Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates

  • Houari, Mohammed Sid Ahmed (Universite Mustapha Stambouli de Mascara, Department of Civil Engineering) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bessaim, Aicha (Universite Mustapha Stambouli de Mascara, Department of Civil Engineering) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.07.10
  • Accepted : 2016.09.30
  • Published : 2016.10.10
⟨ Previous Next ⟩

Abstract

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

Keywords

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. Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  3. Ait Yahia, S., Ait Atmane, H., 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., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  4. Akavci, S.S. (2015), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676.
  5. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  6. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  7. Amirpour, M., Das, R. and Saavedra Flores, E.I. (2016), "Analytical solutions for elastic deformation of functionally graded thick plates with in-plane stiffness variation using higher order shear deformation theory", Compos. Part B: Eng., 94, 109-121. https://doi.org/10.1016/j.compositesb.2016.03.040
  8. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., Int. J., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659
  9. 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., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  10. Aydogdu, M. (2006), "Comparison of various shear deformation theories for bending, buckling, and vibration of rectangular symmetric cross-ply plate with simply supported edges", J. Compos. Mater., 40(23), 2143-2155. https://doi.org/10.1177/0021998306062313
  11. 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., Int. J., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  12. 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
  13. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  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. Braz. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  15. 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., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  16. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  17. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  18. Benveniste. Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mat., 6(2), 147-157. https://doi.org/10.1016/0167-6636(87)90005-6
  19. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  20. 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., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  21. Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  22. Boukhari, A., Atmane, H., Tounsi, A., Adda Bedia, E. and Mahmoud, S. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  23. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  24. 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., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  25. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  26. 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. Computat. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  27. Bousahla, A.A., Benyoucef, S. Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  28. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos., Part B, 42(2), 123-133.
  29. Darilmaz, K. (2015), "Vibration analysis of functionally graded material (FGM) grid systems", Steel Compos. Struct., Int. J., 18(2), 395-408. https://doi.org/10.12989/scs.2015.18.2.395
  30. 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., Int. J., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  31. 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., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  32. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  33. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011a), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007
  34. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011b), "A new exact analytical approach for free vibration of Reissner-Mindlin functionally graded rectangular plates", Int. J. Mech. Sci., 53(1), 11-22. https://doi.org/10.1016/j.ijmecsci.2010.10.002
  35. Jha, D.K., Kant, T. and Singh, R.K. (2013), "Free vibration response of functionally graded thick plates with shear and normal deformations effects", Compos. Struct., 96, 799-823. https://doi.org/10.1016/j.compstruct.2012.09.034
  36. Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates", Compos. Struct., 9(3), 215-246. https://doi.org/10.1016/0263-8223(88)90015-3
  37. Kar, V.R. and Panda, S.K. (2015a), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  38. Kar, V.R. and Panda, S.K. (2015b), "Free vibration responses of temperature dependent functionally graded curved panels under thermal environment", Latin Am. J. Solid. Struct., 12(11), 2006-2024. https://doi.org/10.1590/1679-78251691
  39. Kar, V.R. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircraft Eng. Aerosp. Technol.: Int. J., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  40. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the newmulti-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  41. 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. Computat. Method., 11(5), 1350077. https://doi.org/10.1142/S0219876213500771
  42. Kitipornchai, S., Yang, J. and Liew, K.M. (2006), "Random vibration of the functionally graded laminates in thermal environments", Compos. Meth. Appl. Mech. Eng., 195(9-12), 1075-1095. https://doi.org/10.1016/j.cma.2005.01.016
  43. Klouche Djedid, I., Benachour, A., Houari, M.S.A. and Tounsi, A. (2014), "A n-order four variable refined theory for bending and free vibration of functionally graded plates", Steel Compos. Struct., Int. J., 17(1), 21-46. https://doi.org/10.12989/scs.2014.17.1.021
  44. Koizumi, M. (1993), "The concept of FGM", Ceram. Trans. Funct. Grad. Mater., 34, 3-10.
  45. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  46. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016a), "Large amplitude free vibration analysis of laminated composite spherical panel under hygrothermal environment", Int. J. Struct. Stabil. Dyn., 16(3), 1450105. https://doi.org/10.1142/S0219455414501053
  47. Mahapatra, T.R., Panda, S.K. and Kar, V.R. (2016b), "Nonlinear flexural analysis of laminated composite panel under hygro-thermo-mechanical loading: A micromechanical approach", Int. J. Struct. Stabil. Dyn., 13(3), 1650015.
  48. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016c), "Large amplitude bending behaviour of laminated composite curved panels", Eng. Computat., 33(1), 116-138. https://doi.org/10.1108/EC-05-2014-0119
  49. 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. Modelling, 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  50. Mantari, J.L., Ramos, I.A., Carrera, E. and Petrolo, M. (2016), "Static analysis of functionally graded plates using new non-polynomial displacement fields via Carrera Unified Formulation", Compos. Part B., 89, 127-142. https://doi.org/10.1016/j.compositesb.2015.11.025
  51. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  52. Mori, T. and Tanaka. K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall, 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3
  53. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Rogue, C.M.E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Part B, 43(2), 711-725.
  54. Pandya, B.N. and Kant, T. (1988), "Finite element analysis of laminated composite plates using a higherorder displacementmodel", Compos. Sci. Technol., 32(2), 137-155. https://doi.org/10.1016/0266-3538(88)90003-6
  55. 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
  56. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719
  57. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods 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
  58. Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239. https://doi.org/10.1016/0266-3538(86)90087-4
  59. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016a), "Static, free vibration and transient response of laminated composite curved shallow panel - An experimental approach", Eur. J. Mech. - A/Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014
  60. Sahoo, S.S., Panda, S.K. and Sen, D. (2016b), "Effect of delamination on static and dynamic behavior of laminated composite plate", AIAA J., 54(8), 2530-2544. https://doi.org/10.2514/1.J054908
  61. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Comp., 18(22), 1667-1688.
  62. 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
  63. Srinivas, S., Joga, C.V. and Rao, A.K. (1970), "Bending, vibration and buckling of simply supported thick orthotropic rectangular plate and laminates", Int. J. Solids Struct., 6(11), 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  64. 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
  65. 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(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  66. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., (Accepted)
  67. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3-5), 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7
  68. 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(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  69. Yang, J., Liew, K.M. and Kitipornchai, S. (2005), "Stochastic analysis of compositionally graded plates with system randomness under static loading", Int. J. Mech. Sci., 47(10), 1519-1541. https://doi.org/10.1016/j.ijmecsci.2005.06.006
  70. 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
  71. 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
  72. 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

Cited by

  1. Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method 2018, https://doi.org/10.1016/j.aej.2017.06.001
  2. 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
  3. Free vibration analysis of functionally graded Bernoulli-Euler beams using an exact transfer matrix expression vol.122, 2017, https://doi.org/10.1016/j.ijmecsci.2017.01.011
  4. Vibro-acoustic behaviour of shear deformable laminated composite flat panel using BEM and the higher order shear deformation theory vol.180, 2017, https://doi.org/10.1016/j.compstruct.2017.08.012
  5. 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
  6. Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position 2018, https://doi.org/10.1080/15397734.2017.1329020
  7. A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations 2017, https://doi.org/10.1177/1099636217727577
  8. 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
  9. 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
  10. Dynamic characteristics of temperature-dependent viscoelastic FG nanobeams subjected to 2D-magnetic field under periodic loading vol.123, pp.4, 2017, https://doi.org/10.1007/s00339-017-0829-1
  11. Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory 2017, https://doi.org/10.1177/1077546317711537
  12. Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects vol.187, 2018, https://doi.org/10.1016/j.compstruct.2017.12.004
  13. Nonlocal Timoshenko Beam for Vibrations of Magnetically Affected Inclined Single-Walled Carbon Nanotubes as Nanofluidic Conveyors vol.131, pp.6, 2017, https://doi.org/10.12693/APhysPolA.131.1439
  14. Critical Buckling Load of Chiral Double-Walled Carbon Nanotubes Embedded in an Elastic Medium vol.53, pp.6, 2018, https://doi.org/10.1007/s11029-018-9708-x
  15. 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
  16. 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
  17. Influence of size effect on flapwise vibration behavior of rotary microbeam and its analysis through spectral meshless radial point interpolation vol.123, pp.5, 2017, https://doi.org/10.1007/s00339-017-0955-9
  18. 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
  19. A new refined nonlocal beam theory accounting for effect of thickness stretching in nanoscale beams vol.4, pp.4, 2016, https://doi.org/10.12989/anr.2016.4.4.251
  20. 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
  21. A new analysis of nonlinear free vibration behavior of bi-functionally graded sandwich plates using the p-version of the finite element method 2017, https://doi.org/10.1080/15376494.2017.1410912
  22. Experimental and theoretical investigation of the thermo-mechanical deformation of a functionally graded panel vol.138, 2017, https://doi.org/10.1016/j.engstruct.2017.01.062
  23. Bending analysis of different material distributions of functionally graded beam vol.123, pp.4, 2017, https://doi.org/10.1007/s00339-017-0854-0
  24. Analysis Bending Solutions of Clamped Rectangular Thick Plate vol.2017, 2017, https://doi.org/10.1155/2017/7539276
  25. Exact solutions for coupled responses of thin-walled FG sandwich beams with non-symmetric cross-sections vol.122, 2017, https://doi.org/10.1016/j.compositesb.2017.04.016
  26. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.052
  27. 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
  28. Isogeometric buckling analysis of composite variable-stiffness panels vol.165, 2017, https://doi.org/10.1016/j.compstruct.2017.01.016
  29. 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
  30. An analytical solution for bending, buckling and vibration responses of FGM sandwich plates 2017, https://doi.org/10.1177/1099636217698443
  31. Experimental observation and energy based analytical investigation of matrix cracking distribution pattern in angle-ply laminates vol.92, 2017, https://doi.org/10.1016/j.tafmec.2017.06.007
  32. 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
  33. Dynamic modeling of porous heterogeneous micro/nanobeams vol.132, pp.12, 2017, https://doi.org/10.1140/epjp/i2017-11754-7
  34. A curved hierarchical finite element method for the nonlinear vibration analysis of functionally graded sandwich elliptic plates 2018, https://doi.org/10.1080/15376494.2018.1430277
  35. 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
  36. Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection vol.181, 2017, https://doi.org/10.1016/j.compstruct.2017.08.082
  37. 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
  38. 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
  39. Nonlocal and Surface Effects on Vibration Behavior of Axially Loaded Flexoelectric Nanobeams Subjected to In-Plane Magnetic Field 2017, https://doi.org/10.1007/s13369-017-2943-y
  40. 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
  41. 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
  42. Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates 2017, https://doi.org/10.1177/1099636217701299
  43. 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
  44. 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
  45. Dynamic response of a single-walled carbon nanotube under a moving harmonic load by considering modified nonlocal elasticity theory vol.133, pp.2, 2018, https://doi.org/10.1140/epjp/i2018-11868-4
  46. 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
  47. Buckling Analysis of Orthotropic Nanoscale Plates Resting on Elastic Foundations vol.55, pp.1661-9897, 2018, https://doi.org/10.4028/www.scientific.net/JNanoR.55.42
  48. Axial magnetic field effects on dynamic characteristics of embedded multiphase nanocrystalline nanobeams vol.24, pp.8, 2018, https://doi.org/10.1007/s00542-018-3771-z
  49. 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
  50. Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel pp.1530-7972, 2018, https://doi.org/10.1177/1099636218784846
  51. 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
  52. 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
  53. 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
  54. Thermodynamic effect on the bending response of elastic foundation FG plate by using a novel four variable refined plate theory vol.41, pp.8, 2018, https://doi.org/10.1080/01495739.2018.1452169
  55. Wave dispersion characteristics of embedded graphene platelets-reinforced composite microplates vol.133, pp.4, 2018, https://doi.org/10.1140/epjp/i2018-11956-5
  56. Thermoacoustic Behavior of Laminated Composite Curved Panels Using Higher-Order Finite-Boundary Element Model vol.10, pp.02, 2018, https://doi.org/10.1142/S1758825118500175
  57. 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
  58. An analytical approach for buckling of functionally graded plates vol.5, pp.3, 2016, https://doi.org/10.12989/amr.2016.5.3.141
  59. A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates vol.22, pp.5, 2016, https://doi.org/10.12989/scs.2016.22.5.975
  60. Finite Element Method of Composite Steel-Concrete Beams Considering Interface Slip and Uplift vol.11, pp.None, 2016, https://doi.org/10.2174/1874149501711010531
  61. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.317
  62. Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams vol.6, pp.1, 2016, https://doi.org/10.12989/amr.2017.6.1.013
  63. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  64. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2016, https://doi.org/10.12989/sss.2017.19.3.289
  65. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2016, https://doi.org/10.12989/sem.2017.62.2.143
  66. A novel and simple HSDT for thermal buckling response of functionally graded sandwich plates vol.62, pp.4, 2017, https://doi.org/10.12989/sem.2017.62.4.401
  67. A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams vol.62, pp.6, 2017, https://doi.org/10.12989/sem.2017.62.6.695
  68. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
  69. A new shear deformation plate theory with stretching effect for buckling analysis of functionally graded sandwich plates vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.569
  70. Free vibrations of laminated composite plates using a novel four variable refined plate theory vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.603
  71. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2016, https://doi.org/10.12989/cac.2017.20.2.229
  72. An original single variable shear deformation theory for buckling analysis of thick isotropic plates vol.63, pp.4, 2017, https://doi.org/10.12989/sem.2017.63.4.439
  73. Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory vol.63, pp.4, 2016, https://doi.org/10.12989/sem.2017.63.4.471
  74. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2016, https://doi.org/10.12989/sem.2017.63.5.585
  75. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2016, https://doi.org/10.12989/eas.2017.13.3.255
  76. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  77. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  78. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  79. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  80. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  81. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  82. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  83. A simple quasi-3D sinusoidal shear deformation theory with stretching effect for carbon nanotube-reinforced composite beams resting on elastic foundation vol.13, pp.5, 2016, https://doi.org/10.12989/eas.2017.13.5.509
  84. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  85. Vibration analysis of micro composite thin beam based on modified couple stress vol.64, pp.4, 2017, https://doi.org/10.12989/sem.2017.64.4.403
  86. Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.683
  87. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  88. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  89. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.717
  90. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  91. A nonlocal strain gradient theory for nonlinear free and forced vibration of embedded thick FG double layered nanoplates vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.103
  92. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2016, https://doi.org/10.12989/sem.2018.65.5.621
  93. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2016, https://doi.org/10.12989/anr.2018.6.1.039
  94. Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments vol.65, pp.6, 2018, https://doi.org/10.12989/sem.2018.65.6.645
  95. Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core vol.65, pp.6, 2016, https://doi.org/10.12989/sem.2018.65.6.657
  96. A novel four variable refined plate theory for wave propagation in functionally graded material plates vol.27, pp.1, 2018, https://doi.org/10.12989/scs.2018.27.1.109
  97. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.061
  98. Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles vol.27, pp.2, 2016, https://doi.org/10.12989/scs.2018.27.2.201
  99. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2016, https://doi.org/10.12989/sem.2018.66.2.249
  100. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2016, https://doi.org/10.12989/sss.2018.21.4.397
  101. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2016, https://doi.org/10.12989/gae.2018.14.6.519
  102. Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory vol.27, pp.3, 2018, https://doi.org/10.12989/scs.2018.27.3.311
  103. Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models vol.66, pp.3, 2018, https://doi.org/10.12989/sem.2018.66.3.317
  104. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.353
  105. Nonlocal free vibration analysis of a doubly curved piezoelectric nano shell vol.27, pp.4, 2018, https://doi.org/10.12989/scs.2018.27.4.479
  106. Three dimensional finite elements modeling of FGM plate bending using UMAT vol.66, pp.4, 2018, https://doi.org/10.12989/sem.2018.66.4.487
  107. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.567
  108. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.599
  109. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2016, https://doi.org/10.12989/anr.2018.6.2.147
  110. Quasi-3D static analysis of two-directional functionally graded circular plates vol.27, pp.6, 2016, https://doi.org/10.12989/scs.2018.27.6.789
  111. A new quasi-3D higher shear deformation theory for vibration of functionally graded carbon nanotube-reinforced composite beams resting on elastic foundation vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.771
  112. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2016, https://doi.org/10.12989/scs.2018.28.1.013
  113. Size-dependent free vibration and dynamic analyses of a sandwich microbeam based on higher-order sinusoidal shear deformation theory and strain gradient theory vol.22, pp.1, 2016, https://doi.org/10.12989/sss.2018.22.1.027
  114. Eigenfrequencies of advanced composite plates using an efficient hybrid quasi-3D shear deformation theory vol.22, pp.1, 2018, https://doi.org/10.12989/sss.2018.22.1.121
  115. Single variable shear deformation model for bending analysis of thick beams vol.67, pp.3, 2016, https://doi.org/10.12989/sem.2018.67.3.291
  116. A new plate model for vibration response of advanced composite plates in thermal environment vol.67, pp.4, 2016, https://doi.org/10.12989/sem.2018.67.4.369
  117. Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model vol.28, pp.5, 2016, https://doi.org/10.12989/scs.2018.28.5.629
  118. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2016, https://doi.org/10.12989/sem.2018.67.5.517
  119. Effect of homogenization models on stress analysis of functionally graded plates vol.67, pp.5, 2018, https://doi.org/10.12989/sem.2018.67.5.527
  120. Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory vol.15, pp.4, 2018, https://doi.org/10.12989/eas.2018.15.4.369
  121. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.247
  122. A refined quasi-3D hybrid-type higher order shear deformation theory for bending and Free vibration analysis of advanced composites beams vol.27, pp.4, 2016, https://doi.org/10.12989/was.2018.27.4.269
  123. Surface effects on nonlinear vibration and buckling analysis of embedded FG nanoplates via refined HOSDPT in hygrothermal environment considering physical neutral surface position vol.5, pp.6, 2016, https://doi.org/10.12989/aas.2018.5.6.691
  124. Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation vol.27, pp.5, 2018, https://doi.org/10.12989/was.2018.27.5.311
  125. Critical buckling loads of carbon nanotube embedded in Kerr's medium vol.6, pp.4, 2016, https://doi.org/10.12989/anr.2018.6.4.339
  126. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2016, https://doi.org/10.12989/scs.2019.30.1.013
  127. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2016, https://doi.org/10.12989/sem.2019.69.2.205
  128. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.019
  129. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2016, https://doi.org/10.12989/was.2019.28.1.049
  130. A novel refined shear deformation theory for the buckling analysis of thick isotropic plates vol.69, pp.3, 2019, https://doi.org/10.12989/sem.2019.69.3.335
  131. Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams vol.134, pp.3, 2016, https://doi.org/10.1140/epjp/i2019-12464-x
  132. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2016, https://doi.org/10.12989/sem.2019.69.5.511
  133. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2016, https://doi.org/10.12989/anr.2019.7.2.089
  134. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2016, https://doi.org/10.12989/sem.2019.69.6.637
  135. Static and Dynamic Behavior of Nanotubes-Reinforced Sandwich Plates Using (FSDT) vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.117
  136. A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams vol.57, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.57.175
  137. Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities vol.25, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.25.69
  138. Buckling behavior of rectangular plates under uniaxial and biaxial compression vol.70, pp.1, 2019, https://doi.org/10.12989/sem.2019.70.1.113
  139. A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.325
  140. Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.157
  141. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2016, https://doi.org/10.12989/anr.2019.7.3.191
  142. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2016, https://doi.org/10.12989/gae.2019.18.2.161
  143. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2016, https://doi.org/10.12989/scs.2019.31.5.503
  144. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  145. Chaotic dynamics of a non-autonomous nonlinear system for a smart composite shell subjected to the hygro-thermal environment vol.25, pp.7, 2019, https://doi.org/10.1007/s00542-018-4206-6
  146. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment vol.134, pp.7, 2019, https://doi.org/10.1140/epjp/i2019-12581-6
  147. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  148. Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets vol.134, pp.10, 2019, https://doi.org/10.1140/epjp/i2019-12806-8
  149. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  150. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2016, https://doi.org/10.12989/anr.2019.7.6.443
  151. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2016, https://doi.org/10.1140/epjp/i2019-12662-6
  152. Free Vibration Analysis of Simply Supported P-FGM Nanoplate Using a Nonlocal Four Variables Shear Deformation Plate Theory vol.69, pp.4, 2016, https://doi.org/10.2478/scjme-2019-0039
  153. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  154. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2016, https://doi.org/10.12989/was.2019.29.6.371
  155. Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures vol.73, pp.2, 2020, https://doi.org/10.12989/sem.2020.73.2.109
  156. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  157. A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads vol.7, pp.1, 2020, https://doi.org/10.12989/smm.2020.7.1.027
  158. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  159. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2016, https://doi.org/10.12989/sss.2020.25.4.409
  160. A comprehensive review on the modeling of smart piezoelectric nanostructures vol.74, pp.5, 2016, https://doi.org/10.12989/sem.2020.74.5.611
  161. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201
  162. Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00732-1
  163. Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam vol.26, pp.3, 2016, https://doi.org/10.12989/sss.2020.26.3.361
  164. Nonlinear Dynamic Behavior of Porous and Imperfect Bernoulli-Euler Functionally Graded Nanobeams Resting on Winkler Elastic Foundation vol.8, pp.4, 2020, https://doi.org/10.3390/technologies8040056
  165. Higher-order semi-layerwise models for doubly curved delaminated composite shells vol.91, pp.1, 2021, https://doi.org/10.1007/s00419-020-01755-7
  166. Free vibration and buckling analysis of FGM plates using inverse trigonometric shear deformation theory vol.93, pp.2, 2021, https://doi.org/10.1108/aeat-01-2020-0001