PSI - Issue 26

Merazi Mohamed et al. / Procedia Structural Integrity 26 (2020) 129–138 Merazi et al / Structural Integrity Procedia 00 (2020) 000 – 000

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Fig. 7. Variation of transverse shear stresses through the thickness of an FGM plate for different values of aspect ratio (a/b).

5. Conclusions In the present study, a refined trigonometric shear deformation beam theory based on neutral surface position is proposed for free vibration analysis of functionally graded beams. The theory gives a parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present beam theory and the neutral surface concept, the equations of motion are derived from Hamilton’s principle. Numerical examples show that the proposed theory gives solutions which are almost identical with those obtained using other shear deformation theories. References Attia, A., Tounsi, A., Adda Bedia, E.A.,, Mahmoud, S.R. (2014), “Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories”, Steel and Composite Structures, (In press). Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., Anwar Bég, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates”, Composites: Part B, 60, 274–283. Benachour, A., Hassaine Daouadji, T., Ait Atmane, H., Tounsi, A., Meftah. S.A. (2011), “A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient”, Composites Part B: Engineering, 42(6), 1386–1394. Chakraverty, S., Pradhan, K.K. (2014), “Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions”, Aerospace Science and Technology. 36, 132–156. Ebrahimi, F. (2013), “Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment”, Mechanics of Advanced Materials and Structures, 20(10), 854-870. Jha, D.K., Kant, T., Singh, R.K. (2011), “Stress analysis of transversely loaded functionally graded plates with a higher order shear and normal deformation theory”, Journal of Engg. Mech., 51-49. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O., Mahmoud, S.R. (2014), “Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect” Steel and Composite Structures, (In press). Swaminathan, K., Naveenkumar, D.T. (2014), “Higher order refined computational models for the stability analysis of FGM plates: Analytical solutions”, European Journal of Mechanics A/Solids, 47, 349 – 361. Talha, M, Singh, BN. (2011), “Large amplitude free flexural vibration analysis of shear deformable FGM plates using nonlinear finite element method”, Finite Elem Anal Des, 47(4), 394–401. Merazi, M., Hadji, L., Daouadji, T., Tounsi, A., (2020), “Static analysis of a FGM plate based on the neutral surface concept using the new hyperbolic shear deformation approach, ”, sciencesconf.org:erma19:293548,465-470 Tounsi, A, Houari, M.S.A., Benyoucef, S, Adda Bedia, E.A. (2013a), “A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates”, Aerospace Science and Technology, 24, 209–220.