Structural Engineering and Mechanics

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Effect of material transverse distribution profile on buckling of thick functionally graded material plates according to TSDT

  • Abdelrahman, Wael G. (Department of Aerospace Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2018.12.22
  • Accepted : 2019.11.12
  • Published : 2020.04.10
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Abstract

Several classical and higher order plate theories were used to study the buckling of functionally graded material (FGM) plates. In the great majority of research, a power function is used to represent metal and ceramic material transverse distribution (P-FGM). Therefore, the effect of having other transverse variation of material properties on the buckling behavior of thick rectangular FGM plates was not properly addressed. In the present work, this effect is investigated using the Third order Shear Deformable Theory (TSDT) for the case of simply supported FGM plate. Both a sigmoid function and an exponential functions are used to represent the transverse gradual property variation. The plate governing equations are combined with a Navier type expanded solution of the unknown displacements to derive the buckling equation in terms of the pre-buckling in-plane loads. Finally, the critical in-plane load is calculated for the different buckling modes. The model is verified by a comparison of the calculated buckling loads with available published results of Al-SiC P-FGM plates. The conducted parametric study shows that manufacturing FGM plates with sigmoid variation of properties in the thickness direction increases the buckling load considerably. This improvement is found to be more significant for the case of thick plates than that of thin plates. Results also show that this stiffening-like effect of the sigmoid function profile is more evident for cases where the in-plane loads are applied along the shorter edge of the plate.

Keywords

References

  1. Abdelmalek, A., Bouazza, M. Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: a micromechanical approach", Iran J. Sci. Tech. Trans. Mech. Eng., 43(1), 61-73. https://doi.org/10.1007/s40997-017-0140-y.
  2. Adda-bedia, E.A., Bouazza, M., Tounsi, A., Benzair, A. and Maachouc, M. (2008), "Prediction of stiffness degradation in hygrothermal aged $[{\theta}_m/90_n]_S$ composite laminates with transverse cracking", J. Mat. Process. Tech., 199(1-3), 199-205. https://doi.org/10.1016/j.jmatprotec.2007.08.002.
  3. Amara, K. Bouazza, M. and Fouad, B. (2016), "Postbuckling Analysis of Functionally Graded Beams Using Nonlinear Model", Per. Polytech. Mech. Eng., 60(2), 121-128. https://doi.org/10.3311/ppme.8854.
  4. Antar, K., Amara, K., Benyoucef, S., Bouazza, M. and Ellali, M. (2019), "Hygrothermal effects on the behavior of reinforced-concrete beams strengthened by bonded composite laminate plates", Str. Eng. Mech., 69(3), 327-334. https://doi.org/10.14359/551.
  5. Bakora, A. and Tounsi, A. (2015), "Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundation", Str. Eng. Mech., 56 (1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085.
  6. Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Comp. Str., 21(6), 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347.
  7. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Bedia, E.A. and Hassan, S. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Str. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019.
  8. Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Mod., 34, 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016.
  9. Bouazza, M. and Benseddiq, N. (2015), "Analytical modeling for the thermoelastic buckling behavior of functionally graded rectangular plates using hyperbolic shear deformation theory under thermal loadings", Multidisc. Mod. Mat. Struc., 11(4), 558-578. https://doi.org/10.1108/mmms-02-2015-0008.
  10. Bouazza, M. and Zenkour, A. (2018), "Free vibration characteristics of multilayered composite plates in a hygrothermal environment via the refined hyperbolic theory", Eur. Phys. J. Plus, 133: 217. https://doi.org/10.1140/epjp/i2018-12050-x.
  11. Bouazza, M., Antar, K., Amara, K., Benyoucef, S. and Bedia, E. (2019), "Influence of temperature on the beams behavior strengthened by bonded composite plates", Geomech. Eng., 18(5), 555-566. https://doi.org/10.1016/j.compstruct.2013.01.021.
  12. Bouazza, M., Becheri, T. Boucheta, A. and Benseddiq, N. (2016), "Thermal buckling analysis of nanoplates based on nonlocal elasticity theory with four-unknown shear deformation theory resting on Winkler-Pasternak elastic foundation", Int. J. Comp. Meth. Eng. Sci. Mech., 17, 362-373. https://doi.org/10.1080/15502287.2016.1231239.
  13. Bouazza, M., Benseddiq, N. and Zenkour, A. (2019), "Thermal buckling analysis of laminated composite beams using hyperbolic refined shear deformation theory" J. of Therm. Str., 42(3), 332-340. https://doi.org/10.1080/01495739.2018.1461042.
  14. Bouazza, M., Kenouza, Y., Benseddiq, N. and Zenkour, A. (2017), "A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates", Compos. Str., 182, 533-541. https://doi.org/10.1016/j.compstruct.2017.09.041.
  15. Bouazza, M., Lairedj, A., Benseddiq, N. and Khalkia, S. (2016), "A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates", Mech. Res. Comm., 73, 117-126. https://doi.org/10.1016/j.mechrescom.2016.02.015.
  16. Bouazza, M., Tounsi, A., Adda-Bedia E.A. and Megueni, A. (2011), "Stability analysis of functionally graded plates subject to thermal loads", Shell-like Struc.-Adv. Struc. Mat., 15, 669-680. https://doi.org/10.1007/978-3-642-21855-2_44.
  17. Bouazza, M., Tounsi, A., Adda-Bedia, E.A. and Megueni, A. (2010), "Thermoelastic stability analysis of functionally graded plates: An analytical approach", Comput. Mat. Sci., 49(4), 865-870. https://doi.org/10.1016/j.commatsci.2010.06.038.
  18. Bouazza, M., Tounsi, A., Adda-Bedia, E.A. and Megueni, A. (2011), "Thermal buckling of simply supported FGM square plates", Appl. Mech. Mat., 61, 25-32. https://doi.org/10.4028/www.scientific.net/amm.61.25.
  19. Bouazza, M., Tounsi, A., Benzair, A. and Adda-bedia, E.A. (2007), "Effect of transverse cracking on stiffness reduction of hygrothermal aged cross-ply laminates", J. Mat. Des., 28(4), 1116-1123. https://doi.org/10.1016/j.matdes.2006.02.003.
  20. Bouazza, M., Zenkour, A. and Benseddiq, N. (2018), "Closed-from solutions for thermal buckling analyses of advanced nanoplates according to a hyperbolic four-variable refined theory with small-scale effects", Acta Mech., 229(5), 2251-2265. https://doi.org/10.1007/s00707-017-2097-8.
  21. Bouazza, M., Zenkour, A. and Benseddiq, N. (2018), "Effect of material composition on bending analysis of FG plates via a two-variable refined hyperbolic theory", Arch. Mech., 70 (2), 107-129.
  22. Bouderba, B., Houari, M., Tounsi, A. and Mahmoud S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Str. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397.
  23. Bourada, M., Bouadi, A., Bousahla, A., Senouci, A, Bourada, F., Tounsi, A. and Mahmoud, S. (2019), "Buckling behavior of rectangular plates under uniaxial and biaxial compression", Str. Eng. Mech., 70(1), 113-123. https://doi.org/10.12989/sem.2019.70.1.113.
  24. Bui, T., Van Do, T., Ton, L., Doan, D., Tanaka, S., Pham, D., Nguyen-Van, T., Yu, T. and Hirose, S. (2016), "On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory", Comp. Part B: Eng. , 92, 218-241. https://doi.org/10.1016/j.compositesb.2016.02.048.
  25. El-Haina, F., Bakora, A., Bousahla, A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates," Str. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585.
  26. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on pasternak elastic foundation using higher-order shear deformation plate theories" Smart Struc. Sys., 21(1), 113-122. https://doi.org/10.12989/scs.2016.21.6.1347.
  27. Fellah, M., Draiche, K., Houari, M., Tounsi, A., Saeed, T., Alhodaly, M. and Benguediab, M. (2019), "A novel refined shear deformation theory for the buckling analysis of thick isotropic plates", Str. Eng. Mech., 69(3), 335-345. https://doi.org/10.12989/sem.2019.69.3.335.
  28. Ganapathi, M., Prakash, T. and Sundararajan, N. (2006), "Influence of functionally graded material on buckling of skew plates under mechanical loads", J. Eng. Mech., 132(8), 902-905. https://doi.org/10.1061/(asce)0733-9399(2006)132:8(902).
  29. Ghannadpour, S.A.M., Ovesy, H.R. and Nassirnia, M. (2012), "Buckling analysis of functionally graded plates under thermal loadings using the finite strip method", Comput. Struct.,108, 93-99. https://doi.org/10.1016/j.compstruc.2012.02.011.
  30. Hadji, L., Meziane, M., Abdelhak, Z. and Hassaine, T. (2016), "Static and dynamic behavior of FGM plate using a new first shear deformation plate theory", Str. Eng. & Mech., 57(1), 127-140. https://doi.org/10.12989/sem.2016.57.1.127.
  31. Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", ZAMM J. Appl. Math. Mech., 82(4), 277-283. https://doi.org/10.1002/1521-4001(200204)82:4%3C277::aid-zamm277%3E3.0.co;2-y.
  32. Kiani, Y., Bagherizadeh, E. and Eslami, M.R. (2011), "Thermal buckling of clamped thin rectangular FGM plates resting on Pasternak elastic foundation", ZAMM - J. Appl. Math. Mech. / Z Angew. Math. Mech., 91(7), 581-593. https://doi.org/10.1002/zamm.201000184.
  33. Liu, S., Yu, T., Bui, T., Yin,, S., Thai, D. and Tanaka, S. (2017), "Analysis of functionally graded plates by a simple locking-free quasi-3D hyperbolic plate isogeometric method", Comp. Part B: Eng., 120, 182-196. https://doi.org/10.1016/j.compositesb.2017.03.061.
  34. Mohammadi, M., Saidi, A. and Jomehzadeh, E. (2010), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Comp. Mat., 17(2), 81-93. https://doi.org/10.1007/s10443-009-9100-z.
  35. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47(1), 663-84. https://doi.org/10.1002/(sici)1097-0207(20000110/30)47:1/3%3C663::aid-nme787%3E3.0.co;2-8.
  36. Soltani, K. Bessaim, A., Houari, M., Kaci, A., Benguediab, M., Tounsi, A. and Alhodaly, M. (2019), "A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations", Steel Comp. Str., 30(1), 13-29. https://doi.org/10.12989/scs.2019.30.1.013.
  37. Swaminathan, K., Naveenkumar, D.T., Zenkour, A.M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates - A state-of-the-art review", Composite Structures, 120, 10-31. https://doi.org/10.1016/j.matdes.2006.02.003.
  38. Thai, H.T., Kim, S.E. (2015), "A review of theories for the modeling and analysis of functionally graded plates and shells", Composite Structures, 128, 70-86. https://doi.org/10.1201/9781420092578.ch1.
  39. Valizadeh, N., Natarajan, S., Gonzalez-Estrada, O., Rabczuk, T., Bui, T. and Bordas, S. (2013), "NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter", Compos. Str., 99, 309-326. https://doi.org/10.1016/j.compstruct.2012.11.008.
  40. Vu, T., Khosravifard, A., Hematiyan, M. and Bui, T. (2018), "A new refined simple TSDT-based effective meshfree method for analysis of through-thickness FG plates", Appl. Math. Mod., 57, 514-534. https://doi.org/10.1016/j.apm.2018.01.004.
  41. Yin, S., Hale, J., Yu, T., Bui, T. and Bordas, S. (2014), "Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates", Compos. Str., 118, 121-138. https://doi.org/10.1016/j.compstruct.2014.07.028.
  42. Yin, S., Yu, T., Bui, T., Liu, P. and Hirose, S. (2016), "Buckling and vibration extended isogeometric analysis of imperfect graded Reissner-Mindlin plates with internal defects using NURBS and level sets", Comp. Str., 177, 23-38. https://doi.org/10.1016/j.compstruc.2016.08.005.
  43. Yin, S., Yu, T., Bui, T., Zheng, X. and Tanaka, S. (2016), "In-plane material inhomogeneity of functionally graded plates: A higher-order shear deformation plate isogeometric analysis", Comp. Part B: Eng., 106, 273-284. https://doi.org/10.1016/j.compositesb.2016.09.008.
  44. Yin, S., Yu, T., Bui, T., Zheng, X. and Yi, G. (2017), "Rotation-free isogeometric analysis of functionally graded thin plates considering in-plane material inhomogeneity", Thin-Walled Str., 119, 385-395. https://doi.org/10.1016/j.tws.2017.06.033.
  45. Yu, T., Bui, T., Yin, S., Doan, D., Van Do, T., Wu, C. and Tanaka, S. (2016), "On the thermal buckling analysis of functionally graded plates with internal defects using extended isogeometric analysis", Compos. Str., 136, 684-695. https://doi.org/10.1016/j.compstruct.2015.11.002.
  46. Yu, T., Yin, S., Bui, T., Liu, C. and Wattanasakulpong, N. (2017), "Buckling isogeometric analysis of functionally graded plates under combined thermal and mechanical loads", Compos. Str., 162, 54-69. https://doi.org/10.1016/j.compstruct.2016.11.084.

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