In the present work, effect of hygrothermal environment on vibration and buckling behavior of embedded functionally graded elliptical plate under uniform in plane compression is studied. The properties of elliptical plate vary in transverse direction following power law. The functionally graded elliptical plate is considered to be resting on the Winkler–Pasternak elastic foundation. The governing equations are derived using the principle of virtual work and solved by employing the Rayleigh–Ritz method. The algebraic polynomials are employed to satisfy the different boundary constraints. The advantage of the presented mathematical model over the previously reported methods is that it eliminates the constraints regarding edge conditions, and it is simple and computationally fast. The inclusive results depicting the effect of various parameters namely, material property exponents, foundation parameters, aspect ratio on mechanical and thermomechanical buckling, and natural frequency of embedded functionally graded elliptical plate in a hygrothermal environment are reported after the test of convergence and extensive comparisons. The study shows that increase in foundation moduli lead to an increase in natural frequency and buckling parameter. Furthermore, it is noticed that the temperature and moisture concentration remarkably affect the buckling and vibration behavior of functionally graded elliptical plate.
BeverMBDuwezPE.Gradients in composite materials. Mater Sci Eng1972;
10: 1–8.
2.
WinklerE.Theory of elasticity and strength. Prague, Czechoslovakia: Dominicus, 1867.
3.
HetenyiM.A general solution for the bending of beams on an elastic foundation of arbitrary continuity. J Appl Phys1950;
2: 55–58.
4.
ReissnerE.A note on deflections of plates on a viscoelastic foundation. J Appl Mech ASME1958;
25: 144–145.
5.
Filonenko-BorodichMM. Some approximate theories of elastic foundation. Uchenyie Zapiski Moskovkogo Gosudarstuennogo Universiteta Mekhanika, Moscow, 1940, pp. 3–18.
6.
PasternakPL. Fundamentals of a new method of analyzing structures on an elastic foundation by means of two foundation moduli. Gosudarstvennoe Izdatelstro Liberaturi po Stroitelstvui Arkhitekture, Moscow, 1954.
7.
PradhanSCKumarA.Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method. Compos Mater Sci2010;
50: 239–245.
8.
BouderbaBHouariMSATounsiA.Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations. Steel Compos Struct2013;
14: 85–104.
9.
SoltaniHMKharaziM. Investigation of the incremental and deformation theories of plasticity on the elastoplastic postbuckling of plates. Proc IMechE, Part L: J Materials: Design and Applications2020. DOI: 1464420720922866.
10.
NedriKEL MeicheNTounsiA.Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory. Mech Compos Mater2014;
49: 629–640.
11.
AnjomshoaA.Application of Ritz functions in buckling analysis of embedded orthotropic circular and elliptical micro/nano-plates based on nonlocal elasticity theory. Meccanica2013;
48: 1337–1353.
12.
MeksiABenyoucefSHouariMSA, et al.
A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations. Struct Eng Mech2015;
53: 1215–1240.
13.
SinghPPAzamMSRanjanV.Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions. Proc IMechE, Part C: J Mechanical Engineering Science2019;
233: 2636–2662.
14.
ShariyatMAlipourMM.Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations. Arch Appl Mech2011;
81: 1289–1306.
15.
KumarSMitraARoyH.Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity. Proc IMechE, Part L: J Materials: Design and Applications2018;
232: 371–387.
16.
SahooSSPandaSKSinghV. K.Experimental and numerical investigation of static and free vibration responses of woven glass/epoxy laminated composite plate. P IMechE, Part L: J Materials: Design and Applications2017;
231: 463–478.
17.
MirtalaieSHHajabasiMA.Free vibration analysis of functionally graded thin annular sector plates using the differential quadrature method. Proc IMechE, Part C: J Mechanical Engineering Science2011;
225: 568–583.
18.
ÇeribaşıS.Static and dynamic analyses of thin uniformly loaded super elliptical FGM plates. Mech Adv Mater Struc2012;
19: 323–335.
19.
NaeiMHMasoumiAShamekhiA.Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method. Proc IMechE, Part C: J Mechanical Engineering Science2007;
221: 1241–1247.
20.
BellifaHBenrahouKHHadjiL, et al.
Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. J Braz Soc Mech Sci2016;
38: 265–275.
21.
HasratiEAnsariRRouhiH. Anumerical approach to the elastic/plastic axisymmetric buckling analysis of circular and annular plates resting on elastic foundation. Proc IMechE, Part C: J Mechanical Engineering Science2019;
233: 7041–7061.
22.
ZhongHLiX andHeY.Static flexural analysis of elliptic Reissner–Mindlin plates on a Pasternak foundation by the triangular differential quadrature method. Arch Appl Mech2005;
74: 679–691.
23.
KamranfardMRSaidiARNaderiA.Analytical solution for vibration and buckling of annular sectorial porous plates under in-plane uniform compressive loading. Proc IMechE, Part C: J Mechanical Engineering Science2018;
232: 2211–2228.
24.
BennounMHouariMSATounsi A.Anovel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates. Mech Adv Mater Struct2016;
23: 423–431.
25.
WangCMWangLLiewKM, et al.
Vibration and buckling of super elliptical plates. J Sound Vib1994;
171: 301–314.
26.
YangBMeiJChenD, et al.
3D thermo-mechanical solution of transversely isotropic and functionally graded graphene reinforced elliptical plates. Compos Struct2018;
184: 1040–1048.
27.
MirzaeiM.Thermal buckling of temperature-dependent composite super elliptical plates reinforced with carbon nanotubes. J Therm Stresses2018;
41: 920–935.
28.
SainiRSainiSLalR, et al.
Buckling and vibrations of FGM circular plates in thermal environment. Procedia Struct Integr2019;
14: 362–374.
29.
ArshidEKianiAAmirS.Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface. Proc IMechE, Part L: J Materials: Design and Applications2019;
233: 2140–2159.
30.
BouderbaBHouariMSATounsiA, et al.
Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Struct Eng Mech2016;
58: 397–422.
31.
ManoachEWarminskaAWarminskiJ, et al.
A reduced multimodal thermoelastic model of a circular Mindlin plate. Int J Mech Sci2019,
153: 479–489.
32.
AmirS.Orthotropic patterns of visco-Pasternak foundation in nonlocal vibration of orthotropic graphene sheet under thermo-magnetic fields based on new first-order shear deformation theory. Proc IMechE, Part L: J Materials: Design and Applications2019;
233: 197–208.
33.
ChikhA, et al.
Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Struct Syst2017;
19: 289–297.
34.
WarminskaAManoachEWarminskiJ.A reduced model of a thermo-elastic nonlinear circular plate. In: MATEC web of conferences EDP sciences, 2018.
35.
TebbouneWBenrahouKHHouariMSA, et al.
Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory. Steel Compos Struct2015;
18: 443–465.
36.
NatarajanSDeogekarPSManickamG, et al.
Hygrothermal effects on the free vibration and buckling of laminated composites with cutouts. Compos Struct2014;
108: 848–855.
37.
ChakravertySPradhanKK.Free vibration of functionally graded thin rectangular plates resting on Winkler elastic foundation with general boundary conditions using Rayleigh–Ritz method. Int J Appl Mech2014;
6: 1450043.
38.
YaghoobiHTorabiM.Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions. J Therm Stresses2013;
36: 869–894.
39.
MeyersCAHyerMW.Thermal buckling and postbuckling of symmetrically laminated composite plates. J Therm Stresses1991;
14: 519–540.
40.
TranLVPhung-VanPLeeJ, et al. Isogeometric approach for nonlinear bending and post-buckling analysis of functionally graded plates under thermal environment. arXiv preprint arXiv 2015; 1511.01380.
41.
LeissaAW.Vibration of a simply-supported elliptical plate. J Sound Vib1967;
6: 145–148.
CheungYKThamLGLiWY.Free vibration and static analysis of general plate by spline finite strip. Comput Mech1988;
3: 187–197.
44.
SinghBChakravertyS.Transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables. J Sound Vib1992;
152: 149–155.
45.
SinghBChakravertyS.Use of characteristic orthogonal polynomials in two dimensions for transverse vibration of elliptic and circular plates with variable thickness. J Sound Vib1997;
173: 289–299.
46.
ChakravertySJindalRAgarwalVK.Effect of non–homogeneity on natural frequencies of vibration of plates. Meccanica2007;
42: 585–599.
47.
MazumdarJ.Transverse vibration of elastic plates by the method of constant deflection lines. J. Sound Vib1971;
18: 147–155.
48.
PradhanKKChakravertyS.Free vibration of functionally graded thin elliptic plates with various edge supports. Struct Eng Mech2015;
53: 337–354.
49.
NajafizadehMMHeydariHR.Higher-order theory for buckling of functionally graded circular plates. AIAA J2007;
45: 1153–1160.
50.
GhiasianSEKianiYSadighiM, et al.
Thermal buckling of shear deformable temperature dependent circular/annular FGM plates. Int J Mech Sci2014;
81: 137–148.
