Steel and Composite Structures

  • 제46권4호
  • /
  • Pages.471-483
  • /
  • 2023
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Stability investigation of symmetrically porous advanced composites plates via a novel hyperbolic RPT

  • S.R. Mahmoud (GRC Department, Applied College, King Abdulaziz University) ;
  • E.I. Ghandourah (Department of Nuclear Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • A.H. Algarni (Statistics Department, Faculty of Science, King Abdulaziz University) ;
  • M.A. Balubaid (Department of Industrial Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University) ;
  • Abdeldjebbar Tounsi (Industrial Engineering and Sustainable Development Laboratory, University of Relizane, Faculty of Science & Technology, Mechanical Engineering Department) ;
  • Fouad Bourada (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • 투고 : 2022.04.25
  • 심사 : 2023.01.02
  • 발행 : 2023.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents an analytical hyperbolic theory based on the refined shear deformation theory for mechanical stability analysis of the simply supported advanced composites plates (exponentially, sigmoidal and power-law graded) under triangular, trapezoidal and uniform uniaxial and biaxial loading. The developed model ensures the boundary condition of the zero transverse stresses at the top and bottom surfaces without using the correction factor as first order shear deformation theory. The mathematical formulation of displacement contains only four unknowns in which the transverse deflection is divided to shear and bending components. The current study includes the effect of the geometric imperfection of the material. The modeling of the micro-void presence in the structure is based on the both true and apparent density formulas in which the porosity will be dense in the mid-plane and zero in the upper and lower surfaces (free surface) according to a logarithmic function. The analytical solutions of the uniaxial and biaxial critical buckling load are determined by solving the differential equilibrium equations of the system with the help of the Navier's method. The correctness and the effectiveness of the proposed HyRPT is confirmed by comparing the results with those found in the open literature which shows the high performance of this model to predict the stability characteristics of the FG structures employed in various fields. Several parametric analyses are performed to extract the most influenced parameters on the mechanical stability of this type of advanced composites plates.

키워드

과제정보

This research work was funded by Institutional Fund Projects under grant no. (IFPHI-079-156-2020). Therefore, authors gratefully acknowledge technical and financial support from the Ministry of Education and King Abdulaziz University, Jeddah, Saudi Arabia

참고문헌

  1. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/SCS.2020.35.1.147.
  2. Akbas, S.D. (2018), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 186, 293-302. https://doi.org/10.1016/j.compstruct.2017.12.013.
  3. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2020), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14). https://doi.org/10.1177/1077546320947302.
  4. Akbas, S.D. (2019a). "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459.
  5. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115,73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  6. Avcar, M. Alsaid Alwan, H.H. (2017), "Free Vibration of Functionally Graded Rayleigh Beam", Int. J. Eng. Appl. Sci., 9(2), 127- 137. https://doi.org/10.24107/ijeas.322884.
  7. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/SCS.2019.30.6.603.
  8. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10). https://doi.org/10.1007/s12517-018-3579-2.
  9. Barati, M.R. (2017), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermomechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/SEM.2017.64.6.683.
  10. Barati, M.R. and Shahverdi, H. (2017), "Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions", J. Fluids Struct., 73, 125-136. https://doi.org/10.1016/j.jfluidstructs.2017.06.007.
  11. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. http://dx.doi.org/10.12989/sem.2018.68.6.661.
  12. Bu, G., Ou, Z., Li, Z., Liu, F., Zheng, H., Zou, X. and Xie,Y. (2022), "Static and buckling characteristics of the porous ring reinforced by graphene nanofillers", Eng. Struct., 251, Part A, 113536, https://doi.org/10.1016/j.engstruct.2021.113536.
  13. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condensed Matter., 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  14. Cuong-Le, T., Nguyen, K.D., Lee, J. Rabczuk, T. and Nguyen-Xuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnology, 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  15. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38(2022), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  16. Ebrahimi, F. and Barati, M.R. (2017a), "Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams", Wave. Random Complex Med., 28(2), 326-342. https://doi.org/10.1080/17455030.2017.1346331.
  17. Ebrahimi, F. and Barati, M.R. (2017b), "Buckling analysis of nonlocal strain gradient axially functionally graded nanobeams resting on variable elastic medium", Proceedings Institution Mech. Eng., Part C: J. Mech. Eng. Sci., 232(11), 2067-2078. https://doi.org/10.1177/0954406217713518.
  18. Ebrahimi, F. and Barati, M.R. (2018), "Hygro-thermal vibration analysis of bilayer graphene sheet system via nonlocal strain gradient plate theory", J. Brazil. Soc. Mech. Sci. Eng., 40(9). https://doi.org/10.1007/s40430-018-1350-y.
  19. Ebrahimi, F., Barati, M.R. and Civalek, O. (2019), "Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures", Eng. Comput., 36, 953-964 https://doi.org/10.1007/s00366-019-00742-z.
  20. Ebrahimi, F., Jafari, A. and Barati, M.R. (2017), "Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations", Thin-Wall. Struct., 119, 33-46. https://doi.org/10.1016/j.tws.2017.04.002.
  21. Ebrahimi, F.and Barati, M.R. (2016), "Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory". Appl. Phys., 122, 843. https://doi.org/10.1007/s00339-016-0368-1.
  22. Faleh, N. M., Ahmed, R. A. and Fenjan, R. M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  23. Fuyun, C., Jianzhang, H., Lihua, W., Zheng, Z. (2016), "Buckling analysis of functionally graded thin plate with in-plane material inhomogeneity", Eng. Anal. Bound. Elem., 65, 112-125. https://doi.org/10.1016/j.enganabound.2016.01.007.
  24. Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Physics, 122(9), 829. https://doi.org/10.1007/s00339-016-0324-0.
  25. Jana, P. and Bhaskar, K. (2006), "Stability analysis of simply-supported rectangular plates under non-uniform uniaxial compression using rigorous and approximate plane stress solutions", Thin-Wall. Struct., 44(5), 507-516. https://doi.org/10.1016/j.tws.2006.04.009.
  26. Kang, J.H. and Leissa, A.W. (2005), "Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges", Int. J. Solids Struct., 42(14), 4220-4238. https://doi.org/10.1016/j.ijsolstr.2004.12.011.
  27. Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/SCS.2015.18.3.693.
  28. Kar, V.R. and Panda, S.K. (2016a), "Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties", J. Therm. Stresses, 39(8), 942-959. https://doi.org/10.1080/01495739.2016.1188623.
  29. Kar, V.R. and Panda, S.K. (2016b), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Therm. Stresses, 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118.
  30. Kar, V.R. and Panda, S.K. (2015b), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/SEM.2015.53.4.661.
  31. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/SCS.2018.29.3.349.
  32. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. 34,3-11.
  33. Kolahchi, R, Bidgoli, A.M.M. and Heydari, M.M. (2015), "Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium", Struct Eng. Mech., 55(5), 1001-1014. https://doi.org/10.12989/SEM.2015.55.5.1001.
  34. Kumar, R., Lal, A., Singh, B.N. and Singh, J. (2018), "New transverse shear deformation theory for bending analysis of fgm plate under patch load", Compos. Struct. https://doi.org/10.1016/j.compstruct.2018.10.014.
  35. Li, Z. (2020), "Exploration of the encased nanocomposites functionally graded porous arches: Nonlinear analysis and stability behavior", Appl. Math. Model., 82, 1-16. https://doi.org/10.1016/j.apm.2020.01.037.
  36. Li, Z., Chen, Y., Zheng, J. and Sun, Q. (2020a), "Thermal-elastic buckling of the arch-shaped structures with FGP aluminum reinforced by composite graphene platelets", Thin-Wall. Struct., 157, 107142. https://doi.org/10.1016/j.tws.2020.107142.
  37. Li, Z. and Zheng, J. (2019a), "Nonlinear stability of the encased functionally graded porous cylinders reinforced by graphene nanofillers subjected to pressure loading under thermal effect", Compos. Struct., 233, 111584. https://doi.org/10.1016/j.compstruct.2019.111584.
  38. Li, Z. and Zheng, J. (2019b), "Analytical consideration and numerical verification of the confined functionally graded porous ring with graphene platelet reinforcement", Int. J. Mech. Sci., 161-162, 105079. https://doi.org/10.1016/j.ijmecsci.2019.105079.
  39. Li, Z. and Zheng, J. (2020), "Structural failure performance of the encased functionally graded porous cylinder consolidated by graphene platelet under uniform radial loading", Thin-Wall. Struct., 146, 106454. https://doi.org/10.1016/j.tws.2019.106454.
  40. Li, Z., Zheng, J., Chen, Y., Sun, Q. and Zhang, Z. (2019b), "Effect of temperature variations on the stability mechanism of the confined functionally graded porous arch with nanocomposites reinforcement under mechanical loading", Compos. Part B: Eng., 176, 107330. https://doi.org/10.1016/j.compositesb.2019.107330.
  41. Li, Z., Zheng, J. and Zhang, Z.(2019a), "Mechanics of the confined functionally graded porous arch reinforced by graphene platelets", Eng. Struct., 201, 109817. https://doi.org/10.1016/j.engstruct.2019.109817.
  42. Li, Zh., Zheng, J. and Zhang, Z. (2020b), "Thermal nonlinear performance of the porous metal cylinders with composite graphene nanofiller reinforcement encased in elastic mediums", Int. J. Mech. Sci., 181, 105698-. https://doi.org/10.1016/j.ijmecsci.2020.105698.
  43. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  44. Mahapatra, T. R., Kar, V. R., Panda, S. K. and Mehar, K. (2017), "Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stresses, 40(9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788
  45. Mijuskovic, O., Coric, B. and Scepanovic, B., (2015), "Accurate buckling Loads of Plates with different boundary Conditions under arbitrary edge compression", Int. J. Mech. Sci., 101, 309-323. https://doi.org/10.1016/j.ijmecsci.2015.07.017.
  46. Mirjavadi, S. S., Afshari, B. M., Barati, M. R. and Hamouda, A.M.S. (2018), "Transient response of porous FG nanoplates subjected to various pulse loads based on nonlocal stress-strain gradient theory", European J. Mech. - A/Solids. https://doi.org/10.1016/j.euromechsol.2018.11.004.
  47. Nguyen, T.-K. (2015). "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Materials Design., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.
  48. Ramachandra, L.S. and Panda, S.K. (2012), "Dynamic instability of composite plates subjected to non-uniform in-plane loads", J. Sound Vib., 331(1), 53-65. https://doi.org/10.1016/j.jsv.2011.08.010.
  49. Ramteke, P.M., Patel, B. and Panda, S.K. (2020a), "Time-Dependent Deflection Responses of Porous FGM Structure Including Pattern and Porosity", Int. J. Appl. Mech., 12(09), https://doi.org/10.1142/S1758825120501021.
  50. Ramteke, P.M., Mehar, K., Sharma, N. and Panda, S. (2020b), "Numerical prediction of deflection and stress responses of functionally graded structure for grading patterns (Power-law, sigmoid and exponential) and variable porosity (Even/Uneven)", Scientia Iranica, 28(2), https://doi.org/10.24200/sci.2020.55581.4290.
  51. Sedighi, H.M., Keivani, M. and Abadyan, M. (2015), "Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect", Compos. Part B: Eng., 83, 117-133. https://doi.org/10.1016/j.compositesb.2015.08.029.
  52. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/SSS.2020.26.3.361.
  53. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerospace Sci. Tech., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  54. Singh, S. J. and Harsha, S. P. (2019), "Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading", J. Mech. Sci. Tech., https://doi.org/10.1007/s12206-019-0328-8.
  55. Sofiyev, A. and Avcar, M. (2010), "The stability of cylindrical shells containing an FGM layer subjected to axial load on the pasternak foundation", Eng., 2(4), 228-236. https://doi.org/10.4236/eng.2010.24033.
  56. Sofiyev, A.H., Alizada, A.N., Akin, O., Valiyev, A., Avcar, M. and Adiguzel, S. (2011), "On the stability of FGM shells subjected to combined loads with different edge conditions and resting on elastic foundations", Acta Mechanica, 223(1), 189-204. https://doi.org/10.1007/s00707-011-0548-1.
  57. Timoshenko, S.P. (1921), "Uber die Stabilitat versteifter Platten", Eisenbau, 12, 147-163.
  58. Timoshenko, S.P. (1934), "The stability of the webs of plate girders", Eng-g. 138, 207-209.
  59. Van Vinh, P. and Huy, L.Q. (2022), "Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory", Defence Tech. 18(3), 490-508. https://doi.org/10.1016/j.dt.2021.03.006.
  60. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  61. 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.
  62. Watts, G., Kumar, R., Patel, S.N. and Singh, S. (2021), "Dynamic instability of trapezoidal composite plates under non-uniform compression using moving kriging based meshfree method", Thin-Wall. Struct., 164, 107766. https://doi.org/10.1016/j.tws.2021.107766.
  63. Xiao, X., Bu, G., Ou, Z. and Li, Z. (2022), "Nonlinear in-plane instability of the confined FGP arches with nanocomposites reinforcement under radially-directed uniform pressure", Eng. Struct., 252, 113670. https://doi.org/10.1016/j.engstruct.2021.113670.
  64. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48, 2019-2035. https://doi.org/10.1007/s11012-013-9720-0.