Advances in aircraft and spacecraft science

  • 제10권3호
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  • Pages.281-302
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  • 2023
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  • 2287-528X(pISSN)
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  • 2287-5271(eISSN)
테크노프레스 (Techno-Press)
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Bending analysis of exponentially varied FG plates using trigonometric shear and normal deformation theory

  • Sunil S. Yadav (Structural Engineering Department, Veermata Jijabai Technological Institute) ;
  • Keshav K. Sangle (Structural Engineering Department, Veermata Jijabai Technological Institute) ;
  • Mandar U. Kokane (Structural Engineering Department, Veermata Jijabai Technological Institute) ;
  • Sandeep S. Pendhari (Structural Engineering Department, Veermata Jijabai Technological Institute) ;
  • Yuwaraj M. Ghugal (Structural Engineering Department, Veermata Jijabai Technological Institute)
  • 투고 : 2023.01.25
  • 심사 : 2023.06.20
  • 발행 : 2023.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

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참고문헌

  1. Bakoura, A., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Tounsi, A., ... & Mahmoud, S.R. (2021), "Buckling analysis of functionally graded plates using HSD in conjunction with the stress function method", Comput. Concrete, 27(1), 73-83. https://doi.org/10.12989/cac.2021.27.1.073.
  2. Bennedjadi, M., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., ... & Tounsi, A. (2023), "Visco-elastic foundation effect on buckling response of exponentially graded sandwich plates under various boundary conditions", Geomech. Eng., 32(2), 159-177. https://doi.org/10.12989/gae.2023.32.2.159.
  3. Bhandari, M. and Purohit, K. (2014), "Static response of functionally graded material plate under transverse load for varying aspect ratio", Int. J. Metal., 2014, 1-11. https://doi.org/10.1155/2014/980563.
  4. Bodaghi, M. and Saidi, A.R. (2010), "Levy-type solution for buckling analysis of thick functionally graded rectangular plates based on the higher-order shear deformation plate theory", Appl. Math. Model., 34(11), 3659-3673. https://doi.org/10.1016/j.apm.2010.03.016
  5. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., ... & 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.
  6. Brischetto, S. and Carrera, E. (2010), "Advanced mixed theories for bending analysis of functionally graded plates", Comput. Struct., 88(23-24), 1474-1483. https://doi.org/10.1016/j.compstruc.2008.04.004.
  7. Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T. and Kroplin, B. (2008), "Thermo-mechanical bending of functionally graded plates", J. Therm. Stress., 31(3), 286-308. https://doi.org/10.1080/01495730701876775.
  8. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B: Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  9. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J., 46(1), 194-203. https://doi.org/10.2514/1.32490
  10. Chakraborty, A., Gopalakrishnan, S. and Reddy, J. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539 https://doi.org/10.1016/S0020-7403(03)00058-4.
  11. Chakraverty, S. and Pradhan, K.K. (2014), "Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions", Aerosp. Sci. Technol., 36, 132-156. https://doi.org/10.1016/j.ast.2014.04.005.
  12. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis", Int. J. Solid. Struct., 43(13), 3657-3674. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  13. Fazzolari, F.A. and Carrera, E. (2014a), "Refined hierarchical kinematics quasi-3D Ritz models for free vibration analysis of doubly curved FGM shells and sandwich shells with FGM core", J. Sound Vib., 333(5), 1485-1508. https://doi.org/10.1016/j.jsv.2013.10.030.
  14. Fazzolari, F.A. and Carrera, E. (2014b), "Thermal stability of FGM sandwich plates under various through-the-thickness temperature distributions", J. Therm. Stress., 37(12), 1449-1481.https://doi.org/10.1080/01495739.2014.937251.
  15. Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B: Eng., 72, 1. https://doi.org/10.1016/j.compositesb.2014.12.004.
  16. Garg, A., Belarbi, M.O., Li, L. and Tounsi, A. (2022), "Bending analysis of power-law sandwich FGM beams under thermal conditions", Adv. Aircraft Spacecraft Sci., 9(3), 243-261. https://doi.org/10.12989/aas.2022.9.3.243.
  17. Ghugal, Y.M. and Sayyad, A.S. (2013), "Stress analysis of thick laminated plates using trigonometric shear deformation theory", Int. J. Appl. Mech., 5(1). https://doi.org/10.1142/S1758825113500038.
  18. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., ... & 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.
  19. GulshanTaj, M.G., Chakrabarti, A. and Sheikh, A.H. (2013), "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.
  20. Gupta, A. and Talha, M. (2017), "Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory", Compos. Part B: Eng., 123, 241-261. https://doi.org/10.1016/j.compositesb.2017.05.010.
  21. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & 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/cac.2021.39.1.051.
  22. Hadji, M., Bouhadra, A., Mamen, B., Menasria, A., Bousahla, A.A., Bourada, F., ... & Tounsi, A. (2023), "Combined influence of porosity and elastic foundation parameters on the bending behavior of advanced sandwich structures", Steel Compos. Struct., 46(1), 1-13. https://doi.org/10.12989/scs.2023.46.1.001.
  23. Jha, D.K., Kant, T. and Singh, R.K. (2013), "Stress analysis of transversely loaded functionally graded plates with a higher order shear and normal deformation theory", J. Eng. Mech., 139(12), 1663-1680. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000601.
  24. Kant, T., Jha, D.K. and Singh, R.K. (2014), "A higher-order shear and normal deformation functionally graded plate model: Some recent results", Acta Mechanica, 225(10), 2865-2876. https://doi.org/10.1007/s00707-014-1213-2.
  25. Khan, T., Zhang, N. and Akram, A. (2019), "State of the art review of functionally graded materials" , 2019 2nd International Conference on Computing, Mathematics and Engineering Technologies (iCoMET), 1-9.
  26. Kulkarni, K., Singh, B.N. and Maiti, D.K. (2015), "Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory", Compos. Struct., 134, 147-157. https://doi.org/10.1016/j.compstruct.2015.08.060.
  27. Lu, C.F., Chen, W.Q., Xu, R.Q. and Lim, C.W. (2008), "Semi-analytical elasticity solutions for bi-directional functionally graded beams", Int. J. Solid. Struct., 45(38), 258-275. https://doi.org/10.1016/j.ijsolstr.2007.07.018.
  28. Mashat, D.S., Carrera, E., Zenkour, A.M., Al Khateeb, S.A. and Filippi, M. (2014), "Free vibration of FGM layered beams by various theories and finite elements", Compos. Part B: Eng., 59, 269-278. https://doi.org/10.1016/j.compositesb.2013.12.008.
  29. El Meiche, N., Tounsi, A., Ziane, N. and Mechab, I. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.12989/eas.2018.14.2.103.
  30. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., ... & Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
  31. Merdaci, S. and Belghoul, H. (2019), "High-order shear theory for static analysis of functionally graded plates with porosities", Comptes Rendus Mecanique, 347(3), 207-217. https://doi.org/10.1016/j.crme.2019.01.001.
  32. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  33. Na, K.S. and Kim, J.H. (2006), "Nonlinear bending response of functionally graded plates under thermal loads", J. Therm. Stress., 29(3), 245-261. https://doi.org/10.1080/01495730500360427.
  34. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  35. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos. Part B: Eng., 44(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  36. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3.
  37. Nguyen, T.K., Sab, K. and Bonnet, G. (2008), "First-order shear deformation plate models for functionally graded materials", Compos. Struct., 83 (1), 25-36. https://doi.org/10.1016/j.compstruct.2007.03.004.
  38. Pendhari, S.S., Kant, T., Desai, Y.M. and Subbaiah, C.V. (2012), "Static solutions for functionally graded simply supported plates", Int. J. Mech. Mater. Des., 8(1), 51-69. https://doi.org/10.1007/s10999-011-9175-1.
  39. Pradhan, P., Sutar, M.K. and Pattnaik, S. (2019), "A state of the art in functionally graded materials and their analysis", Mater. Today: Proc., 18, 3931-3936. https://doi.org/https://doi.org/10.1016/j.matpr.2019.07.333.
  40. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. Solid. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
  41. Reddy, J. (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)47:1/3<663::AID-NME787>3.0.CO;2-8.
  42. Saleh, B., Jiang, J., Fathi, R., Al-hababi, T., Xu, Q., Wang, L., ... & Ma, A. (2020), "30 Years of functionally graded materials: An overview of manufacturing methods, applications and future challenges", Compos. Part B: Eng., 201, 108376. https://doi.org/10.1016/j.compositesb.2020.108376.
  43. Sankar, B.V. (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0.
  44. Sayyad, A.S. and Ghugal, Y.M. (2014), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Des., 10(3), 247-267. https://doi.org/10.1007/s10999-014-9244-3.
  45. Sayyad, A.S. and Ghugal, Y.M. (2016), "Cylindrical bending of multilayered composite laminates and sandwiches", Adv. Aircraft Spacecraft Sci., 3(2), 113-148. https://doi.org/10.12989/aas.2016.3.2.113.
  46. Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 09(01), 1750007. https://doi.org/10.1142/S1758825117500077.
  47. Shahrjerdi, A., Mustapha, F., Bayat, M., Sapuan, S.M., Zahari, R. and Shahzamanian, M.M. (2011), "Natural frequency of F.G. rectangular plate by shear deformation theory", IOP Conf. Ser.: Mater. Sci. Eng., 17(1), 012008 https://doi.org/10.1088/1757-899X/17/1/012008.
  48. Srividhya, S., Kumar, B., Gupta, R.K. and Rajagopal, A. (2019), "Nonlinear analysis of FGM plates using generalised higher order shear deformation theory", Int. J. Mater. Struct. Integr., 13(1-3), 3-15. https://doi.org/10.1504/IJMSI.2019.100381.
  49. Srividhya, S., Raghu, P., Rajagopal, A. and Reddy, J. (2018), "Nonlocal nonlinear analysis of functionally graded plates using third-order shear deformation theory", Int. J. Eng. Sci., 125, 1-22. https://doi.org/10.1016/j.ijengsci.2017.12.006.
  50. Swami, S. K. and Ghugal, Y. M. (2021), "Thermoelastic bending analysis of laminated plates subjected to linear and nonlinear thermal loads", Adv. Aircraft Spacecraft Sci., 8(3), 213-237. https://doi.org/10.12989/aas.2021.8.3.213.
  51. Swaminathan, K., Naveenkumar, D. T., Zenkour, A. M. and Carrera, E. (2015), "Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review", Compos. Struct., 120, 10-31. https://doi.org/10.1016/j.compstruct.2014.09.070.
  52. Tahir, S. I., Tounsi, A., Chikh, A., Al-Osta, M. A., Al-Dulaijan, S. U. and Al-Zahrani, M. M. (2022), "The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT", Steel Compos. Struct., 42(4), 501. https://doi.org/10.12989/scs.2022.42.4.501.
  53. Woodward, B. and Kashtalyan, M. (2011), "Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates", Eur. J. Mech.-A/Solid., 30(5), 705-718. https://doi.org/10.1016/j.euromechsol.2011.04.00.
  54. Yadav, S., Damse, S., Pendhari, S., Sangle, K. and Sayyad, A.S. (2022), "Comparative studies between Semi-analytical and shear deformation theories for functionally graded beam under bending", Forc. Mech., 8, 100111. https://doi.org/10.1016/j.finmec.2022.100111.
  55. Yadav, S., Pandare, P., Pendhari, S., Sangle, K. and Ghugal, Y.M. (2023a), "Static analysis of an exponentially varying functionally graded beam using trigonometric shear deformation theory", Compos.: Mech. Comput. Appl., 14(3), 1-23. https://doi.org/10.1615/CompMechComputApplIntJ.2023047080.
  56. Yadav, S.S., Sangle, K.K., Shinde, S.A., Pendhari, S.S. and Ghugal, Y.M. (2023b), "Bending analysis of FGM plates using sinusoidal shear and normal deformation theory", Forc. Mech., 11, 100185 https://doi.org/10.1016/j.finmec.2023.100185.
  57. Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic-metal plate in a hygrothermal environment", Thin Wall. Struct., 170, 108549. https://doi.org/10.1016/j.tws.2021.108549.
  58. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solid. Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  59. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009.
  60. Zhang, H., Jiang, J.Q. and Zhang, Z.C. (2014), "Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates", Appl. Math. Mech., 35(11), 1467-1478. https://doi.org/10.1007/s10483-014-1871-7.
  61. Zhong, Y., Li, R., Liu, Y. and Tian, B. (2009), "On new symplectic approach for exact bending solutions of moderately thick rectangular plates with two opposite edges simply supported", Int. J. Solid. Struct., 46(11-12), 2506-2513. https://doi.org/10.1016/j.ijsolstr.2009.02.001.