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Thermomechanical behavior of Macro and Nano FGM sandwich plates

  • Soumia, Benguediab (Department of Civil Engineering and Hydraulic, Faculty of Technology, University of Saida) ;
  • Tayeb, Kebir (Department of Technical Sciences Center University Salhi Ahmed) ;
  • Fatima Zohra, Kettaf (Department of Mechanical Engineering, University of Sciences and Technology Mohamed Boudiaf Oran) ;
  • Ahmed Amine, Daikh (Department of Technical Sciences Center University Salhi Ahmed) ;
  • Abdelouahed, Tounsi (Laboratory of Materials and Hydrology, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Mohamed, Benguediab (Laboratory of Materials and Reactive Systems, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Mohamed A., Eltaher (Faculty of Engineering, Mechanical Design and Production Dept, Zagazig University)
  • Received : 2022.08.14
  • Accepted : 2023.01.25
  • Published : 2023.01.25
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Abstract

In this work, the static behavior of FGM macro and nano-plates under thermomechanical loading. Equilibrium equations are determined by using virtual work principle and local and non-local theory. The novelty of the current model is using a new displacement field with four variables and a warping function considering the effect of shear. Through this analysis, the considered sandwich FGM macro and nanoplates are a homogeneous core and P-FGM faces, homogeneous faces and an E-FGM core and finally P-FGM faces and an E-FGM core. The analytical solution is obtained by using Navier method. The model is verified with previous published works by other models and very close results are obtained within maximum 1% deviation. The numerical results are performed to present the influence of the various parameters such as, geometric ratios, material index as well as the scale parameters are investigated. The present model can be applicable for sandwich FG plates used in nuclear, aero-space, marine, civil and mechanical applications.

Keywords

References

  1. Abbas, S., Benguediab, S., Draiche, K., Bakora, A. and Benguediab, M. (2020), "An efficient shear deformation theory with stretching effect for bending stress analysis of laminated composite plates", Struct. Eng. Mech., 74(3), 365-380. https://doi.org/10.12989/sem.2020.74.3.001.
  2. Abdelrahman, A.A., Esen, I. and Eltaher, M.A. (2021c), "Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment", Appl. Math. Comput., 407, 126307. https://doi.org/10.1016/j.amc.2021.126307.
  3. Abdelrahman, A.A., Esen, I., Ozarpa, C. and Eltaher, M.A. (2021a), "Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory", Appl. Math. Model., 96, 215-235. https://doi.org/10.1016/j.apm.2021.03.008.
  4. Abdelrahman, A.A., Esen, I., Ozarpa, C., Shaltout, R., Eltaher, M.A. andAssie, A.E. (2021b), "Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory", Smart Struct. Syst., 28(4), 515-533. https://doi.org/10.12989/sss.2021.28.4.515.
  5. Aifantis, E.C. (1999), "Gradient deformation models at nano, micro, and macro scales", J. Eng. Mater. Technol.-Trans., ASME, 121(2), 189-202. https://doi.org/10.1115/1.2812366.
  6. Alazwari, M.A., Eltaher, M.A. and Abdelrahman, A.A. (2022a), "On bending of cutout nanobeams based on nonlocal strain gradient elasticity theory", Steel Compos. Struct., 43(6), 707-723. https://doi.org/10.12989/scs.2022.43.6.707.
  7. Alazwari, M.A., Essen, I., Abdraboh, M.A., Abdelrahman, A.A. and Eltaher, M.A. (2022b), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load", Adv. Nano Res., 12(3), 231-251. https://doi.org/10.12989/anr.2022.12.3.231.
  8. Ameur M., Tounsi A., Mechab I. and Adda Bedia E.A. (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15(8), 1405-1414. https://doi.org/10.1007/s12205-011-1361-z.
  9. Assie, A.E., Mohamed, S.M., Shanab, R.A., Abo-bakr, R.M. and Eltaher, M.A. (2023), "Static buckling of 2D FG porous plates resting on elastic foundation based on unified shear theories", J. Appl. Comput. Mech., 9(1), 239-258. https://doi.org/10.22055/jacm.2022.41265.3723.
  10. Attia, M.A., Melaibari, A., Shanab, R.A. and Eltaher, M.A. (2022), "Dynamic analysis of sigmoid bidirectional FG microbeams under moving load and thermal load: Analytical laplace solution", Math., 10(24), 4797. https://doi.org/10.3390/math10244797.
  11. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3-unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103.
  12. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063.
  13. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017b), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  14. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0.
  15. Bensaid, I., Daikh, A.A. and Drai, A. (2020), "Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects", J. Mech. Eng. Sci., 234(18), 3667-3688. https://doi.org/10.1177/0954406220916481.
  16. Besseghier, A., Heireche, H., Bousahla, A.A., Tounsi, A. and Benzair, A. (2015), "Nonlinear vibration properties of a zigzag single-walled carbon nanotube embedded in a polymer matrix", Adv. Nano Res., 3(1), 29-37. http://doi.org/10.12989/anr.2015.3.1.029.
  17. Besseghier, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory", Smart Struct. Syst., 19(6), 601-614. https://doi.org/10.12989/sss.2017.19.6.601.
  18. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  19. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  20. Daikh, A., Bensaid, I. and Zenkour, A.M. (2020), "Temperature dependent thermomechanical bending response of functionally graded sandwich plates", Eng. Res. Expr., 2(1), 015006. https://doi.org/10.1088/2631-8695/ab638c.
  21. Daikh, A., Guerroudj, M., El Adjrami, M. and Megueni, A. (2020). "Thermal buckling of functionally graded sandwich beams", Adv. Mater. Res., 1156, 43-59. https://doi.org/10.4028/www.scientific.net/amr.1156.43.
  22. Daikh, A.A. and Zenkour, A. (2020), "Bending of functionally graded sandwich nanoplates resting on pasternak foundation under different boundary conditions", J. Appl. Comput. Mech., 6, 1245-1259. https://doi.org/10.22055/jacm.2020.33136.2166.
  23. Daikh, A.A., Houari, M.S.A. and Eltaher, M.A. (2021), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 262, 113347. https://doi.org/10.1016/j.compstruct.2020.113347.
  24. Dastjerdi, S. and Akgoz. B. (2018), "New static and dynamic analyses of macro and nano FGM plates using exact three-dimensional elasticity in thermal environment", Compos. Struct., 192, 626-641. https://doi.org/0.1016/j.compstruct.2018.03.058. 1016/j.compstruct.2018.03.058
  25. Dean, J., Fallah, A.S., Brown, P.M., Louca, L.A. and Clyne, T.W. (2011), "Energy absorption during projectile perforation of lightweight sandwich panels with metallic fibre cores", Compos. Struct., 93(3), 1089-1095. https://doi.org/10.1016/j.compstruct.2010.09.019.
  26. Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.
  27. Eltaher, M.A., Abdraboh, A.M. and Almitani, K.H. (2018), "Resonance frequencies of size dependent perforated nonlocal nanobeam", Microsyst. Technol., 24(9), 3925-3937. https://doi.org/10.1007/s00542-018-3910-6.
  28. Eltaher, M.A., Khater, M.E. and Emam, S.A. (2016), "A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams", Appl. Math. Model., 40(5-6), 4109-4128. https://doi.org/10.1016/j.apm.2015.11.026.
  29. Eltaher, M.A., Wagih, A., Melaibari, A., Alsoruji, G.S. and Attia, M.A. (2022), "Elastoplastic indentation response of sigmoid/power functionally graded ceramics structures", Polym., 14(6), 1225. https://doi.org/10.3390/polym14061225.
  30. Eringen, A.C. (1967), "Theory of micropolar plates", J. Appl. Math. Phys., 18, 12-30. https://doi.org/10.1007/BF01593891.
  31. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  32. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2022a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 38, 3463-3482. https://doi.org/10.1007/s00366-021-01389-5.
  33. Esen, I., Alazwari, M.A., Eltaher, M.A. and Abdelrahman M.A. (2022b), "Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load", Steel Compos. Struct., 42(6), 805-826. https://doi.org/10.12989/scs.2022.42.6.805.
  34. Esen, I., Ozarpa, C. and Eltaher, M.A. (2021), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261, 113552. https://doi.org/10.1016/j.compstruct.2021.113552.
  35. Ghandourah, E.E., Daikh, A.A., Alhawsawi, A.M., Fallatah, O.A. and Eltaher, M.A. (2022), "Bending and buckling of FG-GRNC laminated plates via quasi-3D nonlocal strain gradient theory", Math., 10(8), 1321. https://doi.org/10.3390/math10081321.
  36. Hamed, M.A., Eltaher, M.A., Sadoun, A.M. and Almitani, K.H. (2016), "Free vibration of symmetric and sigmoid functionally graded nanobeams", Appl. Phys. A, 122(9), 1-11. https://doi.org/10.1007/s00339-016-0324-0.
  37. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  38. Hendi, A., Eltaher, M.A., Mohamed, S.A., Attia, M.A. and Abdalla, A.W. (2021), "Nonlinear thermal vibration of pre/post-buckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel Compos. Struct., 41(6), 787-803. https://doi.org/10.12989/scs.2021.41.6.787.
  39. Javaheri, R. and Eslami, M.R. (2002), "Buckling of functionally graded plates under in-plane compressive loading", J. Appl. Math. Mech., 82, 277-283. https://doi.org/10.1002/1521-4001(200204)82:4<277::AIDZAMM277>3.0.CO;2-Y.
  40. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9.
  41. Karamanli, A., Eltaher, M.A., Thai, S. and Vo, T.P. (2023), "Transient dynamics of 2D-FG porous microplates under moving loads using higher order finite element model", Eng. Struct., 278, 115566. https://doi.org/10.1016/j.engstruct.2022.115566.
  42. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399.
  43. Kirchhoff, G.R. (1850), "Uber das gleichgewicht und die bewegungeiner elastischen scheibe", J. Reine Angew. Math., 40, 51-88.
  44. Li, D., Deng, Z. and Xiao, H. (2016), "Thermomechanical bending analysis of functionally graded sandwich plates using four variable refined plate theory", Compos. Part B-Eng., 106, 107-119. https://doi.org/10.1016/j.compositesb.2016.08.041.
  45. Li, D., Deng, Z., Chen, G., Xiao, H. and Zhu, L. (2017), "Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core", Compos. Struct., 169, 29-41. http://doi.org/10.1016/j.compstruct.2017.01.026.
  46. Librescu, L. and Hause, T. (2000), "Recent developments in the modeling and behavior of advanced sandwich constructions: A survey", Compos. Struct., 48(1-3), 1-17. https://doi.org/10.1016/S0263-8223(99)00068-9.
  47. Lindstrom, A. and Hallstrom, S. (2010), "Energy absorption of SMC/balsa sandwich panels with geometrical triggering features", Compos. Struct., 92(11), 2676-2684. https://doi.org/10.1016/j.compstruct.2010.03.018.
  48. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489- 2508. https://doi.org/10.1016/j.apm.2014.10.045.
  49. Malhari Ramteke, P., Kumar Panda, S. and Sharma, N. (2022), "Nonlinear vibration analysis of multidirectional porous functionally graded panel under thermal environment", AIAA J., 60(8), 4923-4933. https://doi.org/10.2514/1.J061635.
  50. Mantari, J.L. (2015), "A refined theory with stretching effect for the dynamics analysis of advanced composites on elastic foundation", Mech. Mater., 86, 31-43. https://doi.org/10.1016/j.mechmat.2015.02.010.
  51. Melaibari, A., Mohamed, S.A., Assie, A.E., Shanab, R.A. and Eltaher, M.A. (2023), "Mathematical and physical analyses of middle/neutral surfaces formulations for static response of bi-directional FG plates with movable/immovable boundary conditions", Math., 11(1), 2. https://doi.org/10.3390/math11010002.
  52. Melaibari, A., Mohamed, S.A., Assie, A.E., Shanab, R.A. and Eltaher, M.A. (2022), "Static response of 2D FG porous plates resting on elastic foundation using midplane and neutral surfaces with movable constraints", Math., 10(24), 4784. https://doi.org/10.3390/math10244784.
  53. Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H. and Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates", Arch. Appl. Mech., 81(11), 1507-1522. https://doi.org/10.1007/s00419-010-0497-5.
  54. Mindlin, R.D. (1951), "Influence of rotary inertia and schear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217.
  55. Mohamed, S., Assie, A.E., Mohamed, N. and Eltaher, M.A. (2022), "Static and stress analyses of bidirectional 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.
  56. 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.
  57. Ramteke, P.M. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  58. Ramteke, P.M. and Panda, S.K. (2021b), "Free vibrational behaviour of multi-directional porous functionally graded structures", Arab. J. Sci. Eng., 46(8), 7741-7756. https://doi.org/10.1007/s13369-021-05461-6.
  59. Ramteke, P.M., Kumar, V., Sharma, N. and Panda, S.K. (2022c), "Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment", Int. J. Nonlin. Mech., 143, 104041. https://doi.org/10.1016/j.ijnonlinmec.2022.104041.
  60. Ramteke, P.M., Mahapatra, B.P., Panda, S.K. and Sharma, N. (2020a), "Static deflection simulation study of 2D functionally graded porous structure", Mater. Today: Proc., 33, 5544-5547. https://doi.org/10.1016/j.matpr.2020.03.537.
  61. Ramteke, P.M., Mehar, K., Sharma, N. and Panda, S.K. (2021a), "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), 811-829.
  62. Ramteke, P.M., Panda, S.K. and Patel, B. (2022a), "Nonlinear eigenfrequency characteristics of multi-directional functionally graded porous panels", Compos. Struct., 279, 114707. https://doi.org/10.1016/j.compstruct.2021.114707.
  63. Ramteke, P.M., Patel, B. and Panda, S.K. (2020b), "Time-dependent deflection responses of porous FGM structure including pattern and porosity", Int. J. Appl. Mech., 12(09), 2050102. https://doi.org/10.1142/S1758825120501021.
  64. Ramteke, P.M., Patel, B. and Panda, S.K. (2021c), "Nonlinear eigenfrequency prediction of functionally graded porous structure with different grading patterns", Wave. Random Complex Media, 1-19. https://doi.org/10.1080/17455030.2021.2005850.
  65. Ramteke, P.M., Sharma, N., Choudhary, J., Hissaria, P. and Panda, S.K. (2022b), "Multidirectional grading influence on static/dynamic deflection and stress responses of porous FG panel structure: A micromechanical approach", Eng. Comput., 38(4), 3077-3097. https://doi.org/10.1007/s00366-021-01449-w.
  66. Reddy, J.N. (1997), Mechanics of Laminated Composites Plates: Theory and Analysis, CRC Press, Boca Raton.
  67. Reddy, J.N. and Cheng, Z.Q. (2001), "Three-dimensional thermomechanical deformations of functionally graded rectangular plates", Eur. J. Mech. A Solid., 20(5), 841-855. https://doi.org/10.1016/S0997-7538(01)01174-3.
  68. Reissner, E. (1945), "The effect of transverse shears deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77. https://doi.org/10.1115/1.4009435.
  69. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017b), "A new quasi-3D HSDT for buckling and vibration of FG plate", Struct. Eng. Mech., 64(6), 737-749. https://doi.org/10.12989/sem.2017.64.6.737.
  70. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1) 137-146. https://doi.org/10.2514/2.1622.
  71. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009.
  72. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  73. Xiang, S., Wang, K.M., Ai, Y.T., Sha, Y.D. and Shi, H. (2009), "Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories", Compos. Struct., 91(1), 31-37. https://doi.org/10.1016/j.compstruct.2009.04.029.
  74. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143.
  75. Zenkour, A. and Alghamdi, N.A. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads", Mech. Adv. Mater. Struct., 17(6), 419-432. https://doi.org/10.1080/15376494.2010.483323.
  76. Zenkour, A. and Abouelregal, A.E. (2015), "Nonlocal thermoelastic nanobeam subjected to a sinusoidal pulse heating and temperature-dependent physical properties", Microsyst. Technol., 21(8), 1767-1776. https://doi.org/10.1007/s00542-014-2294-5.
  77. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method", J. Sound Vib., 319(3-5), 918-939. https://doi.org/10.1016/j.jsv.2008.06.025.
  78. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygrothermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001.
  79. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125.