3650-3677.
[20] Li F., Yuan W., Zhang C., 2021, Free vibration and sound insulation of functionally graded honeycomb sandwich plates, Journal of Sandwich Structures and Materials 24(1): 565-600.
[21] Ghorbanpour Arani A., Shahraki M.E., Haghparast E., 2022, Instability analysis of axially moving sandwich plates with a magnetorheological elastomer core and GNP-reinforced face sheets, journal of brazilian society of mechanical sciences and engineering 44(4):150
[22] Li J., Kardomateas G., Liu L., 2023, Vibration analysis of thick-section sandwich structures in thermal environments, international journal of mechanical sciences 241: 107937.
[23] Liu S., Wang K., Wang B., 2023, Buckling and vibration characteristic of anisotropic sandwich plates with negative Poisson’s ratio based on isogeometric analysis, Mechanics Based Design of Structures and Machines 9:1-16.
[24] Ren H., Zhuang X., Oterkus E., Zhu H., Rabczuk T., 2021, Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method, Engineering Computations 39: 23–44.
[25] Pham Q.H., Nguyen P.C., Tran T.T., 2022, Dynamic response of porous functionally graded sandwich nanoplates using nonlocal higher-order isogeometric analysis, Composite Structure 290: 115565,
[26] Nguyen N.V., Phan D.H., 2023, A refined quasi-3D isogeometric model for dynamic instability of graphene nanoplatelets-reinforced porous sandwich plates, aerospace science and technology 142: 108595.
[27] Hung P.T., Phung-Van P., Thai C.H., 2023, Small scale thermal analysis of piezoelectric–piezomagnetic FG microplates using modified strain gradient theory, International Journal of Mechanics and Materials in Design 19(4): 739-761.
[28] Jin Q., 2021, Interlaminar stress analysis of functionally graded graphene reinforced composite laminated plates based on a refined plate theory, Mechanics of Advanced Materials and Structures 29(25): 4138-4150.
[29] Tharwan M.Y., Daikh A.A., Assie A.E., Alnujaie A., Eltaher M.A., 2023, Refined quasi-3D shear deformation theory for buckling analysis of functionally graded curved nanobeam rested on Winkler/Pasternak/Kerr foundation, Mechanics Based Design of Structures and Machines 1-24.
[30] Hai Van N.T., Hong N.T., 2023, Novel finite element modeling for free vibration and buckling analysis of non-uniform thickness 2D-FG sandwich porous plates using refined Quasi 3D theory, Mechanics Based Design of Structures and Machines 1-27.
[31] Shahmohammadi M.A., Azhari M., Salehipour H., Thai H.T., 2023, Buckling of multilayered CNT/GPL/fibre/polymer hybrid composite plates resting on elastic support using modified nonlocal first-order plate theory, Mechanics Based Design of Structures and Machines 52(3): 1785-1810.
[32] Ghandourah E.E., Daikh A.A., Alhawsawi A.M, Fallatah O.A., EltaherM.A., 2022, Bending and buckling of FG-GRNC laminated plates via quasi-3D nonlocal strain gradient theory, Mathematics 10(8): 1321
[33] Hung D.X., Van Long N., Tu T.M., Trung D.X., 2024, Bending analysis of FGSP nanoplate resting on elastic foundation by using nonlocal quasi-3D theory, Thin Wall Structure 196: 111510.
[34] Daikh A.A., Belarbi M.O., Khechai A., Li L., Ahmed H.M., Eltaher M.A., 2023, Buckling of bi-coated functionally graded porous nanoplates via a nonlocal strain gradient quasi-3D theory, Acta Mechanica 234(8): 3397-3420.
[35] Shahzad M.A., Sahmani S., Safaei B., Basingab M.S., Hameed A.Z., 2023, Nonlocal strain gradient-based meshless collocation model for nonlinear dynamics of time-dependent actuated beam-type energy harvesters at nanoscale, Mechanics Based Design of Structures and Machines 1-35.
[36] Soleimani A., Zamani F., Haghshenas Gorgani H., 2022, Buckling analysis of three-dimensional functionally graded Euler-Bernoulli nanobeams based on the nonlocal strain gradient theory, Journal of Applied and Computational Mechanics 53(1): 24-40.
[37] Li L., Hu Y., Ling L., 2015, Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory, Composite Structure 133: 1079-1092.‏
[38] Jalaei M.H., Civalek Ö.M.E.R., 2019, A nonlocal strain gradient refined plate theory for dynamic instability of embedded graphene sheet including thermal effects, Composite Structure 220: 209-220.‏
[39] Ebrahimi F., Dabbagh A., 2017, On flexural wave propagation responses of smart FG magneto-electro-elastic nanoplates via nonlocal strain gradient theory, Composite Structure 162: 281-293.‏
[40] Ma L.H., Ke L., Reddy J.N., Yang J., Kitipornchai S., Wang Y.S., 2018, Wave propagation characteristics in magneto-electro-elastic nanoshells using nonlocal strain gradient theory, Composite Structure 199: 10-23.‏
[41] Sahmani S., Aghdam M.M., Rabczuk T., 2018, Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory, Composite Structure 186: 68-78.‏
[42] Jamali M., Shojaee T., Mohammadi B., 2020, Analytical buckling and post-buckling characteristics of Mindlin micro composite plate with central opening by use of nonlocal elasticity theory, Journal of Applied and Computational Mechanics 51(1): 231-238.
[43] Barati M.R., Shahverdi H., 2017, An analytical solution for thermal vibration of compositionally graded nanoplates with arbitrary boundary conditions based on physical neutral surface position, Mechanics of Advanced Materials and Structures 24(10): 840-853.‏
[44] Bellifa H., Benrahou K.H., Hadji L., Houari M.S.A., Tounsi A., 2016, Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position, Journal of the Brazilian Society of Mechanical Sciences and Engineering 38(1): 265-275.‏
[45] Farzam-Rad S.A., Hassani B., Karamodin A., 2017, Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface, Composites Part B: Engineering 108: 174-189.‏
[46] Barati A., Norouzi S., 2020, Nonlocal elasticity theory for static torsion of the bi-directional functionally graded microtube under magnetic field, Journal of Applied and Computational Mechanics 51(1): 30-36.
[47] Ghorbanpour-Arani A.A., Khoddami Maraghi Z., Ghorbanpour Arani A., 2023, The Frequency Response of Intelligent Composite Sandwich Plate Under Biaxial In-Plane Forces, Journal of Solid Mechanic 15(1): 1-18.
[48] Mahmoudi A., Benyoucef S., Tounsi A., Benachour A., Adda Bedia E.A., Mahmoud, S.R., 2019, A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations, Journal of Sandwich Structures and Materials 21(6): 1906-1929.‏
[49] Meziane M.A.A., Abdelaziz H.H., Tounsi A., 2014, An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions, Journal of Sandwich Structures and Materials 16(3): 293-318.‏
[50] El Meiche N., Tounsi A., Ziane N., Mechab I., 2011, A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate, International Journal of Mechanical Sciences 53(4): 237-247.‏
[51] Ghorbanpour Arani A., Zarei H.B.A., Haghparast E., 2018, Vibration response of viscoelastic sandwich plate with magnetorheological fluid core and functionally graded-piezoelectric nanocomposite face sheets, Journal of Vibration and Control 24(21): 5169-5185.
[52] Ghorbanpour Arani A., Haghparast E., Zarei H.B.A., 2016, Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field, Physica B: Condensed Matter 495: 35-49.‏
[53] Alipour M.M., Shariyat M., 2011, A power series solution for free vibration of variable thickness Mindlin circular plates with two-directional material heterogeneity and elastic foundations, Journal of Solid Mechanics 3(2): 183-197.‏
[54] Najafizadeh M.M., Raki M., Yousefi P., 2018, Vibration analysis of FG nanoplate based on third-order shear deformation theory (TSDT) and nonlocal elasticity, Journal of Solid Mechanics 10(3):464-475.‏
[55] Molla-Alipour M., Shariyat M., Shaban M., 2020, Free vibration analysis of bidirectional functionally graded conical/cylindrical shells and annular plates on nonlinear elastic foundations, based on a unified differential transform analytical formulation, Journal of Solid Mechanics 12(2): 385-400.‏
[56] Ghorbanpour Arani A., Haghparast E., Zarei, H.B.A., 2016, Vibration of axially moving 3-phase CNTFPC plate resting on orthotropic foundation, Structural Engineering and Mechanics 57(1): 105-126.‏
[57] Thai H.T., Vo T.P., 2013. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Applied mathematical modelling 37(5): 3269-3281.
[58] Shufrin I., Eisenberger M., 2005, Stability and vibration of shear deformable plates––first order and higher order analyses. International Journal of Solids and Structures 42(3-4): 1225-1251.
[59] Haghparast E., Ghorbanpour-Arani A., Ghorbanpour Arani A., 2020. Effect of fluid–structure interaction on vibration of moving sandwich plate with Balsa wood core and nanocomposite face sheets. International Journal of Applied Mechanics 12(07): 2050078.