Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Deflection and bending characteristics of embedded functionally graded porous plate with bi-directional thickness variation subjected to bi-sinusoidal loading

  • Rajat Jain (Department of Mechanical Engineering, Indian Institute of Technology (ISM) Dhanbad) ;
  • Mohammad Sikandar Azam (Department of Mechanical Engineering, Indian Institute of Technology (ISM) Dhanbad)
  • Received : 2023.02.02
  • Accepted : 2024.06.03
  • Published : 2024.06.25
⟨ Previous Next ⟩

Abstract

This work aims to explore the static behaviour of a tapered functionally graded porous plate (FGPP) with even and uneven porosity distributions resting on two parametric elastic foundations. The plate under investigation is subjected to bi-sinusoidal loading and the edges of the plate are exposed to different combinations of edge restrictions. In order to examin the static behaviour, bending factors (BF) related to bending and normal stresses have been evaluated using classical plate theory. To achieve this, the governing equations have been derived employing the energy concept. And to solve it, the Rayleigh-Ritz method with an algebraic function has been utilised; it is simple, precise, and computationally intensive. After convergence and validation analyses, new findings are made available. The BF of the plate have been exhaustively examined to explain the influence of aspect ratios, material property index, porosity factor, taper factor, and Winkler and Pasternak stiffness. It is observed that the BF of an elastically supported FGPP are influenced by the index of material propery and the aspect ratio. Findings also indicate that the impact of porosity is more when it is spread evenly, as opposed to when it is unevenly distributed. Further, the deformed plate's structure is significantly influenced by the different thickness variations. Examination of bending characteristics of FGPP having different new cases of thickness variations with different types of porosity distribution under fifteen different mixed edge constraints is the prime novality of this work. Results presented are reliable enough to be taken into account for future studies.

Keywords

References

  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. Allel, M., Mohamed, A. and Ahmed, B. (2013), "Stability condition for the evaluation of damage in three-point bending of a laminated composite", Steel Compos. Struct., 15(2), 203-220. https://doi.org/10.12989/scs.2013.15.2.203.
  3. Amar, L.H.H., Kaci, A., Yeghnem, R. and Tounsi, A. (2018), "A new four-unknown refined theory based on modified couple stress theory for size-dependent bending and vibration analysis of functionally graded micro-plate", Steel Compos. Struct,, 26(1), 89-102. https://doi.org/10.12989/scs.2018.26.1.089.
  4. Asemi, K., Salehi, M. and Sadighi, M. (2014), "Three dimensional static and dynamic analysis of two dimensional functionally graded annular sector plates", Struct. Eng. Mech., 51(6), 1067-1089. https://doi.org/10.12989/sem.2014.51.6.1067.
  5. Bai, L., Gong, C., Chen, X., Sun, Y., Xin, L., Pu, H., Peng, Y. and Luo, J. (2020), "Mechanical properties and energy absorption capabilities of functionally graded lattice structures: Experiments and simulations", Int. J. Mech. Sci., 182, 105735. https://doi.org/10.1016/j.ijmecsci.2020.105735.
  6. Bekkaye, T.H.L., Fahsi, B., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2020), "Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory", Comput. Concrete, 26(5), 439-450. https://doi.org/10.12989/cac.2020.26.5.439.
  7. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123.
  8. Benscoter, S.U. (1944), "A Symmetrically loaded base slab on an elastic foundation", Transact. Amer. Soc. Civil Eng., 109(1), 763-776. https://doi.org/10.1061/TACEAT.0005687.
  9. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F., Tounsi, A., Ghazwani, M.H. and Mahmoud, A.S. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821.
  10. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Adda Bedia, E.A. and Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
  11. Bouamoud, A. (2019), "Thermomechanical bending investigation of FGM sandwich plates using four shear deformation plate theory", Steel Compos. Struct., 32(5), 611-632. https://doi.org/10.12989/scs.2019.32.5.611.
  12. Bouderba, B. (2018), "Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory", Steel Compos. Struct., 27(3), 311-325. https://doi.org/10.12989/scs.2018.27.3.311.
  13. Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T. and Kroplin, B. (2008), "Thermo-mechanical bending of functionally graded plates", J. Thermal Stresses, 31(3), 286-308. https://doi.org/10.1080/01495730701876775.
  14. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  15. Chen, C.-S. (2005), "Nonlinear vibration of a shear deformable functionally graded plate", Compos. Struct., 68(3), 295-302. https://doi.org/10.1016/j.compstruct.2004.03.022.
  16. Civalek, O. and Emsen, E. (2009), "Discrete singular convolution method for bending analysis of Reissner/Mindlin plates using geometric transformation", Steel Compos. Struct., 9(1), 59-75. https://doi.org/10.12989/scs.2009.9.1.059.
  17. Civalek, O. and Yavas, A. (2006), "Large deflection static analysis of rectangular plates on two parameter elastic foundations", Int. J. Sci. Technol., 1(1), 43-50. https://doi.org/10.1299/jsmea.44.483.
  18. Di Sciuva, M. and Sorrenti, M. (2021), "Bending and free vibration analysis of functionally graded sandwich plates: An assessment of the Refined Zigzag Theory", J. Sandw. Struct. Mater., 23(3), 760-802. https://doi.org/10.1177/1099636219843970.
  19. Do, N.-T. and Pham, Q. H. (2023), "Nonlinear static analysis of functionally graded porous sandwich plates resting on Kerr foundation", Mech. Adv. Mater. Struct., 1-14. https://doi.org/10.1080/15376494.2023.2218845.
  20. Ferreira, A.J.M., Batra, R.C., Roque, C.M.C., Qian, L.F. and Martins, P. (2005), "Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method", Compos. Struct., 69(4), 449-457. https://doi.org/10.1016/j.compstruct.2004.08.003.
  21. Filonenko-Borodich, M.M. (1940), "Some approximate theories of elastic foundation", Uchenyie Zapiski Moskovkogo Gosudarstuennogo Universiteta Mekhanika, Moscow, 46, 3-18. https://cir.nii.ac.jp/crid/1582824500340875904.
  22. Ghorbanpour Arani, A., Khani, M. and Khoddami Maraghi, Z. (2018), "Dynamic analysis of a rectangular porous plate resting on an elastic foundation using high-order shear deformation theory", J. Vib. Control, 24(16), 3698-3713. https://doi.org/10.1177/1077546317709388.
  23. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., Hussain, M. and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
  24. Gupta, A. and Talha, M. (2015), "Recent development in modeling and analysis of functionally graded materials and structures", Progress Aeros. Sci., 79, 1-14. https://doi.org/10.1016/j.paerosci.2015.07.001.
  25. Gupta, S. and Chalak, H.D. (2022), "Bending and free vibration analysis of FG sandwich beams using higher-order zigzag theory", Steel Compos. Struct., 45(4), 483-499. https://doi.org/10.12989/SCS.2022.45.4.483.
  26. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051.
  27. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/scs.2017.25.6.717.
  28. 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.
  29. Hamzehkolaei, N.S., Malekzadeh, P. and Vaseghi, J. (2011), "Thermal effect on axisymmetric bending of functionally graded circular and annular plates using DQM", Steel Compos. Struct., 11(4), 341-358. https://doi.org/10.12989/scs.2011.11.4.341.
  30. Hetenyi, M. (1950), "A general solution for the bending of beams on an elastic foundation of arbitrary continuity", J. Appl. Phys., 21(1), 55-58. https://doi.org/10.1063/1.1699420.
  31. Jain, R. and Azam, M.S. (2023), "Static behaviour of elastically supported transversely inhomogeneous porous functionally graded plate with different thickness variations under a variety of external loadings", Mech. Based Des. Struct. Machines, 52(07), 4098-4132. https://doi.org/10.1080/15397734.2023.2219740.
  32. Jain, R., Azam, M.S. and Singh, P.P. (2024), "Bending analysis of functionally graded plates resting on elastic foundation: A Rayleigh-Ritz approach and ANN method", Mech. Adv. Mater. Struct., 1-19. https://doi.org/10.1080/15376494.2024.2307474.
  33. Kaci, A., Tounsi, A. and Bakhti, K. (2012), "Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates", Steel Compos. Struct., 12(6), 491-504. https://doi.org/10.12989/scs.2012.12.6.491.
  34. Keddouri, A., Hadji, L. and Tounsi, A. (2019), "Static analysis of functionally graded sandwich plates with porosities", Adv. Mater. Res., 8(3), 155-177. https://doi.org/10.12989/amr.2019.8.3.155.
  35. Kerr, A.D., (1964), "Elastic and viscoelastic foundation models'". https://doi.org/10.1115/1.3629667
  36. Kumar, R. and Khare, S. (2022), "Effect of uniform and nonuniform porosity on free vibration of functionally graded circular plate", Int. J. Comput. Mater. Sci. Eng., 2250001. https://doi.org/10.1142/S2047684122500014.
  37. Kumar, R., Lal, A., Singh, B.N. and Singh, J. (2020), "Non-linear analysis of porous elastically supported FGM plate under various loading", Compos. Struct., 233, 111721. https://doi.org/10.1016/j.compstruct.2019.111721.
  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. Naghavi, M., Sarrami-Foroushani, S. and Azhari, F. (2022), "Bending analysis of functionally graded sandwich plates using the refined finite strip method", J. Sandw. Struct. Mater., 24(1), 448-483. https://doi.org/10.1177/10996362211020448.
  40. Nguyen, T.-K., Thai, T. and Vo, T. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., 18, 91-120. https://doi.org/10.12989/scs.2015.18.1.091.
  41. Pasternak, P.L. (1954), "Fundamentals of a new method of analyzing structures on an elastic foundation by means of two foundation moduli", Proceedings of the Gosudarstvennoe Izdatelstro Liberaturi Po Stroitelstvui Arkhitekture, 4-7. https://cir.nii.ac.jp/crid/1583950399307292288.
  42. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations", Comput. Concrete, 25(4), 311-325. https://doi.org/10.12989/cac.2020.25.4.311.
  43. Rizov, V.I. (2018), "Nonlinear delamination analysis of Mulyilayered functionally graded circular shafts in torsion", J. Appl. Mech. Technical Phys., 59(6), 1104-1110. https://doi.org/10.1134/S0021894418060160.
  44. Sah, S.K. and Ghosh, A. (2022), "Effect of porosity on the thermal buckling analysis of power and sigmoid law functionally graded material sandwich plates based on sinusoidal shear deformation theory", Int. J. Struct. Stab. Dyn., 22(05), 2250063. https://doi.org/10.1142/S0219455422500638.
  45. Swaminathan, K. and Sangeetha, D.M. (2017), "Thermal analysis of FGM plates-A critical review of various modeling techniques and solution methods", Compos. Struct., 160, 43-60. https://doi.org/10.1016/j.compstruct.2016.10.047.
  46. Taskin, V. and Demirhan, P.A. (2021), "Static analysis of simply supported porous sandwich plates", Struct. Eng. Mech., 77(4), 549-557. https://doi.org/10.12989/sem.2021.77.4.549.
  47. Tash, F.Y. and Bahram N.N. (2020), "An analytical solution for bending of transversely isotropic thick rectangular plates with variable thickness", Appl. Mathem. Modelling, 77, 1582-1602. https://doi.org/10.1016/j.apm.2019.08.017.
  48. Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  49. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "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", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511
  50. Udupa, G., Rao, S. S. and Gangadharan, K. V. (2014), "Functionally graded composite materials: An overview", Procedia Materials Science, 5, 1291-1299. https://doi.org/10.1016/j.mspro.2014.07.442.
  51. Vinh, P.V. (2022), "Analysis of bi-directional functionally graded sandwich plates via higher-order shear deformation theory and finite element method", J. Sandw. Struct. Mater., 24(2), 860-899. https://doi.org/10.1177/10996362211025811.
  52. Watari, F., Yokoyama, A., Omori, M., Hirai, T., Kondo, H., Uo, M. and Kawasaki, T. (2004), "Biocompatibility of materials and development to functionally graded implant for bio-medical application", Compos. Sci. Technol., 64(6), 893-908. https://doi.org/10.1016/j.compscitech.2003.09.005.
  53. Winkler, E. (1867), "Theory of elasticity and strength", Prague: Dominicus.
  54. Wu, C.-P. and Yu, L.-T. (2018), "Quasi-3D static analysis of two-directional functionally graded circular plates", Steel Compos. Struct., 27(6), 789-801. https://doi.org/10.12989/scs.2018.27.6.789.
  55. Wu, H., Yang, J. and Kitipornchai, S. (2020), "Mechanical analysis of functionally graded porous structures: A review", Int. J. Struct. Stab. Dyn., 20(13), 2041015. https://doi.org/10.1142/S0219455420410151.
  56. Yin, Z., Gao, H. and Lin, G. (2021), "Bending and free vibration analysis of functionally graded plates made of porous materials according to a novel the semi-analytical method", Eng. Anal. Bound. Elements, 133, 185-199. https://doi.org/10.1016/j.enganabound.2021.09.006.
  57. Zarga, D. (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.
  58. Zenkour, A.M. (2020), "Quasi-3D refined theory for functionally graded porous plates: Displacements and stresses", Phys. Mesomech., 23(1), 39-53. https://doi.org/10.1134/S1029959920010051.
  59. Zenkour, A.M. and Radwan, A.F. (2018), "Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory", Archives Civil Mech. Eng., 18(2), 645-658. https://doi.org/10.1016/j.acme.2017.10.003.
  60. Zenkour, A.M. (2003), "An exact solution for the bending of thin rectangular plates with uniform, linear, and quadratic thickness variations", Int. J. Mech. Sci., 45(2), 295-315. https://doi.org/10.1016/S0020-7403(03)00050-X.
  61. Zine, A., Bousahla, A.A., Bourada, F., Benrahou, K.H., Tounsi, A., Bedia, E.A., Mahmoud, S.R. and Tounsi, A. (2020), "Bending analysis of functionally graded porous plates via a refined shear deformation theory", Comput. Concrete, 26(1), 63-74. https://doi.org/10.12989/cac.2020.26.1.063.