Functionally graded materials (FGM) are an advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. In this work, the effect of the material homogenization scheme on the flexural response of a thin to moderately thick FGM plate is studied. The plate is subjected to different loading and boundary conditions. The formulation is developed based on the first-order shear deformation theory. The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power-law distribution of the volume fraction of the constituents. The variation of volume fraction through the thickness is computed using two different homogenization techniques, namely rule of mixtures and Mori–Tanaka scheme. Comparative studies have been carried out to demonstrate the efficiency of the present formulation. The results obtained from the two techniques have been compared with the analytical solutions available in the literature. In addition to the above a parametric study bringing out the effect of boundary conditions, loads, and power-law index has also been presented.
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Shen, H.-S.: Functionally Graded Materials: Nonlinear Analysis of Plates and Shells. CRC Press, Boca Raton (2009)
Jha, D.K., Kant, T., Singh, R.K.: A critical review of recent research on functionally graded plates. Compos. Struct. 96, 833–849 (2013)
Birman, V., Byrd, L.W.: Modeling and analysis of functionally graded materials and structures. Appl. Mech. Rev. 60(5), 195–216 (2007)
Gupta, A., Talha, M.: Recent developments in modeling and analysis of functionally graded materials and structures. Prog. Aerosp. Sci. 79, 1–14 (2015)
Zuiker, J.R.: Functionally graded materials: choice of micromechanics model and limitations in property variation. Compos. Eng. 5(7), 807–819 (1995)
Klusemann, B., Svendsen, B.: Homogenization methods for multi-phase elastic composites: comparison and benchmarks. Tech. Mech. 30(4), 374–386 (2010)
Reiter, T., Dvorak, G.J.: Micro mechanical modeling of functionally graded materials. In: IUTAM Symposium on Transformation Problems in Composite and Active Materials. Solid Mechanics and Its Applications, vol. 60, pp. 173–184 (1998)
Gasik, M.M.: Micromechanical modelling of functionally graded materials. Comput. Mater. Sci. 13(1–3), 42–55 (1998)
Reddy, J.N.: Analysis of functionally graded plates. Int. J. Numer. Meth. Eng. 47(1–3), 663–684 (2000)
Praveen, G.N., Reddy, J.N.: Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates. Int. J. Solids Struct. 35(33), 4457–4476 (1998)
Hasin, Z.: Assessment of the self consistent scheme approximation: conductivity of particulate composites. J. Compos. Mater. 2(3), 284–300 (1968)
Hasin, Z., Shtrikman, S.: A variational approach to the theory of elastic behavior of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)
Vel, S.S., Batra, R.C.: Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA J. 40(7), 1421–1433 (2002)
Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21(5), 571–574 (1973)
Benveniste, Y.: A new approach to the application of Mori–Tanaka’s theory in composite materials. Mech. Mater. 6(2), 147–157 (1987)
Willis, J.R.: Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25(3), 185–202 (1977)
Hill, R.: A self consistent mechanics of composite materials. J. Mech. Phys. Solids 13(4), 213–222 (1965)
Bhaskar, K., Vardan, T.K.: The contradicting assumptions of zero transverse normal stress and strain in thin plate theory—a justification. J. Appl. Mech. 68(4), 660–662 (2001)
Ferreira, A.J.M., Batra, R.C., Rouque, C.M.C., Qian, L.F., Martins, P.A.L.S.: Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos. Struct. 69(4), 449–457 (2005)
Shen, H.-S., Wang, Z.-X.: Assessment of Voigt and Mori–Tanaka models for vibration analysis of functionally graded plates. Compos. Struct. 94(7), 2197–2208 (2012)
Ardestani, M.M., Soltani, B., Shams, Sh.: Analysis of functionally graded stiffened plates based on FSDT utilizing reproducing kernel particle method. Compos. Struct. 112, 231–240 (2014)
Taj, G., Chakrabarti, A.: Static and dynamic analysis of functionally graded skew plates. J. Eng. Mech. 139(7), 848–857 (2013)
Reddy, J.N., Chin, C.D.: Thermo mechanical analysis of functionally graded cylinders and plates. J. Therm. Stress. 21(6), 593–626 (1998)
Reddy, J.N., Cheng, Z.-Q.: Three-dimensional thermomechanical deformations of functionally graded rectangular plates. Eur. J. Mech. A. Solids 20(5), 841–855 (2001)
Kashtalyan, M.: Three-dimensional elasticity solution for bending of functionally graded rectangular plates. Eur. J. Mech. A. Solids 23(5), 853–864 (2004)
Elishakoff, I., Gentilini, C.: Three-dimensional flexure of rectangular plates made of functionally graded materials. J. Appl. Mech. 72(5), 788–791 (2005)
Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics, 3rd edn. Wiley, New York (2017)
Zenkour, A.M.: Generalized shear deformation theory for bending analysis of functionally graded plates. Appl. Math. Model. 30(1), 67–84 (2006)
Matsunaga, H.: Stress analysis of functionally graded plates subjected to thermal and mechanical loadings. Compos. Struct. 87(4), 344–357 (2009)
Hosseini-Hashemi, S., Taher, H.R.D., Akhavan, H., Omidi, M.: Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Appl. Math. Model. 34(5), 1276–1291 (2010)
Talha, M., Singh, B.N.: Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl. Math. Model. 34(12), 3991–4011 (2010)
Singha, M.K., Prakash, T., Ganapathi, M.: Finite Element analysis of functionally graded plates under transverse load. Finite Elem. Anal. Des. 47(4), 453–460 (2011)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC Press, Boca Raton (2004)
Reddy, J.N.: Theory and Analysis of Elastic Plates and Shells, 2nd edn. CRC Press, Boca Raton (2007)
Cowper, G.R.: The shear coefficient in Timoshenko’s beam theory. J. Appl. Mech. 33(2), 335–340 (1966)
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 functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique. Compos. B Eng. 44(1), 657–674 (2013)
Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. B Eng. 42(2), 123–133 (2011)
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Srividhya, S., Basant, K., Gupta, R.K. et al. Influence of the homogenization scheme on the bending response of functionally graded plates. Acta Mech 229, 4071–4089 (2018). https://doi.org/10.1007/s00707-018-2223-2