Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method
Restricted accessResearch articleFirst published online January, 2022
Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method
In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.
KerrADAlexanderH.An application of the extended Kantorovich method to the stress analysis of clamped rectangular plate. Acta Mech1968; 6: 180–196.
2.
Ramachandra RaoNValsarajanKV.Large deflection analysis of clamped skew sandwich plates by parametric differentiation. Comput Struct1983; 17: 599–602.
3.
HuytonPYorkCB.Buckling of skew plates with continuity or rotational edge restraint. J Aerosp Eng2001; 14: 92–32.
4.
SinghaMKGanapathiM.Large amplitude free flexural vibrations of laminated composite skew plates. Int J Non-Lin Mech2004; 39: 1709–1720.
5.
SundararajanNPrakashTGanapathM.Nonlinear free flexural vibrations of functionally graded rectangular and skew plates under thermal environments. Finite Elem Anal Des2005; 42: 152–168.
6.
DeyPSinghaMK.Dynamic stability analysis of composite skew plates subjected to periodic in-plane load. Thin-Walled Struct2006; 44: 937–942.
7.
GanapathiMPrakashTSundararajanN.Influence of functionally graded material on buckling of skew plates under mechanical loads. J Eng Mech2006; 132: 902–905.
CivalekO.Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods. Appl Math Model2007; 31: 606–624.
10.
SinghaMKDaripaR.Nonlinear vibration of symmetrically laminated composite skew plates by finite element method. Int J Non-Lin Mech2007; 42: 1144–1152.
11.
PrakashTSinghaMKGanapathiM.Thermal post buckling analysis of FGM skew plates. Eng Struct2008; 30: 22–32.
12.
WankhadeRL.Geometric nonlinear analysis of skew plates using finite element method. Int J Adv Eng Technol2011; 2: 154–163.
13.
ChunP-jFuGLimYM.Analytical solutions for skewed thick plates subjected to transverse loading. Struct Eng Mech2011; 38: 549–571.
14.
ChunP-JLimYM.Analytical behavior prediction for skewed thick plates on elastic foundation. Math Prob Eng2011; 2011: Article ID 509724.
15.
JoodakyAKargarnovinMHJafari MehrabadiS, et al. Bending and deflection analysis of thin FGM skew plates using extended Kantorovich method. Am J Scient Res2012; 46: 67–78.
16.
JoodakyAJoodakyIHedayatiM, et al. Deflection and stress analysis of thin FGM skew plates on Winkler foundation with various boundary conditions using extended Kantorovich method. Compos Part B: Eng2013; 51: 191–196.
17.
Gulshan TajMNAChakrabartiA.Buckling analysis of functionaly graded skew plates: an efficient finite element approach. Int J Appl Mech2013; 05: 1350041.
18.
TajGChakrabartiA.Static and dynamic analysis of functionally graded skew plates. J Eng Mech2013; 139: 848–857.
Gulshan TajMNAChakrabartiAPrakashV.Vibration characteristics of functionally graded material skew plate in thermal environment. Int J Mech Mechatron Eng2014; 8: 142–153.
21.
AsemiKSalamiSSalehiM, et al. Dynamic and static analysis of FGM skew plates with 3D elasticity based graded finite element modeling. Latin Am J Solids Struct2014; 11: 504–533.
22.
WangXWangYYuanZ.Accurate vibration analysis of skew plates by the new version of the differential quadrature method. Appl Math Model2014; 38: 926–937.
23.
ManjunathGAAthresh KumarRArvindB, et al. Finite element modelling for stress analysis of a rhombic skew plate structure. Int J Eng Res Technol2014; 3: 2378–2388.
24.
ManjunathGAAthresh KumarRArvindB, et al. Dynamic instability of composite skew plates using boundary characteristic orthogonal polynomials. Int J Appl Mech2014; 06: 1450078.
25.
KumarRKumarAPandaSK.Parametric resonance of composite skew plate under non-uniform in-plane loading. Struct Eng Mech2015; 55: 435–459.
26.
KumarAPandaSKKumarR.Buckling behaviour of laminated composite skew plates with various boundary conditions subjected to linearly varying in-plane edge loading. Int J Mech Sci2015; 100: 136–144.
27.
Garcia-MaciasECastro-TrigueroRSaavedra FloresEI, et al. Static and free vibration analysis of functionally graded carbon nanotube reinforced skew plates. Compos Struct2016; 140: 473–490.
28.
KetabdariMJAllahverdiABoreyriS, et al. Free vibration analysis of homogeneous and FGM skew plates resting on variable Winkler-Pasternak elastic foundation. Mech Ind2016; 17: 107–111.
29.
ParidaSMohantySC.Thermoelastic vibration analysis of functionally graded skew plate using nonlinear finite element method. Struct Eng Mech2017; 40: 1111–1133.
30.
ParidaSMohantySC.Free vibration analysis of functionally graded skew plate in thermal environment using higher order theory. Int J Appl Mech2018; 10: 1850007–1850033.
31.
ParidaSMohantySC.Vibration and stability analysis of functionally graded skew plate using higher order shear deformation theory. Int J Appl Comput Math2018; 4: 122.
32.
Gholami ShahrestaniMAzhariMForoughiH.Elastic and inelastic buckling of square and skew FGM plates with cutout resting on elastic foundation using isoparametric spline finite strip method. Acta Mech2018; 229: 2079–2096.
33.
WangXYuanZ.Buckling analysis of isotropic skew plates under general in-plane loads by the modified differential quadrature method. Appl Math Model2018; 56: 83–95.
34.
KatariyaPVPandaSKMahapatraTR.Bending and vibration analysis of skew sandwich plate. Aircraft Eng Aerosp Technol2018; 90: 885–895.
35.
ChakravertySPradhanKK.Flexural vibration of functionally graded thin skew plates resting on elastic foundations. Int J Dyn Control2018; 6: 97–121.
36.
VinyasMNischithGLojaMAR, et al. Numerical analysis of the vibration response of skew magneto-electro-elastic plates based on the higher-order shear deformation theory. Compos Struct2019; 214: 132–142.
37.
Ahmed HassanAHKurganN.Buckling of thin skew isotropic plate resting on Pasternak elastic foundation using extended Kantorovich method. Heliyon2020; 6: e04236–11.
38.
Ahmed HassanAHKurganN.Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method. Eng Sci Technol2020; 23: 788–800.
39.
MansouriMHShariyatM.Differential quadrature thermal buckling analysis of general quadrilateral orthotropic auxetic FGM plates on elastic foundations. Thin-Walled Struct2017; 112: 194–207.
40.
DucNDKimSEChanDQ.Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT. J Therm Stress2018; 41: 331–365.
41.
DucNDQuanTQ.Nonlinear response of imperfect eccentrically stiffened FGM cylindrical panels on elastic foundation subjected to mechanical loads. Eur J Mech-A/Solids2014; 46: 60–71.
42.
DucNDCongPHAnhVM, et al. Mechanical and thermal stability of eccentrically stiffened functionally graded conical shell panels resting on elastic foundations and in thermal environment. J Compos Struct2015; 132: 597–609.
43.
DucNDTuanNDTranP, et al. Nonlinear dynamic analysis of sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments. Int J Mech Sci2015; 101–102: 338–348.
44.
DucNDNguyenPDKhoaND.Nonlinear dynamic analysis and vibration of eccentrically stiffened S-FGM elliptical cylindrical shells surrounded on elastic foundations in thermal environments. J Thin-walled Struct2017; 117: 178–189.
45.
DucND.Nonlinear thermal dynamic analysis of eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations using the Reddy’s third-order shear deformation shell theory. Eur J Mech-A/Solids2016; 58: 10–30.
46.
DucND.Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation. J Compos Struct2013; 102: 306–314.
DucNDQuanTQ.Nonlinear dynamic analysis of imperfect FGM double curved thin shallow shells with temperature-dependent properties on elastic foundation. J Vib Control2015; 21: 1340–1362.
49.
DucNDKimSEManhDT, et al. Effect of eccentrically oblique stiffeners and temperature on the nonlinear static and dynamic response of S-FGM cylindrical panels. Thin-walled Struct2020; 146: 106438.
50.
PhucPMDucND.The effect of cracks on the stability of the functionally graded plates with variable-thickness using HSDT and phase-field theory. J Compos Part B: Eng2019; 175: 107086.
51.
NguyenPDQuangVDAnhVTT, et al. Nonlinear vibration of carbon nanotube reinforced composite truncated conical shells in thermal environment. Int J Struct Stab Dyn2019; 19: 1950158.
52.
DatNDKhoaNDNguyenPD, et al. An analytical solution for nonlinear dynamic response and vibration of FG-CNT reinforced nanocomposite elliptical cylindrical shells resting on elastic foundations. ZAMM-Zeitsch Angew Math Mech2019. DOI: 10.1002/zamm.201800238.
53.
VuongPMDucND.Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory. Int J Mech Mater Des2019. DOI: 10.1007/s10999-019-09473-x.
54.
KhoaNDThiemHTDucND.Nonlinear buckling and postbuckling of imperfect piezoelectric S-FGM circular cylindrical shells with metal-ceramic-metal layers in thermal environment using Reddy’s third-order shear deformation shell theory. J Mech Adv Mater Struct2019; 26: 248–259.
55.
ChanDQQuanTQKimSE, et al. Nonlinear dynamic response and vibration of shear deformable piezoelectric functionally graded truncated conical panel in thermal environments. Eur J Mech-A/Solids2019; 77: 103795.
56.
UguralAC.1999. Stresses in plates and shells. 2nd ed. New York: McGraw-Hill.
