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Finite element analysis of functionally graded sandwich plates under nonlinear sense for aerospace applications

  • GulshanTaj, M.N.A. (Department of Civil Engineering, Sona College of Technology) ;
  • Chakrabarti, Anupam (Department of Civil Engineering, Indian Institute of Technology Roorkee) ;
  • Malathy, R. (Department of Civil Engineering, Sona College of Technology) ;
  • Kumar, S.R.R. Senthil (Department of Civil Engineering, Sona College of Technology)
  • 투고 : 2020.04.15
  • 심사 : 2021.08.02
  • 발행 : 2021.11.10

초록

Owing to the increase in demand for composite materials for different applications in aircraft structures, the nonlinear response of functionally graded ceramic-metal sandwich plates under mechanical loading is studied in the present research work. Geometric nonlinearity (GNL) is considered by Green-strain components and further assumes the form of von Kármán strains. It is ascertained that the effective mechanical properties vary through the thickness direction as a function of volume fraction of ceramic and metal constituents and obeys power law equation. Higher order displacement model proposed by Reddy is incorporated in the study to arrive for 2D isoparametric finite element C0 formulation. A nine node Lagrangian element is accomplished to model the assumed plate geometry. Different thickness schemes are proposed to model the sandwich plate with graded layer as core/ face sheets. Although the model can handle thickness scheme of any kind, results are exposed for four types of symmetric sandwich plates. Comparison statement between isotropic and graded plates is drawn in each case by appropriate selection of power law exponent value. The present investigation may be useful for design engineers/researchers to arrive for particular thickness scheme based on the results, while performing large deformation analysis of functionally graded sandwich plates (FGSP).

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참고문헌

  1. Amir, S., Ghannadpour, M. and Kiani, P. (2018), "Nonlinear spectral collocation analysis of imperfect functionally graded plates under end-shortening", Struct. Eng. Mech., 66(5), 557-568. https://doi.org/10.12989/sem.2018.66.5.557.
  2. Birman, V. and Byrd, L.W. (2007), "Modeling and analysis of functionally graded materials and structures", ASME Appl. Mech. Rev., 60(5), 195-216. https://doi.org/10.1115/1.2777164.
  3. Birman, V. and Byrd, LW. (2007) "Modeling and analysis of functionally graded materials and structures", ASME Appl. Mech. Rev., 60(5), 195-216. https://doi.org/195-216.10.1115/1.2777164.
  4. Bouazza, M., Zenkour, A.M. 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. https://doi.org/10.24423/aom.2757.
  5. Bouderba, B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397.
  6. Cheng, Z.Q. (2001), "Nonlinear bending of inhomogeneous plates", Eng. Struct., 23(10), 1359-1363. https://doi.org/10.1016/S0141-0296(01)00017-7.
  7. Cook, R.D., Malkus, D.S. and Plesha, M.E. (1989), Concept and Application of Finite Element Analysis, 3rd Edition, John Wiley and Sons, NewYork, USA.
  8. Ebrahimi, F. and Heidari, E. (2018), "Thermo-elastic analysis of rotating functionally graded micro-discs incorporating surface and nonlocal effects", Adv. Aircraft Spacecraft Sci., 5(3), 295-318. https://doi.org/10.12989/aas.2018.5.3.295.
  9. Fukui, Y., Yamanaka, N. and Wakashima, K. (1993), "The stresses and strains in a thick walled tube for functionally graded material under uniform thermal loading", JSME Int. J. Ser. A, 36(4), 156-162. https://doi.org/10.1299/jsmea1993.36.2_156.
  10. Gulshan Taj, M.N.A. and Chakrabarti, A. (2013a), "Static and dynamic analysis of functionally graded skew plates", ASCE J. Eng. Mech., 139(7), 848-857. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000523.
  11. Gulshan Taj, M.N.A. and Chakrabarti, A. (2013b), "Dynamic response of functionally graded skew shell panel", Lat. Am. J. Solid. Struct., 10(6), 1243-1266. https://doi.org/10.1590/S1679-78252013000600009.
  12. Gulshan Taj, M.N.A., Chakrabarti, A. and Sheikh, A.H. (2013c), "Analysis of functionally graded plates using higher order shear deformation theory", Appl. Math. Model., 37(18-19), 8484-8494. https://doi.org/10.1016/j.apm.2013.03.058.
  13. Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I. and Addabedia, E.A. (2011), "Free vibration of functionally graded sandwich plates using four-variable refined plate theory", App. Math. and Mech. 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9.
  14. Han, X. and Liu, G.R. (2002), "Effects of SH waves in a functionally graded plate", Mech. Res. Commun. 29(5), 327-338. https://doi.org/10.1016/S0093-6413(02)00316-6.
  15. Lal, A., Jagtap, K.R. and Singh, B.N. (2017), "Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Comput. Des., 2(3), 165-193. https://doi.org/10.12989/acd.2017.2.3.165.
  16. Ma, L.S. and Wang T.J. (2003), "Nonlinear bending and postbuckling of a functionally graded circular plate under mechanical and thermal loadings", Int. J. Solid. Struct., 40(13-14), 3311-3330. https://doi.org/10.1016/S0020-7683(03)00118-5.
  17. Nikbakhta, S., Jedari Salami, S. and Shakeri, M. (2019), "A 3D full layer-wise method for yield achievement in Functionally Graded Sandwich Plates with general boundary conditions", Eur. J. Mech. A/Solid., 75, 330-347. https://doi.org/10.1016/j.euromechsol.2019.02.011.
  18. Noda, N. (1991), "Thermal stresses in materials with temperature-dependent properties", Appl. Mech. Rev., 44(9), 383-397. https://doi.org/10.1115/1.3119511.
  19. Oatao, Y., Tanigawa, Y. and Ishimaru, O. (2000), "Optimization of material composition of functionally graded plate for thermal stress relaxation using a genetic algorithm", J. Therm. Stress., 23(3), 257-271. https://doi.org/10.1080/014957300280434.
  20. Ootao, Y. and Tanigawa, Y. (1999), "Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating", J. Therm. Stress., 22(1), 35-55. https://doi.org/10.1080/014957399281048.
  21. Ootao, Y. and Tanigawa, Y. (2005), "Three-dimensional solution for transient thermal stresses of functionally graded rectangular plate due to nonuniform heat supply", Int. J. Mech. Sci., 47(11), 1769-1788.10.1016/j.ijmecsci.2005.06.003.
  22. Pica, A., Wood, R.D. and Hinton, E. (1979), "Finite element analysis of geometrically nonlinear plate behavior using a Mindlin formulation", Comput. Struct., 11(3), 203-215. https://doi.org/10.1016/0045-7949(80)90160-1.
  23. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35(33), 4457-4471. https://doi.org/10.1016/S0020-7683(97)00253-9.
  24. Qian, L.F. and Batra, R.C. (2004), "Transient thermoelastic deformations of a thick functionally graded plate", J. Therm. Stress., 27(8), 705-740. https://doi.org/10.1080/01495730490440145.
  25. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plate", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  26. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47.
  27. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165.
  28. Reddy, J.N., Wang, C.M. and Kitipornchai, S. (1999), "Axisymmetric bending of functionally graded circular and annular plates", Eur. J. Mech. A/Solid., 18(2), 185-199. https://doi.org/10.1016/S0997-7538(99)80011-4.
  29. Rouzegar, J. and Gholami, M. (2014), "Thermo-elastic bending analysis of functionally graded sandwich plates by hyperbolic shear deformation theory", Sci. Iranica, 22(2), 561-577. https://doi.org/10.1007/s00419-019-01621-1.
  30. Shen, H.S. and Wang, Z.X. (2010), "Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations", Compos. Struct., 92(10), 2517-2524. https://doi.org/10.1016/j.compstruct.2010.02.010.
  31. Singh, V.D., Jadvani, N. and Kalita, K. (2018), "Stress and strain analysis of functionally graded plates with circular cutout", Adv. Mater. Res., 5(2), 81-92. https://doi.org/10.12989/amr.2016.5.2.081.
  32. Suresh, S. and Mortensen, A. (1998), Fundamentals of Functionally Graded Materials, 1st Edition, IOM Communications Limited, London, UK.
  33. Talha, M. and Ashokkumar, C.R. (2014), "Structural kinematics based damage zone prediction in gradient structures using vibration database", Int. J. Comput. Mater., 3(2), 1450007. https://doi.org/10.1142/S2047684114500079.
  34. Woo, J. and Meguid, S.A. (2001), "Nonlinear analysis of functionally graded plates and shallow shells", Int. J. Solid. Struct., 38(42-43), 7409-7421. https://doi.org/10.1016/S0020-7683(01)00048-8.
  35. Woodward, B. and Kashtalyan, M. (2011), "3D elasticity analysis of sandwich panels with graded core under distributed and concentrated loadings", Int. J. Mech. Sci., 53(10), 872-885. https://doi.org/10.1016/j.ijmecsci.2011.07.011.
  36. Yang, J. and Shen, H.S. (2003a), "Non-linear analysis of FGM plates under transverse and in-plane loads", Int. J. Nonlin. Mech., 38(4), 467-482. https://doi.org/10.1016/S0020-7462(01)00070-1.
  37. Yang, J. and Shen, H.S. (2003b), "Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions", Compos. Part B, 34(2), 103-115. https://doi.org/10.1016/S1359-8368(02)00083-5.
  38. Ye, R., Zhao, N., Yang, D., Cui, J., Gaidai, O. and Ren, P. (2020), "Bending and free vibration analysis of sandwich plates with functionally graded soft core, using the new refined higher-order analysis model", J. Sandw. Struct. Mater., 23(2), 680-710. https://doi.org/10.1177/1099636220909763.
  39. Zenkour, A.M. and Aljadani, M.H. (2018), "Mechanical buckling of functionally graded plates using a refined higher-order shear and normal deformation plate theory", Adv. Aircraft Spacecraft Sci., 5(6), 615-632. https://doi.org/10.12989/aas.2018.5.6.615.