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Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories

  • Yahia, Sihame Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Atmane, Hassen Ait (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Advanced Materials and Structures Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2014.04.30
  • Accepted : 2014.10.29
  • Published : 2015.03.25

Abstract

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions" J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  3. Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stress., 35, 677-694. https://doi.org/10.1080/01495739.2012.688665
  4. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., 48, 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  5. Bakhti, K., Kaci, A., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Large deformation analysis for functionally graded carbon nanotube-reinforced composite plates using an efficient and simple refined theory", Steel Compos. Struct., 14(4), 335-347. https://doi.org/10.12989/scs.2013.14.4.335
  6. Benachour, A., Daouadji Tahar, H., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42, 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  7. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale rffects on mechanical buckling properties of zigzag double-walled carbon nanotubes", Compos. Part B, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020
  8. Benzair, A., Tounsi, A., Besseghier, A., Heireche, H., Moulay, N. and Boumia, L. (2008), "The thermal effect on vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 41, 225404. https://doi.org/10.1088/0022-3727/41/22/225404
  9. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  10. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  11. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  12. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14, 5-33. https://doi.org/10.1177/1099636211426386
  13. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  14. Bouremana, M, Houari, M.S.A, Tounsi, A, Kaci, A. and Adda Bedia, E.A. (2013), "A new first shear deformation beam theory based on neutral surface position for functionally graded beams", Steel Compos. Struct., 15(5), 467-479. https://doi.org/10.12989/scs.2013.15.5.467
  15. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A., (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Meth., 11(6), 1-18.
  16. Chen, C.S., Hsu, C.Y. and Tzou, G.J. (2009), "Vibration and stability of functionally graded plates based on a higher-order deformation theory", J. Reinf. Plast. Compos., 28(10), 1215-1234. https://doi.org/10.1177/0731684408088884
  17. Chen, W.Q., Wang, H.M. and Bao, R.H. (2007), "On calculating dispersion curves of waves in a functionally graded elastic plate", Compos. Struct., 81, 233-242. https://doi.org/10.1016/j.compstruct.2006.08.009
  18. Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  19. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53, 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  20. 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
  21. Han, X. and Liu, G.R. (2002), "Effects of SH waves in a functionally graded plate", Mech. Res. Commun., 29, 327-338. https://doi.org/10.1016/S0093-6413(02)00316-6
  22. Han, X., Liu, G.R., Xi, Z.C. and Lam, K.Y. (2001), "Transient responses in a functionally graded cylinder", Int. J. Solid. Struct., 38, 3021-3037. https://doi.org/10.1016/S0020-7683(00)00219-5
  23. Han, X., Liu, G.R. and Lam, K.Y. (2002), "Transient waves in plates of functionally graded materials", Int. J. Numer. Meth. Eng., 52, 851-865.
  24. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  25. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008), "Sound wave propagation in single- walled carbon nanotubes using nonlocal elasticity", Physica E, 40, 2791-2799. https://doi.org/10.1016/j.physe.2007.12.021
  26. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-111. https://doi.org/10.1016/j.ijmecsci.2013.09.004
  27. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multi-layered 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
  28. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Method., 11(5), 135007.
  29. 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
  30. Klouche Djedid, I., Benachour, A., Houari, M.S.A., Tounsi, A. and Ameur, M. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., 17(1), 21-46. https://doi.org/10.12989/scs.2014.17.1.021
  31. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O. and Mahmoud, S.R. (2014), "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
  32. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higherorder deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  33. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct. (in Press)
  34. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  35. Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Bas. Des. Struct. Mach., 41, 421-433. https://doi.org/10.1080/15397734.2013.763713
  36. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318(1-2), 176-192. https://doi.org/10.1016/j.jsv.2008.03.056
  37. 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)47:1/3<663::AID-NME787>3.0.CO;2-8
  38. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightw. Struct., 1(1), 1-21. https://doi.org/10.3850/S201042861100002X
  39. Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., 17(3), 321-338 https://doi.org/10.12989/scs.2014.17.3.321
  40. Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., 15, 221-245. https://doi.org/10.12989/scs.2013.15.2.221
  41. Sayyad, A.S. and Ghugal, Y.M. (2014), "Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory", Struct. Eng. Mech., 51(5), 867-891. https://doi.org/10.12989/sem.2014.51.5.867
  42. Semmah, A, Tounsi, A., Zidour, M., Heireche, H. and Naceri, M. (2014), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Full., Nanotub. Carbon Nanostr., 23, 518-522.
  43. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. https://doi.org/10.1007/BF01176650
  44. Sun, D. and Luo, S.N. (2011a), "The wave propagation and dynamic response of rectangular functionally graded material plates with completed clamped supports under impulse load", Eur. J. Mech., A/Solid., 30, 396-408. https://doi.org/10.1016/j.euromechsol.2011.01.001
  45. Sun, D. and Luo, S.N. (2011b), "Wave propagation of functionally graded material plates in thermal environments", Ultrasonics, 51, 940-952. https://doi.org/10.1016/j.ultras.2011.05.009
  46. Swaminathan, K. and Naveenkumar, D.T. (2014), "Higher order refined computational models for the stability analysis of FGM plates-Analytical solutions", Eur. J. Mech. A/Solid., 47, 349-361. https://doi.org/10.1016/j.euromechsol.2014.06.003
  47. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034
  48. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013a), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  49. Tounsi, A., Semmah,, A. and Bousahla, A.A. (2013b), "Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech., ASCE, 3, 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  50. Tounsi, A, Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013c), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  51. 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
  52. 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
  53. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Tech., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002
  54. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826- 2832. https://doi.org/10.1016/j.compstruct.2011.05.022
  55. Yaghoobi, H. and Torabi, M. (2013), "Exact solution for thermal buckling of functionally graded plates resting on elastic foundations with various boundary conditions", J. Therm. Stress., 36, 869-894. https://doi.org/10.1080/01495739.2013.770356
  56. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48, 2019- 2035. https://doi.org/10.1007/s11012-013-9720-0
  57. Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: an assessment of a simple refined nth-order shear deformation theory", Compos. Part B, 62, 54-64. https://doi.org/10.1016/j.compositesb.2014.02.014
  58. Zenkour, A.M. 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, 419-432. https://doi.org/10.1080/15376494.2010.483323
  59. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2
  60. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

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  47. Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions vol.182, 2017, https://doi.org/10.1016/j.compstruct.2017.09.008
  48. Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory vol.113, 2016, https://doi.org/10.1016/j.ijmecsci.2016.04.014
  49. A nonlocal quasi-3D trigonometric plate model for free vibration behaviour of micro/nanoscale plates vol.56, pp.2, 2015, https://doi.org/10.12989/sem.2015.56.2.223
  50. Free vibration investigation of nano mass sensor using differential transformation method vol.123, pp.3, 2017, https://doi.org/10.1007/s00339-017-0796-6
  51. Further investigation of the body torques on a square solar sail due to the displacement of the sail attachment points vol.50, 2016, https://doi.org/10.1016/j.ast.2016.01.007
  52. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0922-5
  53. Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.279
  54. Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution vol.122, pp.12, 2016, https://doi.org/10.1007/s00339-016-0542-5
  55. Non-linear thermal post-buckling analysis of FGM Timoshenko beam under non-uniform temperature rise across thickness vol.19, pp.3, 2016, https://doi.org/10.1016/j.jestch.2016.05.014
  56. Bending analysis of FGM plates using a sinusoidal shear deformation theory vol.23, pp.6, 2016, https://doi.org/10.12989/was.2016.23.6.543
  57. A new higher-order shear and normal deformation theory for functionally graded sandwich beams vol.19, pp.3, 2015, https://doi.org/10.12989/scs.2015.19.3.521
  58. A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.547
  59. Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations vol.13, pp.1, 2017, https://doi.org/10.1007/s10999-015-9318-x
  60. Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations vol.119, 2017, https://doi.org/10.1016/j.tws.2017.04.002
  61. Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1347
  62. Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects vol.120, 2017, https://doi.org/10.1016/j.ijmecsci.2016.11.025
  63. The influence of hygrothermal effects on the cross-ply composite laminate with transverse cracking in transient mode vol.18, pp.1, 2017, https://doi.org/10.1051/meca/2016004
  64. Sequential multilayer fusion based assessment model for spacecraft launch success ratio vol.48, 2016, https://doi.org/10.1016/j.ast.2015.11.005
  65. Size-dependent thermally affected wave propagation analysis in nonlocal strain gradient functionally graded nanoplates via a quasi-3D plate theory vol.232, pp.1, 2018, https://doi.org/10.1177/0954406216674243
  66. Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes vol.514, 2017, https://doi.org/10.1016/j.physb.2017.03.030
  67. Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium vol.47, pp.6, 2017, https://doi.org/10.1007/s13538-017-0524-x
  68. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory vol.57, pp.4, 2016, https://doi.org/10.12989/sem.2016.57.4.617
  69. Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position vol.38, pp.1, 2016, https://doi.org/10.1007/s40430-015-0354-0
  70. Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory vol.18, pp.6, 2015, https://doi.org/10.12989/scs.2015.18.6.1493
  71. Influence of various temperature distributions on critical speed and vibrational characteristics of rotating cylindrical microshells with modified lengthscale parameter vol.132, pp.6, 2017, https://doi.org/10.1140/epjp/i2017-11551-4
  72. Estimation of sound transmission loss of polymer/hollow microsphere composites vol.50, pp.15, 2016, https://doi.org/10.1177/0021998315602943
  73. An analytical method for free vibration analysis of functionally graded sandwich beams vol.23, pp.1, 2016, https://doi.org/10.12989/was.2016.23.1.059
  74. A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities vol.25, pp.3, 2018, https://doi.org/10.1080/15376494.2016.1255820
  75. Nonlocal strain gradient based wave dispersion behavior of smart rotating magneto-electro-elastic nanoplates vol.4, pp.2, 2017, https://doi.org/10.1088/2053-1591/aa55b5
  76. Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory vol.18, pp.4, 2016, https://doi.org/10.12989/sss.2016.18.4.755
  77. Analysis of functionally graded beam using a new first-order shear deformation theory vol.57, pp.2, 2016, https://doi.org/10.12989/sem.2016.57.2.315
  78. Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation vol.5, pp.1, 2016, https://doi.org/10.12989/amr.2016.5.1.035
  79. Free vibration analysis of homogeneous and FGM skew plates resting on variable Winkler-Pasternak elastic foundation vol.17, pp.1, 2016, https://doi.org/10.1051/meca/2015051
  80. Static and dynamic behavior of FGM plate using a new first shear deformation plate theory vol.57, pp.1, 2016, https://doi.org/10.12989/sem.2016.57.1.127
  81. Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory 2017, https://doi.org/10.1007/s00542-017-3529-z
  82. Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers vol.228, pp.2, 2017, https://doi.org/10.1007/s00707-016-1716-0
  83. Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field 2017, https://doi.org/10.1080/01495739.2017.1393781
  84. On the bending and stability of nanowire using various HSDTs vol.3, pp.4, 2015, https://doi.org/10.12989/anr.2015.3.4.177
  85. Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams vol.322, 2017, https://doi.org/10.1016/j.cma.2017.05.007
  86. Static analysis of the FGM plate with porosities vol.21, pp.1, 2016, https://doi.org/10.12989/scs.2016.21.1.123
  87. Free Vibration Analysis of Smart Porous Plates Subjected to Various Physical Fields Considering Neutral Surface Position vol.42, pp.5, 2017, https://doi.org/10.1007/s13369-016-2348-3
  88. Correction method of the manned spacecraft low altitude ranging based on γ ray vol.50, 2016, https://doi.org/10.1016/j.ast.2015.12.028
  89. Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept vol.20, pp.5, 2016, https://doi.org/10.12989/scs.2016.20.5.963
  90. On thermal stability of plates with functionally graded coefficient of thermal expansion vol.60, pp.2, 2016, https://doi.org/10.12989/sem.2016.60.2.313
  91. A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates vol.107, 2016, https://doi.org/10.1016/j.ijengsci.2016.07.008
  92. Effect of porosity on vibrational characteristics of non-homogeneous plates using hyperbolic shear deformation theory vol.22, pp.4, 2016, https://doi.org/10.12989/was.2016.22.4.429
  93. Vibration analysis of bonded double-FGM viscoelastic nanoplate systems based on a modified strain gradient theory incorporating surface effects vol.123, pp.3, 2017, https://doi.org/10.1007/s00339-017-0784-x
  94. Evanescent waves in FGM spherical curved plates: an analytical treatment 2017, https://doi.org/10.1007/s11012-017-0800-4
  95. Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory vol.166, 2017, https://doi.org/10.1016/j.compstruct.2017.01.036
  96. Determination and verification of Johnson–Cook model parameters at high-speed deformation of titanium alloys vol.45, 2015, https://doi.org/10.1016/j.ast.2015.05.001
  97. On wave propagation in nanoporous materials vol.116, 2017, https://doi.org/10.1016/j.ijengsci.2017.03.007
  98. A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position vol.8, pp.3, 2015, https://doi.org/10.12989/gae.2015.8.3.305
  99. A layerwise semi-analytical method for modeling guided wave propagation in laminated and sandwich composite strips with induced surface excitation vol.51, 2016, https://doi.org/10.1016/j.ast.2016.01.023
  100. Numerical investigation of nonlinear thermomechanical deflection of functionally graded CNT reinforced doubly curved composite shell panel under different mechanical loads vol.161, 2017, https://doi.org/10.1016/j.compstruct.2016.10.135
  101. Dynamic modeling of smart shear-deformable heterogeneous piezoelectric nanobeams resting on Winkler–Pasternak foundation vol.122, pp.11, 2016, https://doi.org/10.1007/s00339-016-0466-0
  102. Free vibration of anisotropic single-walled carbon nanotube based on couple stress theory for different chirality vol.36, pp.3, 2017, https://doi.org/10.1177/0263092317700153
  103. Investigation of the Instability of FGM box beams vol.54, pp.3, 2015, https://doi.org/10.12989/sem.2015.54.3.579
  104. A computational shear displacement model for vibrational analysis of functionally graded beams with porosities vol.19, pp.2, 2015, https://doi.org/10.12989/scs.2015.19.2.369
  105. Free vibration of refined higher-order shear deformation composite laminated beams with general boundary conditions vol.108, 2017, https://doi.org/10.1016/j.compositesb.2016.09.093
  106. Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity vol.62, 2017, https://doi.org/10.1016/j.ast.2016.12.002
  107. On guided wave propagation in fully clamped porous functionally graded nanoplates vol.143, 2018, https://doi.org/10.1016/j.actaastro.2017.12.011
  108. Equivalent property between the one-half order and first-order shear deformation theories under the simply supported boundary conditions vol.131-132, 2017, https://doi.org/10.1016/j.ijmecsci.2017.07.005
  109. Finite element modeling for structural strength of quadcoptor type multi mode vehicle vol.53, 2016, https://doi.org/10.1016/j.ast.2016.03.020
  110. Thermomechanical deflection and stress responses of delaminated shallow shell structure using higher-order theories vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.09.071
  111. Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.223
  112. Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory vol.10, pp.5, 2016, https://doi.org/10.12989/eas.2016.10.5.1033
  113. Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading vol.109, 2017, https://doi.org/10.1016/j.compositesb.2016.10.050
  114. A refined theory with stretching effect for the flexure analysis of laminated composite plates vol.11, pp.5, 2016, https://doi.org/10.12989/gae.2016.11.5.671
  115. Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel vol.29, pp.1, 2016, https://doi.org/10.1016/j.cja.2015.12.007
  116. Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.205
  117. Wave propagation of a functionally graded beam in thermal environments vol.19, pp.6, 2015, https://doi.org/10.12989/scs.2015.19.6.1421
  118. Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation vol.160, 2017, https://doi.org/10.1016/j.compstruct.2016.10.027
  119. Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate vol.30, pp.12, 2016, https://doi.org/10.1080/01694243.2016.1140703
  120. Low-velocity impact response of functionally graded doubly curved panels with Winkler–Pasternak elastic foundation: An analytical approach vol.162, 2017, https://doi.org/10.1016/j.compstruct.2016.11.094
  121. Dynamic behavior of FGM beam using a new first shear deformation theory vol.10, pp.2, 2016, https://doi.org/10.12989/eas.2016.10.2.451
  122. Evaluation of heat dissipation and structural response of a cellular panel as a heat exchanger 2018, https://doi.org/10.1177/1099636217749274
  123. Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory vol.21, pp.6, 2016, https://doi.org/10.12989/scs.2016.21.6.1287
  124. Nonlinear bending of a two-dimensionally functionally graded beam vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.087
  125. Buckling optimization of variable-stiffness composite panels based on flow field function vol.181, 2017, https://doi.org/10.1016/j.compstruct.2017.08.081
  126. A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates vol.182, 2017, https://doi.org/10.1016/j.compstruct.2017.09.041
  127. Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory 2017, https://doi.org/10.1016/j.aej.2017.07.003
  128. Elastic-plastic fracture of functionally graded circular shafts in torsion vol.5, pp.4, 2016, https://doi.org/10.12989/amr.2016.5.4.299
  129. A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.047
  130. A study on thermal buckling load of clamped functionally graded beams under linear and nonlinear thermal gradient across thickness 2016, https://doi.org/10.1177/1464420716649213
  131. A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium vol.55, pp.4, 2015, https://doi.org/10.12989/sem.2015.55.4.743
  132. Hygro-thermo-mechanical behavior of classical composites using a new trigonometrical shear strain shape function and a compact layerwise approach vol.160, 2017, https://doi.org/10.1016/j.compstruct.2016.10.014
  133. A novel four variable refined plate theory for laminated composite plates vol.22, pp.4, 2016, https://doi.org/10.12989/scs.2016.22.4.713
  134. Size-dependent thermoelastic analysis of a functionally graded nanoshell vol.32, pp.03, 2018, https://doi.org/10.1142/S0217984918500331
  135. An efficient shear deformation theory for wave propagation of functionally graded material plates vol.57, pp.5, 2016, https://doi.org/10.12989/sem.2016.57.5.837
  136. Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations vol.10, pp.6, 2016, https://doi.org/10.12989/eas.2016.10.6.1429
  137. Vibration analysis of functionally graded piezoelectric nanoscale plates by nonlocal elasticity theory: An analytical solution vol.100, 2016, https://doi.org/10.1016/j.spmi.2016.08.046
  138. Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory vol.4, pp.1, 2016, https://doi.org/10.12989/anr.2016.4.1.031
  139. Homogenization of hexagonal and re-entrant hexagonal structures and wave propagation of the sandwich plates with symplectic analysis vol.114, 2017, https://doi.org/10.1016/j.compositesb.2017.01.048
  140. Assessment of conservative force models from GRACE accelerometers and precise orbit determination vol.49, 2016, https://doi.org/10.1016/j.ast.2015.11.034
  141. A unified solution for vibration analysis of plates with general structural stress distributions vol.8, pp.6, 2016, https://doi.org/10.1016/j.ijnaoe.2016.05.013
  142. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM 2017, https://doi.org/10.1080/19475411.2017.1377312
  143. A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates vol.22, pp.2, 2016, https://doi.org/10.12989/scs.2016.22.2.257
  144. An efficient and simple shear deformation theory for free vibration of functionally graded rectangular plates on Winkler-Pasternak elastic foundations vol.22, pp.3, 2016, https://doi.org/10.12989/was.2016.22.3.329
  145. Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory vol.59, pp.2, 2016, https://doi.org/10.12989/sem.2016.59.2.343
  146. Free vibration of symmetric and sigmoid functionally graded nanobeams vol.122, pp.9, 2016, https://doi.org/10.1007/s00339-016-0324-0
  147. Aero-hygro-thermal stability analysis of higher-order refined supersonic FGM panels with even and uneven porosity distributions vol.73, 2017, https://doi.org/10.1016/j.jfluidstructs.2017.06.007
  148. Magnetic field modeling based on geometrical equivalence principle for spherical actuator with cylindrical shaped magnet poles vol.49, 2016, https://doi.org/10.1016/j.ast.2015.11.021
  149. Nonlocal thermo-elastic wave propagation in temperature-dependent embedded small-scaled nonhomogeneous beams vol.131, pp.11, 2016, https://doi.org/10.1140/epjp/i2016-16383-0
  150. Coupled vibration characteristics of shear flexible thin-walled functionally graded sandwich I-beams vol.110, 2017, https://doi.org/10.1016/j.compositesb.2016.11.025
  151. Isogeometric buckling analysis of composite variable-stiffness panels vol.165, 2017, https://doi.org/10.1016/j.compstruct.2017.01.016
  152. Critical buckling load of chiral double-walled carbon nanotube using non-local theory elasticity vol.3, pp.4, 2015, https://doi.org/10.12989/anr.2015.3.4.193
  153. Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution vol.40, pp.3, 2016, https://doi.org/10.1016/j.apm.2015.09.038
  154. A simple hyperbolic shear deformation theory for vibration analysis of thick functionally graded rectangular plates resting on elastic foundations vol.11, pp.2, 2016, https://doi.org/10.12989/gae.2016.11.2.289
  155. Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation vol.22, pp.1, 2016, https://doi.org/10.12989/scs.2016.22.1.091
  156. Forced vibration analysis of functionally graded porous deep beams vol.186, 2018, https://doi.org/10.1016/j.compstruct.2017.12.013
  157. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11666-6
  158. Updating Bayesian detection of mechanical constants of thin-walled box girders based on Powell theory vol.9, pp.8, 2017, https://doi.org/10.1177/1687814017726910
  159. Thermal buckling optimisation of composite plates using firefly algorithm vol.29, pp.4, 2017, https://doi.org/10.1080/0952813X.2016.1259267
  160. A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates vol.22, pp.3, 2016, https://doi.org/10.12989/scs.2016.22.3.473
  161. Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories vol.67, 2018, https://doi.org/10.1016/j.euromechsol.2017.09.004
  162. First-principles calculations of typical anisotropic cubic and hexagonal structures and homogenized moduli estimation based on the Y-parameter: Application to CaO, MgO, CH and Calcite CaCO3 vol.101, 2017, https://doi.org/10.1016/j.jpcs.2016.10.010
  163. A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation vol.20, pp.2, 2016, https://doi.org/10.12989/scs.2016.20.2.227
  164. Thermal effects on nonlocal vibrational characteristics of nanobeams with non-ideal boundary conditions vol.18, pp.6, 2016, https://doi.org/10.12989/sss.2016.18.6.1087
  165. Investigation of the effects of viscous damping mechanisms on structural characteristics in coupled shear walls vol.116, 2016, https://doi.org/10.1016/j.engstruct.2016.02.031
  166. Postbuckling analysis of laminated composite shells under shear loads vol.21, pp.2, 2016, https://doi.org/10.12989/scs.2016.21.2.373
  167. Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations vol.56, pp.1, 2015, https://doi.org/10.12989/sem.2015.56.1.085
  168. Bending analysis of different material distributions of functionally graded beam vol.123, pp.4, 2017, https://doi.org/10.1007/s00339-017-0854-0
  169. Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO 2 nanoparticles and fiber reinforced polymer (FRP) layer vol.103, 2017, https://doi.org/10.1016/j.soildyn.2017.09.009
  170. Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory vol.22, pp.3, 2016, https://doi.org/10.12989/was.2016.22.3.291
  171. Transverse cracking based numerical analysis and its effects on cross-ply laminates strength under thermo-mechanical degradation vol.60, pp.6, 2016, https://doi.org/10.12989/sem.2016.60.6.1063
  172. A general bi-Helmholtz nonlocal strain-gradient elasticity for wave propagation in nanoporous graded double-nanobeam systems on elastic substrate vol.168, 2017, https://doi.org/10.1016/j.compstruct.2017.02.090
  173. On nonlocal characteristics of curved inhomogeneous Euler–Bernoulli nanobeams under different temperature distributions vol.122, pp.10, 2016, https://doi.org/10.1007/s00339-016-0399-7
  174. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation vol.72, 2018, https://doi.org/10.1016/j.ast.2017.11.004
  175. Wave propagation in anisotropic plates using trigonometric shear deformation theory vol.24, pp.13, 2017, https://doi.org/10.1080/15376494.2016.1227500
  176. Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory vol.122, pp.9, 2016, https://doi.org/10.1007/s00339-016-0368-1
  177. Wave dispersion characteristics of axially loaded magneto-electro-elastic nanobeams vol.122, pp.11, 2016, https://doi.org/10.1007/s00339-016-0465-1
  178. Powell inversion mechanical model of foundation parameters with generalized Bayesian theory vol.18, pp.7, 2017, https://doi.org/10.1631/jzus.A1600440
  179. Analytical solution of nonlinear cylindrical bending for functionally graded plates vol.9, pp.5, 2015, https://doi.org/10.12989/gae.2015.9.5.631
  180. A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load vol.5, pp.2, 2016, https://doi.org/10.12989/amr.2016.5.2.107
  181. Vibration analysis of functionally graded graphene platelet reinforced cylindrical shells with different porosity distributions pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1444235
  182. Fracture problems, vibration, buckling, and bending analyses of functionally graded materials: A state-of-the-art review including smart FGMS pp.1548-0046, 2018, https://doi.org/10.1080/02726351.2017.1410265
  183. On modeling of wave propagation in a thermally affected GNP-reinforced imperfect nanocomposite shell pp.1435-5663, 2018, https://doi.org/10.1007/s00366-018-0669-4
  184. Nonlocal Thermal and Mechanical Buckling of Nonlinear Orthotropic Viscoelastic Nanoplates Embedded in a Visco-Pasternak Medium vol.10, pp.08, 2018, https://doi.org/10.1142/S1758825118500862
  185. Buckling of magneto-electro-hygro-thermal piezoelectric nanoplates system embedded in a visco-Pasternak medium based on nonlocal theory pp.1432-1858, 2018, https://doi.org/10.1007/s00542-018-4082-0
  186. Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings pp.1435-5663, 2018, https://doi.org/10.1007/s00366-018-0646-y
  187. Influence of micro-structural defects on post-buckling and large-amplitude vibration of geometrically imperfect gradient plate vol.94, pp.1, 2018, https://doi.org/10.1007/s11071-018-4344-5
  188. On the shear buckling of porous nanoplates using a new size-dependent quasi-3D shear deformation theory pp.1619-6937, 2018, https://doi.org/10.1007/s00707-018-2247-7
  189. 基于Jeeves模式搜索理论地基参数的更新Bayes探测法 vol.19, pp.9, 2018, https://doi.org/10.1631/jzus.A1700573
  190. A modified couple stress theory for buckling analysis of higher order inhomogeneous microbeams with porosities pp.2041-2983, 2018, https://doi.org/10.1177/0954406218791642
  191. Dynamic analysis of graded small-scale shells with porosity distributions under transverse dynamic loads vol.133, pp.9, 2018, https://doi.org/10.1140/epjp/i2018-12152-5
  192. Static and Stability Characteristics of Geometrically Imperfect FGM Plates Resting on Pasternak Elastic Foundation with Microstructural Defect vol.43, pp.9, 2018, https://doi.org/10.1007/s13369-018-3240-0
  193. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
  194. Size-dependent vibration analysis of a three-layered porous rectangular nano plate with piezo-electromagnetic face sheets subjected to pre loads based on SSDT pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1487612
  195. Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field pp.2041-2983, 2018, https://doi.org/10.1177/0954406218781680
  196. Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity vol.133, pp.5, 2018, https://doi.org/10.1140/epjp/i2018-11993-0
  197. Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories vol.133, pp.5, 2018, https://doi.org/10.1140/epjp/i2018-12015-1
  198. Smart electrical and magnetic stability analysis of exponentially graded shear deformable three-layered nanoplate based on nonlocal piezo-magneto-elasticity theory pp.1530-7972, 2018, https://doi.org/10.1177/1099636218760667
  199. Thermal and Small-Scale Effects on Vibration of Embedded Armchair Single-Walled Carbon Nanotubes vol.51, pp.1661-9897, 2018, https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
  200. Effect of rotation on Rayleigh waves in a fiber-reinforced solid anisotropic magneto-thermo-viscoelastic media pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1445322
  201. Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates vol.133, pp.4, 2018, https://doi.org/10.1140/epjp/i2018-11956-5
  202. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529
  203. Accumulative Bayesian detection of displacement constants of a hybrid indeterminate box girder with variable scale gradient theory vol.11, pp.2, 2019, https://doi.org/10.1177/1687814018824164