DOI QR코드

DOI QR Code

Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM

  • Alhaifi, Khaled (Department of Automotive and Marine Engineering, College of Technological Studies-PAAET) ;
  • Arshid, Ehsan (Department of Mechanical Engineering, Qom Branch, Islamic Azad University) ;
  • Khorshidvand, Ahmad Reza (Department of Mechanical Engineering, South Tehran Branch, Islamic Azad University)
  • 투고 : 2020.01.09
  • 심사 : 2021.05.20
  • 발행 : 2021.06.25

초록

In the current study, large deflection analysis of a functionally graded saturated porous (FGSP) rectangular plate subjected to transverse loading which is located on a nonlinear three-parameter elastic foundation is provided. The constitutive law for the porous materials is written based on Biot's model which considers the effect of fluids within the pores. The mechanical properties of the plate are changed through its thickness according to different functions which are called porosity distributions. The shear deformation effects are taken into account, accordingly, the first-order shear deformation theory (FSDT) is used to describe the displacement components of the plate. Employing the Minimum total potential energy principle and calculus of variation, the governing equations, and associated boundary conditions are extracted. A generalized differential quadrature method (GDQM) is used to solve them for various boundary conditions. The results for the simpler state are validated with the previously published works and then the effects of different parameters on the deflection of the plate are investigated. It is seen increasing the porosity and Skempton coefficient, enhances and reduces the deflection of the structure, respectively. The results of this study may help to design and manufacture more reliable engineering structures that are exposed to loads.

키워드

참고문헌

  1. Abdelaziz, H.H., Meziane, M.A.A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693.
  2. Akbas, S.D. (2017), "Vibration and Static Analysis of Functionally Graded Porous Plates", Shahid Chamran Univ. Ahvaz, 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107.
  3. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.
  4. Akgoz, B. and Civalek, O. (2014), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Vib. Control, 20(4), 606-616. https://doi.org/10.1177/1077546312463752.
  5. Akgoz, B. and Civalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronautica, 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021.
  6. Amir, S., Arshid, E. and Ghorbanpour Arani, M.R. (2019), "Size-Dependent Magneto-Electro-Elastic Vibration Analysis of FG Saturated Porous Annular/ Circular Micro Sandwich Plates Embedded with Nano-Composite Face sheets Subjected to Multi-Physical Pre Loads", Smart Struct. Syst., 23(5), 429-447. https://doi.org/10.12989/sss.2019.23.5.429.
  7. Amir, S., Arshid, E. and Khoddami Maraghi, Z. (2020), "Free vibration analysis of magneto-rheological smart annular three-layered plates subjected to magnetic field in viscoelastic medium", Smart Struct. Syst., 25(5), 581-592. https://doi.org/10.12989/sss.2020.25.5.581.
  8. Arshid, E., Amir, S. and Loghman, A. (2020a), "Bending and buckling behaviors of heterogeneous temperature-dependent micro annular/circular porous sandwich plates integrated by FGPEM nano-Composite layers", J. Sandw. Struct. Mater., 109963622095502. https://doi.org/10.1177/1099636220955027.
  9. Arshid, E., Amir, S. and Loghman, A. (2020b), "Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT", Int. J. Mech. Sci., 180, 105656. https://doi.org/10.1016/j.ijmecsci.2020.105656.
  10. Arshid, E. and Khorshidvand, A.R. (2018), "Free vibration analysis of saturated porous FG circular plates integrated with piezoelectric actuators via differential quadrature method", Thin-Wall. Struct., 125, 220-233. https://doi.org/10.1016/j.tws.2018.01.007
  11. Arshid, E., Khorshidvand, A.R. and Khorsandijou, S.M. (2019a), "The Effect of Porosity on Free Vibration of SPFG Circular Plates Resting on visco-Pasternak Elastic Foundation Based on CPT, FSDT and TSDT", Struct. Eng. Mech., 70(1), 97-112. http://dx.doi.org/10.12989/sem.2019.70.1.097.
  12. Arshid, E., Kiani, A. and Amir, S. (2019b), "Magneto-electroelastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface", Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 223(10), 2140-2159. https://doi.org/10.1177/1464420719832626.
  13. Barati, M. (2017), "Investigating dynamic characteristics of porous double-layered FG nanoplates in elastic medium via generalized nonlocal strain gradient elasticity", Eur. Phys. J.Plus, 132(9), 378. https://doi.org/10.1140/epjp/i2017-11670-x
  14. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081
  15. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429.
  16. Bert, C.H.W., Jang, S.K. and Striz, A.G. (1989), "Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature", Comput. Mech., 5(2-3), 217-226. https://doi.org/10.1007/BF01046487
  17. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Rev., 49(1), 1-28. https://doi.org/10.1115/1.3101882.
  18. Biot, M.A. (1964), "Theory of Buckling of a Porous Slab and Its Thermoelastic Analogy", J. Appl. Mech., 31(2), 194-198. https://doi.org/10.1115/1.3629586.
  19. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085.
  20. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  21. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A Novel Higher Order Shear and Normal Deformation Theory Based on Neutral Surface Position for Bending Analysis of Advanced Composite Plates", Int. J. Comput. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825.
  22. Brush, D.O., Almroth, B.O. and Hutchinson, J.W. (1975), "Buckling of bars, plates, and shells", J. Appl. Mech., 42, 911.
  23. Chan, D.Q., Nguyen, P.D., Quang, V.D., Anh, V.T.T. and Duc, N. D. (2019), "Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load", Steel Compos. Struct., 31(3), 243-259. https://doi.org/10.12989/scs.2019.31.3.243.
  24. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/J.COMPSTRUCT.2015.07.052.
  25. Civalek, O. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struc., 26(2), 171-186. https://doi.org/10.1016/J.ENGSTRUCT.2003.09.005.
  26. Cong, P.H., Chien, T.M., Khoa, N.D. and Duc, N.D. (2018), "Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy's HSDT", Aerosp. Sci. Technol., 77, 419-428. https://doi.org/10.1016/J.AST.2018.03.020.
  27. Detournay, E. and Cheng, A.H.D. (1993), "Fundamentals of Poroelasticity", Anal. Design Method., 113-171. https://doi.org/10.1016/B978-0-08-040615-2.50011-3.
  28. Driz, H., Hafida, M., Bakora, A., Benachour, A., Tounsi, A. and Bedia, E.A.A. (2018), "A new and simple HSDT for isotropic and functionally graded sandwich plates", Steel Compos. Struct., 26(4), 387-405. https://doi.org/10.12989/scs.2018.26.4.387.
  29. Ebrahimi, F., Barati, M.R. and Civalek, O. (2020), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. with Comput., 36(3), 953-964. https://doi.org/10.1007/s00366-019-00742-z.
  30. Ebrahimi, F., Seyfi, A., Dabbagh, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107. https://doi.org/10.12989/sem.2019.71.1.099.
  31. Etchessahar, M., Sahraoui, S. and Brouard, B. (2001), "Bending vibrations of a rectangular poroelastic plate", Comptes Rendus de l'Academie Des Sciences - Series IIB - Mechanics, 329(8), 615-620. https://doi.org/10.1016/S1620-7742(01)01375-7.
  32. Ghorbanpour Arani, A., Atabakhshian, V., Loghman, A., Shajari, A. R. and Amir, S. (2012), "Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method", Physica B: Condensed Matter, 407(13), 2549-2555. https://doi.org/10.1016/j.physb.2012.03.065
  33. Gurses, M., Akgoz, B. and Civalek, O. (2012), "Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl. Math. Comput., 219(6), 3226-3240. https://doi.org/10.1016/j.amc.2012.09.062.
  34. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235.
  35. Heydari, M. M., Nabi, A.H. and Heydari, M. (2014), "Nonlinear bending behavior of orthotropic Mindlin plate resting on orthotropic Pasternak foundation using GDQM", Nonlinear Dynam., 78(3), 1645-1657. https://doi.org/10.1007/s11071-014-1545-4.
  36. Kim, J., Zur, K.K. and Reddy, J.N. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888. https://doi.org/10.1016/J.COMPSTRUCT.2018.11.023.
  37. Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin-Wall.Struct., 46(3), 333-337. https://doi.org/10.1016/J.TWS.2007.06.006.
  38. Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., 6(4), 319-333. https://doi.org/10.12989/scs.2006.6.4.319.
  39. Mercan, K., Ebrahimi, F. and Civalek, O. (2020), "Vibration of angle-ply laminated composite circular and annular plates", Steel Compos. Struct., 34(1), 141-154. https://doi.org/10.12989/scs.2020.34.1.141.
  40. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  41. Mohammadimehr, M., Arshid, E., Alhosseini, S.M.A.R., Amir, S., and Arani, M.R.G. (2019), "Free vibration analysis of thick cylindrical MEE composite shells reinforced CNTs with temperature-dependent properties resting on viscoelastic foundation", Struct. Eng. Mech., 70(6), 683. https://doi.org/10.12989/SEM.2019.70.6.683.
  42. Mojahedin, A., Jabbari, M., Khorshidvand, A.R.R. and Eslami, M. R.R. (2016), "Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory", Thin-Wall. Struct., 99, 83-90. https://doi.org/10.1016/J.TWS.2015.11.008.
  43. Nguyen, D.D. and Ha, N. (2011), "The bending analysis of thin composite plate under steady temperature field", J. Sci. Math.s-Phys., 27, 77-83.
  44. Numanoglu, H.M., Akgoz, B. and Civalek, O. (2018), "On dynamic analysis of nanorods", Int. J. Eng. Sci., 130, 33-50. https://doi.org/10.1016/j.ijengsci.2018.05.001.
  45. Reddy, J.N.J., Wang, C.M.C. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4.
  46. Rezaei, A.S.S. and Saidi, A.R.R. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060. https://doi.org/10.1016/j.compstruct.2015.08.125.
  47. Sadoughifar, A., Farhatnia, F., Izadinia, M. and Tal, B. (2019), "Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM", Steel Compos. Struct., 33(2), 307-318. https://doi.org/10.12989/scs.2019.33.2.307.
  48. Sahmani, S., Fattahi, A.M. and Ahmed, N.A. (2019), "Size-dependent nonlinear forced oscillation of self-assembled nanotubules based on the nonlocal strain gradient beam model", J. Braz. Soc. Mech. Sci. Eng., 41(5), 239. https://doi.org/10.1007/s40430-019-1732-9.
  49. 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.
  50. Shen, H.S. (2000), "Nonlinear bending of shear deformable laminated plates under transverse and in-plane loads and resting on elastic foundations", Compos. Struct., 50(2), 131-142. https://doi.org/10.1016/S0263-8223(00)00088-X.
  51. Shen, H.S. and Wang, Z.X. (2010), "Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations", Compos. Structures, 92(10), 2517-2524. https://doi.org/10.1016/J.COMPSTRUCT.2010.02.010.
  52. Shu, C. (2012), Differential Quadrature and Its Application in Engineering. Springer Science & Business Media.
  53. Singh, B. N., Lal, A. and Kumar, R. (2008), "Nonlinear bending response of laminated composite plates on nonlinear elastic foundation with uncertain system properties", Eng. Struct., 30(4), 1101-1112. https://doi.org/10.1016/J.ENGSTRUCT.2007.07.007.
  54. Striz, A.G., Jang, S.K. and Bert, C.W. (1988), "Nonlinear bending analysis of thin circular plates by differential quadrature", Thin-Wall. Struct., 6(1), 51-62. https://doi.org/10.1016/0263-8231(88)90025-0
  55. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of plates and shells. McGraw-hill.
  56. Ventsel, E. and Krauthammer, T. (2001), Thin plates and shells: theory: analysis, and applications. CRC press.
  57. Wang, Y.Q., Zhao, H.L., Ye, C. and Zu, J.W. (2018), "A Porous Microbeam Model for Bending and Vibration Analysis Based on the Sinusoidal Beam Theory and Modified Strain Gradient Theory", Int. J. Appl. Mech., 10(5), 1850059. https://doi.org/10.1142/S175882511850059X.
  58. Yang, J. and Shen, H.S. (2003), "Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions", Compos. Part B: Eng., 34(2), 103-115. https://doi.org/10.1016/S1359-8368(02)00083-5.
  59. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  60. Zhao, J., Choe, K., Xie, F., Wang, A., Shuai, C. and Wang, Q. (2018), "Three-dimensional exact solution for vibration analysis of thick functionally graded porous (FGP) rectangular plates with arbitrary boundary conditions", Compos. Part B: Eng., 155, 369-381. https://doi.org/10.1016/J.COMPOSITESB.2018.09.001.