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Neutral surface-based static and free vibration analysis of functionally graded porous plates

  • J.R. Cho (Department of Naval Architecture and Ocean Engineering, Hongik University)
  • Received : 2023.03.25
  • Accepted : 2023.10.25
  • Published : 2023.11.25
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Abstract

The functionally graded (FG) porous plates are usually characterized by the non-symmetric elastic modulus distribution through the thickness so that the plate neutral surface does not coincide with the mid-surface. Nevertheless, the conventional analysis models were mostly based on the plate mid-surface so that the accuracy of resulting numerical results is questionable. In this context, this paper presents the neutral surface-based static and free vibration analysis of FG porous plates and investigates the differences between the mid- and neutral surface-based analysis models. The neutral surface-based numerical method is formulated using the (3,3,2) hierarchical model and approximated by the last introduced natural element method (NEM). The volume fractions of metal and ceramic are expressed by the power-law function and the cosine-type porosity distributions are considered. The proposed numerical method is demonstrated through the benchmark experiment, and the differences between two analysis models are parametrically investigated with respect to the thickness-wise material and porosity distributions. It is found from the numerical results that the difference cannot be negligible when the material and porosity distributions are remarkably biased in the thickness direction.

Keywords

Acknowledgement

This work was supported by 2023 Hongik University Research Fund. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1100924, RS-2023-00240618).

References

  1. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Comput. Mech., 3(3), 199-207. https://doi.org/10.22055/jacm.2017.21540.1107.
  2. Babuska, I., Szabo, B.A. and Actis, R.L. (1992), "Hierarchical models for laminated composites", Int. J. Numer. Methods Engng., 33, 503-535. https://doi.org/10.1016/j.ijmecsci.2013.06.007.
  3. Chami, G.B.M., Kahil, A., Hadji, L., Madan, R. and Tounsi, A. (2023), "Free vibration analysis of multi-directional porous functionally graded sandwich plates", Steel Compos. Struct., 46(2), 263-277. https://doi.org/10.12989/scs.2023.46.2.263.
  4. 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.
  5. Cho, J.R. (2020), "Natural element approximation of hierarchical models of plate-like elastic structures", Finite. Elem. Anal. Des., 180, 103439. https://doi.org/10.1016/j.finel.2020.103439.
  6. Cho, J.R. (2021), "Level-wise strain recovery and error estimation for natural element hierarchical plate models", Int. J. Numer. Methods Engng., 122(12), 3120-3136. https://doi.org/10.1002/nme.6659.
  7. Cho, J.R. and Ha, D.Y. (2002) "Optimal tailoring of 2D volume-fraction distributions for heat-resisting functionally graded materials using FDM", Comput. Meth. Appl. Mech. Engrg., 191(29-30), 3195-3211. https://doi.org/10.1016/S0045-7825(02)00256-6.
  8. Cho, J.R. and J.T. Oden, J.T. (1997), "Locking and boundary layer in hierarchical models for thin elastic structures", Comput. Meth. Appl. Mech. Engrg., 149, 33-48. https://doi.org/10.1016/S0045-7825(97)00057-1.
  9. Cho, J.R. and Lee, H.W. (2006), "A Petrov-Galerkin natural element method securing the numerical integration accuracy", J. Mech. Sci. Technol., 20(1), 94-109. https://doi.org/10.1007/BF02916204.
  10. Cho, J.R. and Oden, J.T. (1996), "A priori modeling error estimates of hierarchical models or elasticity problems for plate- and shell-like structures", Math. Comput. Model., 23(10), 117-133. https://doi.org/10.1016/0895-7177(96)00058-1.
  11. Dat, N.D., Quan, T.Q. and Duc, N.D. (2021), "Nonlinear thermal dynamic buckling and global optimization of smart sandwich plate with porous homogeneous core and carbon nanotube reinforced nanocomposite layers", Euro. J. Mech. A Solids, 90, 104351. https://doi.org/10.1016/j.euromechsol.2021.104351.
  12. Dat, P.T., Thom, D.V. and Luat, D.T. (2016), "Free vibration of functionally graded sandwich plates with stiffners based on the third-order shear deformation theory", Viet. J. Mech., 38(2), 103-122. https://doi.org/10.15625/0866-7136/38/2/6730.
  13. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. Part B Eng., 160, 661-676. https://doi.org/10.1016/j.compositesb.2018.12.020.
  14. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40, 141. https://doi.org/10.1007/s40430-018-1065-0.
  15. Foroutan, K. and Dai, L. (2022), "Post-buckling analysis of sandwich FG porous cylindrical shells with a viscoelstic core", Steel Compos. Struct., 45(3), 349-367. https://doi.org/10.12989/scs.2022.45.3.349.
  16. Jha, D.K., Kant, T. and Singh, R.K (2013), "A critical review of recent research on functionally graded pates", Compos. Struct., 96, 833-849. https://doi.org/10.1016/j.compstruct.2012.09.001.
  17. Ji, S., Gu, Q. and Xia, B. (2006), "Porosity dependence of mechanical properties of solid materials", J. Mater. Sci., 41(6), 1757-1768. https://doi.org/10.1007/s10853-006-2871-9.
  18. Kieback, B., Neubrand, A. and Riedel, H. (2003), "Processing techniques for functionally graded materials", Mater. Sci. Eng. A, 362, 81-105. https://doi.org/10.1016/S0921-5093(03) 00578-1.
  19. Kim, J.S., 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, 89-888. https://doi.org/10.1016/j.compstruct.2018.11.023.
  20. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  21. Liu, G.R., Han, X. and Lam, K.Y. (2001), "Material characterization of FGM plates using elastic waves and an inverse procedure", J. Compos. Mater., 35(11), 954-971. https://doi.org/10.1106/86AQ-JY72-5VKT-K.
  22. Mohamed, S., Assie, A.E., Mohamed, N. and Eltaher, M.A. (2022), "Static and stress analyses of bi0directional FG porous plate using unified higher order kinematics theories", Steel Compos. Struct., 45(3), 305-330. https://doi.org/10.12989/SCS.2022.45.3.305
  23. Muller, P., Mognol, P. and Hascoet, J.Y. (2013), "Modeling and control of a direct laser powded deposition process for functionally graded materials (FGM) parts manufacturing", J. Mater. Process. Technol., 21(5), 685-692. https://doi.org/10.1016/j.jmatprotec.2012.11.020.
  24. Naebe, M. and Shirvanimoghaddam, K. (2016), "Functionally graded materials: A review of fabrication and properties", Appl. Mater. Today, 5, 223-245. https://doi.org/10.1016/j.apmt.2016.10.001.
  25. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mech. A/Solids 18(2), 185-199. https://doi.org/10.1016/ S0997-7538(99)80011-4.
  26. Shahverdi, H. and Barati, M.R. (2017) "Vibration analysis of porous functionally graded nanoplates", Int. J. Eng. Sci., 120, 82-99. https://doi.org/10.22055/jacm.2017.21540.1107.
  27. Stein, E. and Ohnimus, S. (1996) "Dimensional adaptivity in linear elasticity with hierarchical test-spaces for h- and p-refinement processes", Eng. Comput., 12, 107-119. https://doi.org/10.1007/BF01299396.
  28. Sukumar, N., Moran, B. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Methods Engng., 43, 839-887. https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<839::AID-NME423>3.0.CO;2-R.
  29. Thai, H.T. and Kim, S.E. (2013), "Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation", Int. J. Mech. Sci., 75, 34-44. https://doi.org/10.1016/j.ijmecsci.2013.06.007.
  30. Thai, H.T. and Kim, S.E. (2015) "A review of theories for the modeling and analysis of functionally graded plates and shells", Compos. Struct., 128, 70-86. https://doi.org/10.1016/j.compstruct.2015.03.010.
  31. Van Do, T., Doan, D.H., Tho, N.C. and Duc, N.D. (2022), "Thermal buckling analysis of cracked functionally graded plates", Int. J. Struct. Stab. Dyn., 22(08), 2250089. https://doi.org/ 10.1142/S0219455422500894.
  32. Van Do, T., Pham, V.V. and Nguyen, H.N. (2020), "On the development of refined plate theory for static bending behavior of functionally graded plates", Math. Prob. Eng., 2020, 2836763. https://doi.org/10.1155/2020/2836763.
  33. Vinh, P.V., Chinh, N.V. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech. A/Solids, 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743.
  34. 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.
  35. Xavior, M.A., Nishanth, D., Navin Kumar, N. and Jeyapandiarajan, P. (2020), "Symthesis and testing of FGM made of ABS plastic material", Mater. Today, 22(4), 1838-1844. https://doi.org/ 10.1016/j.matpr.2020.03.018.
  36. 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. Boundary Elem., 133, 185-199. https://doi.org/10.1016/j.enganabound.2021.09.006.
  37. 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.
  38. Zhu, J.C., Lai, Z.H., Jeon, J. and Lee, S. (2001) "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1-3), 130135. https://doi.org/10.1016/S0254-0584(00)00355-2.
  39. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells," Int. J. Numer. Methods Engng., 3(2), 275-290. https://doi.org/10.1002/nme.1620030211.