Journal of Applied and Computational Mechanics
A New Quasi-3D Model for Functionally Graded Plates
Document Type : Research Paper
Authors
Department of Civil Engineering, SRES’s Sanjivani College of Engineering, Savitribai Phule Pune University, Kopargaon-423601, Maharashtra, India
Abstract
This article investigates the static behavior of functionally graded plate under mechanical loads by using a new quasi 3D model. The theory is designated as fifth-order shear and normal deformation theory (FOSNDT). Properties of functionally graded material are graded across the transverse direction by using the rule of mixture i.e. power-law. The effect of thickness stretching is considered to develop the present theory. In this theory, axial and transverse displacement components respectively involve fifth-order and fourth-order shape functions to evaluate shear and normal strains. The theory involves nine unknowns. Zero transverse shear stress conditions are satisfied by employing constitutive relations. Analytical solutions are obtained by implementing the double Fourier series technique. The results predicted by the FOSNDT are compared with existing results. It is pointed out that the present theory is helpful for accurate structural analysis of isotropic and functionally graded plates compared to other plate models.
Keywords
Main Subjects
[1] Jha, D. K., Kant, T., Singh, R. K., A critical review of recent research on functionally graded plates, Composite Structures, 96, 2013, 833-849.
[2] Swaminathan, K., Naveenkumar, D. T., Zenkour, A. M., Carrera, E., Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review, Composite Structures, 120, 2015, 10-31.
[3] Swaminathan, K., Sangeetha, D. M., Thermal analysis of FGM plates-A critical review of various modeling technique and solution methods, Composite Structures, 160, 2017, 43-60.
[4] Sayyad, A. S., Ghugal, Y. M., On the free vibration analysis of laminated composite and sandwich beams: A review of recent literature with some numerical results, Composite Structures, 129, 2015, 177–201.
[5] Sayyad, A. S., Ghugal, Y. M., Bending, buckling and free vibration of laminated composite and sandwich plates: A critical review of literature, Composite Structures, 171, (2017a), 486–504.
[6] Reddy, J. N., Analysis of functionally graded plates, International Journal of Numerical Methods in Engineering, 47, 2000, 663-684.
[7] Reddy, J. N., Cheng, Z. Q., Frequency of functionally graded plates with three-dimensional asymptotic approach, ASCE Journal of Engineering Mechanics, 129, 2003, 896-900.
[8] Zenkour, A. M., Generalized shear deformation theory for bending analysis of functionally graded plates, Applied Mathematical Modelling, 30, 2006, 67-84.
[9] Zhong, Z., Shang, E., Closed-form solutions of three-dimensional functionally graded plates, Mechanics of Advanced Materials and Structures, 15, 2008, 353-363.
[10] Lu, C. F., Lim, W., Chen, W. Q., Exact solutions for free vibrations of functionally graded thick plates on elastic foundations, Mechanics of Advanced Materials and Structures, 16, 2009, 576-584.
[11] Ameur, M., Tounsi, A., Mechab, I., Bedia, E. A. A., A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations, KSCE Journal of Civil Engineering, 15, 2011, 1405-1414.
[12] Jha, D. K., Kant, T., Singh, R. K., Stress analysis of transversely loaded functionally graded plates with a higher order shear and normal deformation theory, ASCE Journal of Engineering Mechanics, 139, 2013, 1663-1680.
[13] Neves, A. M. A., Ferreira, A. J. M., Carrera, E. M., Cinfera, M., Jorge, R., Static, free vibration and buckling analysis of functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique, Composite Structures,44, 2013, 657-674.
[14] Thai, H. T., Choi, D. H., Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory, KSCE Journal of Civil Engineering, 8(6), 2014, 1813-1824.
[15] Najafizadeh, M. M., Mohammadi, J., Khazaeinejad, P., Vibration characteristics of functionally graded plates with non-ideal boundary conditions, Mechanics ofAdvanced Materials and Structures, 19, 2012, 543-550.
[16] Neves, A. M. A., Ferreira, A. J. M., Carrera, E., Cinefra, A., Roque, C. M. C., Jorge, R. M. N., Soares, C. M. M., A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates. Composite Structures, 94, 2012, 1814-1825.
[17] Thai, H. T., Thuc, P. V., A new sinusoidal shear deformation theory for bending, buckling and vibration of functionally graded plates, Applied Mathematical Modelling, 37, 2013, 3269-3281.
[18] Thai, H. T., Kim, S. E., A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates, Composite Structures, 96, 2013, 165-17.
[19] Mechab, I., Mechab, B., Benaissa, S., Static and dynamic analysis of functionally graded plates using four-variable refined plate theory by the new function, Composites Part-B 45,2013,748-757.
[20] Thai, H. T., Choi, D. H., Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory, KSCE Journal of Civil Engineering, 8(6), 2014, 1813-1824.
[21] Reddy, K. S. K., Kant, T., Three-dimensional elasticity solution for free vibrations of exponentially graded plates, Journal of Engineering Mechanics, 140, 2014, 1-9.
[22] Thai, H. T., Choi, D. H., Levy solution for free vibration analysis of functionally graded plates based on a refined plate theory, KSCE Journal of Civil Engineering, 8(6), 2014, 1813-1824.
[23] Hadaji, L., Khelifa, Z., Abbes, A. B. E., A new higher order shear deformation model for functionally graded beams, KSCE Journal Civil Engineering, 20, 2016, 1835–1841.
[24] Mantari, J. L., Ramos, I. A., Carrera, E., Petrolo, M., Static analysis of functionally graded plates using new non polynomial displacement fields via Carrera unified formulation, Composites Part-B, 89, 2016, 127–142.
[25] Amirpour, M., Das, R., Flores, E. I., Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory,Composite Structures, 94, 2016, 109–121.
[26] Thai, C. H., Zenkour, A. M., Wahab, M. A., Xuan, H. N., A four unknown shear and normal deformation theory for functionally graded isotropic and sandwich plate based on isogeometric analysis, Composites Part-B, 139, 2016, 77-95.
[27] Li, L., Zhang, D. G., Free vibration analysis of rotating functionally graded rectangular plates, Composite Structures, 136, 2016, 493-504.
[28] Park, M., Choi, D. H., A simplified first-order shear deformation theory for bending, buckling and free vibration analyses of isotropic plates on elastic foundations, KSCE Journal of Civil Engineering, 22(4), 2017, 1235-1249.
[29] Sayyad, A. S., Ghugal, Y. M., A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates, International Journal of Applied Mechanics, 9(1), 2017, 1-36.
[30] Naik, N. S., Sayyad, A. S., 1D analysis of laminated composite and sandwich plates using a new fifth-order plate theory. Latin American Journal of Solids and Structures, 15, 2018, 1-17.
[31] Sayyad, A. S., Ghugal, Y. M., Modeling and analysis of functionally graded sandwich beams: A review, Mechanics of Advanced Materials and Structures, (In Press) DOI: 10.1080/15376494.2018.1447178.
[32] Akbas, S. D., Vibration and static analysis of functionally graded porous plates, Journal of Applied and Computational Mechanics, 3(3), 2017, 199-207.
[33] Zenkour, A. M., A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities, Composite Structures, 201, 2018, 38-48.
[34] Avcar, M., Mohammed W. K. M., Free vibration of functionally graded beams resting on Winkler-Pasternak foundation, Arabian Journal of Geosciences, 11 (10), 2018, 1-8.
[35] Avcar, M., Alwan, H. H. A., Free vibration of functionally graded Rayleigh beam, International Journal of Engineering & Applied Sciences, 9(2), 2017, 127-137.
[36] Sobhy, M., Radwan, A. F., A new quasi 3D nonlocal plate theory for vibration and buckling of FGM nanoplates, International Journal of Applied Mechanics, 9(1), 2017, 1-29.
[37] Avcar, M., Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam, Structural Engineering and Mechanics, 55 (4), 2015, 871-884.
[38] Hebali, H., Tounsi, A., Houari, M. S. A., Bessaim, A., Bedia, E. A. A., New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates, Journal of Engineering Mechanics, 140, 2014, 374-383.
[39] Mercan, K., Baltacıoglu, A. K., Civalek, O., Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method, Composite Structures, 186, 2018, 139-153.
[40] Akbas, S. D., Stability of a non-homogenous porous plate by using generalized differential quadrature method, International Journal of Engineering and Applied Sciences, 9, 2017, 147-155.
[41] Akbas, S. D., Thermal effects on the vibration of functionally graded deep beams with porosity, International Journal of Applied Mechanics, 9(5), 2017, 1-18.
[42] Akbas, S. D., On post-buckling behavior of edge cracked functionally graded beams under axial loads, International Journal of Structural Stability and Dynamics, 15 (4), 2015, 1-21.
[43] Akbas, S. D., Post-buckling analysis of axially functionally graded three-dimensional beams, International Journal of Applied Mechanics, 7 (3), 2015, 1-20.
[44] Ersoy, H., Mercan, K., Civalek, O., Frequencies of FGM shells and annular plates by the methods of discrete singular convolution and differential quadrature methods, Composite Structures, 183, 2018, 7-20.
[45] Nasihatgozar, M., Khalili S. M. R., Free vibration of a thick sandwich plate using higher order shear deformation theory and DQM for different boundary conditions, Journal of Applied andComputational Mechanics, 3, 2017, 16-24.
[46] Dastjerdi, S., Akgoz, B., New static and dynamic analyses of macro and nano FGM plates using exact three-dimensional elasticity in thermal environment, Composite Structures, 192, 2018, 626-641.
[47] Civalek, O., Free vibration of carbon nanotubes reinforced (CNTR) and functionally graded shells and plates based on FSDT via discrete singular convolution method, Composites Part B: Engineering, 111, 2017, 45-59.
[48] Civalek, O., Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches, Composites Part B: Engineering, 50, 2013, 171–179.
[49] Civalek, O., Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method, International Journal of Mechanical Sciences, 49 (6), 2007, 752-765.
[50] Akgoz, B., Civalek, O., Nonlinear vibration analysis of laminated plates resting on nonlinear two parameters elastic foundations, Steel and Composite Structures, 11 (5), 403-421.
[51] Ghumare, S. M., Sayyad, A. S., A new fifth order shear and normal deformation theory for static bending and elastic buckling of P-FGM beams, Latin American Journal of Solids and Structures, 14, 2017, 1893-1911.
[52] Pagano, N. J., Exact solution for composite laminates in cylindrical bending, Journal of Composite Materials, 3, 1969, 398-411.
[53] Kirchhoff, G. R., Uber das gleichgewicht und die bewegung einer elastischen Scheibe, International Journal of Pure Applied Mathematics, 40, 1850, 51-88.
[54] Mindlin, R. D., Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates, ASME Journal of Applied Mechanics, 18, 1951, 31-38.
[55] Reddy, J. N., A simple higher order theory for laminated composite plates. Journal of Applied Mechanics, 51, 1984, 745-752.
[56] Sayyad, A. S., Ghugal, Y. M., A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates, International Journal of Mechanics and Materials in Design, 3, 2014, 247–267.
[57] Sayyad, A. S., Ghugal, Y. M., Bending of shear deformable plates resting on Winkler foundations according to trigonometric plate theory, Journal of Applied and Computational Mechanics, 4(3), 2018, 187-201.
)
