DOI QR코드

DOI QR Code

Static analysis of the FGM plate with porosities

  • Benferhat, R. (Laboratoire de Geomateriaux, Departement de Genie Civil, Universite Hassiba Benbouali de Chlef) ;
  • Hassaine Daouadji, T. (Departement de Genie Civil, Universite Ibn Khaldoun de Tiaret) ;
  • Hadji, L. (Departement de Genie Civil, Universite Ibn Khaldoun de Tiaret) ;
  • Said Mansour, M. (Laboratoire de Geomateriaux, Departement de Genie Civil, Universite Hassiba Benbouali de Chlef)
  • Received : 2015.03.21
  • Accepted : 2016.03.05
  • Published : 2016.05.20

Abstract

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

Keywords

References

  1. Ait Atmane, H., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater., 1-14.
  2. Ait Yahia, S., Ait Atmane, H., Sid Ahmed Houari, M. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  3. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  4. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  5. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  6. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2010), "Refined and advanced models for multilayered plates and shells embedding functionally graded material layers", Mech. Adv. Mater. Struct., 17(8), 603-621. https://doi.org/10.1080/15376494.2010.517730
  7. Cinefra, M., Carrera, E., Della Croce, L. and Chinosi, C. (2012), "Refined shell elements for the analysis of functionally graded structures", Compos. Struct., 94(2), 415-422. https://doi.org/10.1016/j.compstruct.2011.08.006
  8. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., Int. J., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361
  9. Hassaine Daouadji, T., Tounsi, A., Hadji, L., Hadj, H.A. and El Abbes, A.B. (2012), "A theoretical analysis for static and dynamic behavior of functionally graded plates", Mater. Phys. Mech., 14, 110-128.
  10. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  11. Kiani, Y., Akbarzadeh, A.H., Chen, Z.T. and Eslami, M.R. (2011), "Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation", Compos. Struct., 94(8), 2474-2484. https://doi.org/10.1016/j.compstruct.2012.02.028
  12. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B, 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9
  13. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sic., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X
  14. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  15. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2011), "Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions", Mech. Res. Commun., 38(5), 368-371. https://doi.org/10.1016/j.mechrescom.2011.04.011
  16. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012a), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005
  17. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Soares, C.M.M. and Jorge, R.M.N. (2012b), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 43(2), 711-725.
  18. Ravikiran, K., Kashif, A. and Ganesan, G. (2008), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32 (12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  19. Ravikiran, K., Kashif, A. and Ganesan, N. (2013), "Static analysis of functionally graded beams using higher order shear deformation theory", Appl. Math. Model., 32(12), 2509-2525. https://doi.org/10.1016/j.apm.2007.09.015
  20. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  21. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Method. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  22. Sepahi, O., Forouzan, M.R. and Malekzadeh, P. (2008), "Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM", Compos. Struct., 92(10), 2369-2378. https://doi.org/10.1016/j.compstruct.2010.03.011
  23. Sepahi, O., Forouzan, M.R. and Malekzadeh, P. (2010), "Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM", Compos. Struct., 92(10), 2369-2378. https://doi.org/10.1016/j.compstruct.2010.03.011
  24. Sid Ahmed Houari, M., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  25. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  26. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  27. Werner, H. (1999), "A three-dimensional solution for rectangular plate bending free of transversal normal stresses", Numer..Method..Eng., 15(4), 295-302. https://doi.org/10.1002/(SICI)1099-0887(199904)15:4<295::AID-CNM245>3.0.CO;2-S
  28. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of $ZrO_2$-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1-3), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2

Cited by

  1. On vibrations of porous nanotubes vol.125, 2018, https://doi.org/10.1016/j.ijengsci.2017.12.009
  2. Vibration analysis of non-uniform porous beams with functionally graded porosity distribution pp.2041-3076, 2018, https://doi.org/10.1177/1464420718780902
  3. Non-linear study of mode II delamination fracture in functionally graded beams vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.263
  4. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  5. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  6. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  7. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  8. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  9. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  10. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  11. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2016, https://doi.org/10.12989/was.2017.25.4.329
  12. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  13. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  14. Investigating vibration behavior of smart imperfect functionally graded beam subjected to magnetic-electric fields based on refined shear deformation theory vol.5, pp.4, 2017, https://doi.org/10.12989/anr.2017.5.4.281
  15. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  16. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  17. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  18. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  19. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  20. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2016, https://doi.org/10.12989/was.2018.27.1.059
  21. An efficient and simple refined theory for free vibration of functionally graded plates under various boundary conditions vol.16, pp.1, 2016, https://doi.org/10.12989/gae.2018.16.1.001
  22. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  23. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  24. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  25. Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations vol.72, pp.1, 2016, https://doi.org/10.12989/sem.2019.72.1.061
  26. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  27. Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory vol.24, pp.4, 2019, https://doi.org/10.12989/cac.2019.24.4.369
  28. Effect of porosity in interfacial stress analysis of perfect FGM beams reinforced with a porous functionally graded materials plate vol.72, pp.3, 2016, https://doi.org/10.12989/sem.2019.72.3.293
  29. On the stability of isotropic and composite thick plates vol.33, pp.4, 2019, https://doi.org/10.12989/scs.2019.33.4.551
  30. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  31. Free vibration analysis of angle-ply laminated composite and soft core sandwich plates vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.663
  32. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2016, https://doi.org/10.12989/scs.2019.33.5.699
  33. Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory vol.24, pp.6, 2019, https://doi.org/10.12989/cac.2019.24.6.489
  34. A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation vol.34, pp.4, 2016, https://doi.org/10.12989/scs.2020.34.4.511
  35. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  36. Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory vol.25, pp.3, 2020, https://doi.org/10.12989/cac.2020.25.3.225
  37. An inclined FGM beam under a moving mass considering Coriolis and centrifugal accelerations vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.061
  38. Improved analytical solution for slip and interfacial stress in composite steel-concrete beam bonded with an adhesive vol.9, pp.2, 2016, https://doi.org/10.12989/amr.2020.9.2.133
  39. A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells vol.26, pp.2, 2020, https://doi.org/10.12989/cac.2020.26.2.185
  40. Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model vol.26, pp.2, 2020, https://doi.org/10.12989/sss.2020.26.2.253
  41. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633
  42. Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate vol.9, pp.5, 2016, https://doi.org/10.12989/csm.2020.9.5.473
  43. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2016, https://doi.org/10.12989/amr.2020.9.4.265
  44. Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation vol.9, pp.6, 2016, https://doi.org/10.12989/csm.2020.9.6.499
  45. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  46. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  47. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2016, https://doi.org/10.12989/sem.2021.77.2.217
  48. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2016, https://doi.org/10.12989/csm.2021.10.1.061
  49. Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations vol.77, pp.6, 2016, https://doi.org/10.12989/sem.2021.77.6.797
  50. Limit Elastic Analysis of Functionally Graded Rotating Disks Under Thermo-Mechanical Loading vol.13, pp.3, 2016, https://doi.org/10.1142/s1758825121500332