Steel and Composite Structures

  • 제18권2호
  • /
  • Pages.409-423
  • /
  • 2015
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A new simple shear and normal deformations theory for functionally graded beams

  • Bourada, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Houari, Mohammed Sid Ahmed (Material and Hydrology 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)
  • 투고 : 2014.04.30
  • 심사 : 2014.07.27
  • 발행 : 2015.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

키워드

참고문헌

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  52. Elastic analysis effect of adhesive layer characteristics in steel beam strengthened with a fiber-reinforced polymer plates vol.59, pp.1, 2016, https://doi.org/10.12989/sem.2016.59.1.083
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  54. Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory vol.19, pp.1, 2015, https://doi.org/10.12989/scs.2015.19.1.093
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  58. 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
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  62. 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
  63. Nonlinear magneto-electro-mechanical vibration analysis of double-bonded sandwich Timoshenko microbeams based on MSGT using GDQM vol.21, pp.1, 2016, https://doi.org/10.12989/scs.2016.21.1.001
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  67. 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
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  75. Miniature test techniques for life management of operating equipment vol.323, 2017, https://doi.org/10.1016/j.nucengdes.2017.03.007
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  77. 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
  78. Estimation of sound transmission loss of polymer/hollow microsphere composites vol.50, pp.15, 2016, https://doi.org/10.1177/0021998315602943
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  83. 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
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  87. 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
  88. 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
  89. 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
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  98. 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
  99. 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
  100. An elastic element of the forced oscillation apparatus for dynamic wind tunnel measurements vol.50, 2016, https://doi.org/10.1016/j.ast.2016.01.011
  101. Flexoelectric effect on the bending and vibration responses of functionally graded piezoelectric nanobeams based on general modified strain gradient theory vol.186, 2018, https://doi.org/10.1016/j.compstruct.2017.10.083
  102. Thermal Effects on the Vibration of Functionally Graded Deep Beams with Porosity vol.09, pp.05, 2017, https://doi.org/10.1142/S1758825117500764
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  104. Bending analysis of thin functionally graded plate under in-plane stiffness variations vol.44, 2017, https://doi.org/10.1016/j.apm.2017.02.009
  105. Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions vol.18, pp.2, 2016, https://doi.org/10.12989/sss.2016.18.2.267
  106. Coupled twist–bending static and dynamic behavior of a curved single-walled carbon nanotube based on nonlocal theory vol.23, pp.7, 2017, https://doi.org/10.1007/s00542-016-2933-0
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  108. 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
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  110. Thermal stability analysis of solar functionally graded plates on elastic foundation using an efficient hyperbolic shear deformation theory vol.10, pp.3, 2016, https://doi.org/10.12989/gae.2016.10.3.357
  111. Flutter suppression of plates subjected to supersonic flow using passive constrained viscoelastic layers and Golla–Hughes–McTavish method vol.52, 2016, https://doi.org/10.1016/j.ast.2016.02.022
  112. Interfacial stresses in RC beam bonded with a functionally graded material plate vol.60, pp.4, 2016, https://doi.org/10.12989/sem.2016.60.4.693
  113. 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
  114. Frequency Analysis of Functionally Graded Curved Pipes Conveying Fluid vol.2016, 2016, https://doi.org/10.1155/2016/7574216
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  116. 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
  117. 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
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  119. 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
  120. Non-linear transient and damping analysis of a long cylindrical sandwich panel with embedded SMA wires vol.47, 2015, https://doi.org/10.1016/j.ast.2015.09.016
  121. Thermal stresses in a non-homogeneous orthotropic infinite cylinder vol.59, pp.5, 2016, https://doi.org/10.12989/sem.2016.59.5.841
  122. Effect of fiber tension on the deformation of a carbon composite plate for space radio telescopes vol.45, 2015, https://doi.org/10.1016/j.ast.2015.04.019
  123. Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams vol.24, pp.11, 2017, https://doi.org/10.1080/15376494.2016.1196795
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  125. Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam vol.122, pp.7, 2016, https://doi.org/10.1007/s00339-016-0196-3
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  127. 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
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  129. 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
  130. 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
  131. Nonlinear analysis of size-dependent and material-dependent nonlocal CNTs vol.153, 2016, https://doi.org/10.1016/j.compstruct.2016.07.013
  132. Vibration Analysis of Rectangular Magnetostrictive Plate Considering Thickness Variation in Two Directions vol.07, pp.04, 2015, https://doi.org/10.1142/S1758825115500593
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  134. 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
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  137. 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
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  139. Hygrothermal Effects on the Free Vibration Behavior of Composite Plate Using nth-Order Shear Deformation Theory: a Micromechanical Approach 2019, https://doi.org/10.1007/s40997-017-0140-y
  140. 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
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  149. Rotational effect on Rayleigh, Love and Stoneley waves in non-homogeneous fibre-reinforced anisotropic general viscoelastic media of higher order vol.58, pp.1, 2016, https://doi.org/10.12989/sem.2016.58.1.181
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  151. 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
  152. Mechanical and hygrothermal behaviour of functionally graded plates using a hyperbolic shear deformation theory vol.20, pp.4, 2016, https://doi.org/10.12989/scs.2016.20.4.889
  153. Designing a stronger interface through graded structures in amorphous/nanocrystalline ZrCu/Cu multilayered films vol.27, pp.22, 2016, https://doi.org/10.1088/0957-4484/27/22/225701
  154. A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory vol.54, pp.4, 2015, https://doi.org/10.12989/sem.2015.54.4.693
  155. 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
  156. 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
  157. 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
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  159. Elastic buckling of current-carrying double-nanowire systems immersed in a magnetic field vol.227, pp.12, 2016, https://doi.org/10.1007/s00707-016-1679-1
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  166. 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
  167. 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
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  170. 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
  171. 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
  172. Nonlocal vibration analysis of FG nano beams with different boundary conditions vol.4, pp.2, 2016, https://doi.org/10.12989/anr.2016.4.2.085
  173. Finite element model updating of a space vehicle first stage motor based on experimental test results vol.45, 2015, https://doi.org/10.1016/j.ast.2015.06.014
  174. Elastic bending and stress analysis of carbon nanotube-reinforced composite plate: Experimental, numerical, and simulation 2017, https://doi.org/10.1002/adv.21821
  175. 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
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  177. 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
  178. 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
  179. Wave propagation in anisotropic plates using trigonometric shear deformation theory vol.24, pp.13, 2017, https://doi.org/10.1080/15376494.2016.1227500
  180. 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
  181. Effect of shear deformation on adhesive stresses in plated concrete beams: Analytical solutions vol.15, pp.3, 2015, https://doi.org/10.12989/cac.2015.15.3.337
  182. Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation vol.40, pp.2, 2017, https://doi.org/10.1080/01495739.2016.1229146
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  184. 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
  185. Nonlinear vibration of FGM doubly curved panels resting on elastic foundations in thermal environments vol.47, 2015, https://doi.org/10.1016/j.ast.2015.10.011
  186. 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
  187. 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
  188. Free vibration analysis of pre-stressed FGM Timoshenko beams under large transverse deflection by a variational method vol.19, pp.2, 2016, https://doi.org/10.1016/j.jestch.2015.12.012
  189. 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
  190. Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0712-5
  191. Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties vol.123, pp.1, 2017, https://doi.org/10.1007/s00339-016-0591-9
  192. Influence of the porosities on the free vibration of FGM beams vol.21, pp.3, 2015, https://doi.org/10.12989/was.2015.21.3.273
  193. The nonlinear dynamic and vibration of the S-FGM shallow spherical shells resting on an elastic foundations including temperature effects vol.123, 2017, https://doi.org/10.1016/j.ijmecsci.2017.01.043
  194. 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
  195. Nonlinear Flexural Analysis of Laminated Composite Panel Under Hygro-Thermo-Mechanical Loading — A Micromechanical Approach vol.13, pp.03, 2016, https://doi.org/10.1142/S0219876216500158
  196. 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
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  198. 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
  199. A parametric study on the stress analysis and transient response of thick-laminated-faced cylindrical sandwich panels with transversely flexible core vol.48, 2016, https://doi.org/10.1016/j.ast.2015.10.016
  200. 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
  201. 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
  202. Elasticity solution for a cantilever beam with exponentially varying properties vol.58, pp.2, 2017, https://doi.org/10.1134/S0021894417020213
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  204. 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
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  206. 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
  207. Thermo-acoustic analysis of higher-order shear deformable laminated composite sandwich flat panel pp.1530-7972, 2018, https://doi.org/10.1177/1099636218784846
  208. Instability of functionally graded micro-beams via micro-structure-dependent beam theory vol.39, pp.7, 2018, https://doi.org/10.1007/s10483-018-2343-8
  209. 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
  210. 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
  211. 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
  212. 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
  213. 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
  214. 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
  215. An analytical approach for buckling of functionally graded plates vol.5, pp.3, 2015, https://doi.org/10.12989/amr.2016.5.3.141
  216. Bending analysis of an imperfect advanced composite plates resting on the elastic foundations vol.5, pp.3, 2015, https://doi.org/10.12989/csm.2016.5.3.269
  217. A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates vol.22, pp.5, 2015, https://doi.org/10.12989/scs.2016.22.5.975
  218. Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory vol.22, pp.6, 2015, https://doi.org/10.12989/scs.2016.22.6.1239
  219. Hygrothermal effects on buckling of composite shell-experimental and FEM results vol.22, pp.6, 2016, https://doi.org/10.12989/scs.2016.22.6.1445
  220. Mechanical behaviour of FGM sandwich plates using a quasi-3D higher order shear and normal deformation theory vol.61, pp.1, 2015, https://doi.org/10.12989/sem.2017.61.1.049
  221. Finite Element Method of Composite Steel-Concrete Beams Considering Interface Slip and Uplift vol.11, pp.None, 2015, https://doi.org/10.2174/1874149501711010531
  222. A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation vol.12, pp.1, 2015, https://doi.org/10.12989/gae.2017.12.1.009
  223. A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams vol.19, pp.2, 2017, https://doi.org/10.12989/sss.2017.19.2.115
  224. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2015, https://doi.org/10.12989/scs.2017.23.3.317
  225. Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams vol.6, pp.1, 2015, https://doi.org/10.12989/amr.2017.6.1.013
  226. 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
  227. Buckling temperature of a single-walled boron nitride nanotubes using a novel nonlocal beam model vol.5, pp.1, 2017, https://doi.org/10.12989/anr.2017.5.1.001
  228. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2015, https://doi.org/10.12989/sss.2017.19.3.289
  229. Wave propagation in functionally graded beams using various higher-order shear deformation beams theories vol.62, pp.2, 2015, https://doi.org/10.12989/sem.2017.62.2.143
  230. Analysis of functionally graded plates using a sinusoidal shear deformation theory vol.19, pp.4, 2017, https://doi.org/10.12989/sss.2017.19.4.441
  231. 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
  232. Displacement Analytical Solution of a Circular Hole in Layered Composite Materials considering Shear Stress Effect vol.26, pp.3, 2015, https://doi.org/10.1177/096369351702600303
  233. A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams vol.5, pp.2, 2015, https://doi.org/10.12989/anr.2017.5.2.113
  234. 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
  235. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2015, https://doi.org/10.12989/sss.2017.19.6.601
  236. 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
  237. 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
  238. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading vol.20, pp.2, 2015, https://doi.org/10.12989/cac.2017.20.2.229
  239. 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
  240. Rotating effects on hygro-mechanical vibration analysis of FG beams based on Euler-Bernoulli beam theory vol.63, pp.4, 2015, https://doi.org/10.12989/sem.2017.63.4.471
  241. A simple analytical approach for thermal buckling of thick functionally graded sandwich plates vol.63, pp.5, 2015, https://doi.org/10.12989/sem.2017.63.5.585
  242. Elastic analysis of interfacial stress concentrations in CFRP-RC hybrid beams: Effect of creep and shrinkage vol.6, pp.3, 2015, https://doi.org/10.12989/amr.2017.6.3.257
  243. An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities vol.13, pp.3, 2015, https://doi.org/10.12989/eas.2017.13.3.255
  244. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2015, https://doi.org/10.12989/gae.2017.13.3.385
  245. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2015, https://doi.org/10.12989/scs.2017.25.2.157
  246. Surface effects on vibration and buckling behavior of embedded nanoarches vol.64, pp.1, 2017, https://doi.org/10.12989/sem.2017.64.1.001
  247. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2015, https://doi.org/10.12989/sem.2017.64.2.145
  248. 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
  249. An analytical solution for bending and vibration responses of functionally graded beams with porosities vol.25, pp.4, 2015, https://doi.org/10.12989/was.2017.25.4.329
  250. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2015, https://doi.org/10.12989/scs.2017.25.3.257
  251. 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
  252. 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, 2015, https://doi.org/10.12989/eas.2017.13.5.509
  253. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2015, https://doi.org/10.12989/sem.2017.64.4.391
  254. 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
  255. Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory vol.64, pp.6, 2015, https://doi.org/10.12989/sem.2017.64.6.683
  256. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2015, https://doi.org/10.12989/sem.2017.64.6.737
  257. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.693
  258. A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.717
  259. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2015, https://doi.org/10.12989/scs.2017.25.6.735
  260. Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory vol.16, pp.2, 2015, https://doi.org/10.12989/gae.2018.16.2.141
  261. The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams vol.68, pp.1, 2018, https://doi.org/10.12989/sem.2018.68.1.053
  262. 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
  263. Experimental Study and Theoretical Analysis on Flexural Mechanical Propertiesof Reinforced Timber Beams vol.27, pp.1, 2018, https://doi.org/10.1177/096369351802700103
  264. Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory vol.65, pp.5, 2015, https://doi.org/10.12989/sem.2018.65.5.621
  265. Thermal stability analysis of temperature dependent inhomogeneous size-dependent nano-scale beams vol.7, pp.1, 2015, https://doi.org/10.12989/amr.2018.7.1.001
  266. Forced vibration analysis of cracked functionally graded microbeams vol.6, pp.1, 2015, https://doi.org/10.12989/anr.2018.6.1.039
  267. Post-buckling responses of a laminated composite beam vol.26, pp.6, 2015, https://doi.org/10.12989/scs.2018.26.6.733
  268. Development of super convergent Euler finite elements for the analysis of sandwich beams with soft core vol.65, pp.6, 2015, https://doi.org/10.12989/sem.2018.65.6.657
  269. 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
  270. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.027
  271. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.061
  272. Static analysis of functionally graded non-prismatic sandwich beams vol.3, pp.2, 2015, https://doi.org/10.12989/acd.2018.3.2.165
  273. Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects vol.21, pp.4, 2018, https://doi.org/10.12989/cac.2018.21.4.431
  274. Three dimensional dynamic response of functionally graded nanoplates under a moving load vol.66, pp.2, 2015, https://doi.org/10.12989/sem.2018.66.2.249
  275. A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory vol.21, pp.4, 2015, https://doi.org/10.12989/sss.2018.21.4.397
  276. Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates vol.14, pp.6, 2015, https://doi.org/10.12989/gae.2018.14.6.519
  277. 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
  278. 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
  279. Free vibration of FGM plates with porosity by a shear deformation theory with four variables vol.66, pp.3, 2015, https://doi.org/10.12989/sem.2018.66.3.353
  280. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2015, https://doi.org/10.12989/gae.2018.15.1.711
  281. Vibration and instability of nanocomposite pipes conveying fluid mixed by nanoparticles resting on viscoelastic foundation vol.21, pp.5, 2018, https://doi.org/10.12989/cac.2018.21.5.569
  282. Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis vol.27, pp.4, 2015, https://doi.org/10.12989/scs.2018.27.4.465
  283. 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
  284. 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
  285. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.567
  286. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.599
  287. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2015, https://doi.org/10.12989/anr.2018.6.2.147
  288. Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions vol.66, pp.6, 2018, https://doi.org/10.12989/sem.2018.66.6.761
  289. 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
  290. Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams vol.19, pp.5, 2015, https://doi.org/10.1007/s42107-018-0046-z
  291. Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter vol.28, pp.1, 2015, https://doi.org/10.12989/scs.2018.28.1.013
  292. Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field vol.67, pp.1, 2015, https://doi.org/10.12989/sem.2018.67.1.021
  293. Technical and economical assessment of applying silica nanoparticles for construction of concrete structures vol.22, pp.1, 2018, https://doi.org/10.12989/cac.2018.22.1.117
  294. Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation vol.67, pp.2, 2018, https://doi.org/10.12989/sem.2018.67.2.125
  295. 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, 2015, https://doi.org/10.12989/sss.2018.22.1.027
  296. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2015, https://doi.org/10.12989/scs.2018.28.3.381
  297. Single variable shear deformation model for bending analysis of thick beams vol.67, pp.3, 2015, https://doi.org/10.12989/sem.2018.67.3.291
  298. Numerical study for vibration response of concrete beams reinforced by nanoparticles vol.67, pp.3, 2018, https://doi.org/10.12989/sem.2018.67.3.311
  299. Non-linear longitudinal fracture in a functionally graded beam vol.7, pp.4, 2015, https://doi.org/10.12989/csm.2018.7.4.441
  300. Evaluation of vibroacoustic responses of laminated composite sandwich structure using higher-order finite-boundary element model vol.28, pp.5, 2015, https://doi.org/10.12989/scs.2018.28.5.629
  301. Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix vol.67, pp.5, 2015, https://doi.org/10.12989/sem.2018.67.5.517
  302. 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
  303. Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory vol.6, pp.3, 2018, https://doi.org/10.12989/anr.2018.6.3.279
  304. Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory vol.15, pp.3, 2015, https://doi.org/10.12989/eas.2018.15.3.285
  305. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2015, https://doi.org/10.12989/sss.2018.22.3.303
  306. Nonlinear Performance of Concrete Beam Reinforced with Prestressed Hybrid Cfrp/Gfrp Composite Sheet vol.27, pp.5, 2015, https://doi.org/10.1177/096369351802700505
  307. Co-rotational 3D beam element for nonlinear dynamic analysis of risers manufactured with functionally graded materials (FGMs) vol.173, pp.None, 2015, https://doi.org/10.1016/j.engstruct.2018.05.092
  308. 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
  309. An analytical solution for free vibration of functionally graded beam using a simple first-order shear deformation theory vol.27, pp.4, 2015, https://doi.org/10.12989/was.2018.27.4.247
  310. 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, 2015, https://doi.org/10.12989/was.2018.27.4.269
  311. Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory vol.22, pp.5, 2015, https://doi.org/10.12989/sss.2018.22.5.527
  312. 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
  313. Critical buckling loads of carbon nanotube embedded in Kerr's medium vol.6, pp.4, 2015, https://doi.org/10.12989/anr.2018.6.4.339
  314. A novel hyperbolic shear deformation theory for the mechanical buckling analysis of advanced composite plates resting on elastic foundations vol.30, pp.1, 2015, https://doi.org/10.12989/scs.2019.30.1.013
  315. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2015, https://doi.org/10.12989/sem.2019.69.2.205
  316. Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.019
  317. Dynamic and wave propagation investigation of FGM plates with porosities using a four variable plate theory vol.28, pp.1, 2015, https://doi.org/10.12989/was.2019.28.1.049
  318. 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
  319. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2015, https://doi.org/10.12989/acc.2019.7.1.051
  320. Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT vol.69, pp.5, 2015, https://doi.org/10.12989/sem.2019.69.5.511
  321. Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT vol.7, pp.2, 2015, https://doi.org/10.12989/anr.2019.7.2.089
  322. Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method vol.7, pp.2, 2015, https://doi.org/10.12989/anr.2019.7.2.109
  323. Free vibration of imperfect sigmoid and power law functionally graded beams vol.30, pp.6, 2019, https://doi.org/10.12989/scs.2019.30.6.603
  324. Vibration analysis of different material distributions of functionally graded microbeam vol.69, pp.6, 2015, https://doi.org/10.12989/sem.2019.69.6.637
  325. A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams vol.57, pp.None, 2015, https://doi.org/10.4028/www.scientific.net/jnanor.57.175
  326. Assessing the Effects of Porosity on the Bending, Buckling, and Vibrations of Functionally Graded Beams Resting on an Elastic Foundation by Using a New Refined Quasi-3D Theory vol.55, pp.2, 2015, https://doi.org/10.1007/s11029-019-09805-0
  327. 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
  328. A novel first order refined shear-deformation beam theory for vibration and buckling analysis of continuously graded beams vol.6, pp.3, 2015, https://doi.org/10.12989/aas.2019.6.3.189
  329. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2015, https://doi.org/10.12989/anr.2019.7.3.191
  330. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2015, https://doi.org/10.12989/gae.2019.18.2.161
  331. Free and forced analysis of perforated beams vol.31, pp.5, 2015, https://doi.org/10.12989/scs.2019.31.5.489
  332. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2015, https://doi.org/10.12989/scs.2019.31.5.503
  333. 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
  334. 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
  335. Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation vol.134, pp.7, 2015, https://doi.org/10.1140/epjp/i2019-12739-2
  336. Regenerative Bayesian detection of foundation constant with variable scale gradient theory vol.20, pp.8, 2015, https://doi.org/10.1631/jzus.a1800467
  337. 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
  338. Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method vol.12, pp.20, 2019, https://doi.org/10.3390/ma12203401
  339. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2015, https://doi.org/10.12989/cac.2019.24.4.347
  340. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2015, https://doi.org/10.12989/anr.2019.7.6.443
  341. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2015, https://doi.org/10.1140/epjp/i2019-12662-6
  342. Interaction Between Thermal Field and Two-Dimensional Functionally Graded Materials: A Structural Mechanical Example vol.11, pp.10, 2015, https://doi.org/10.1142/s1758825119500996
  343. 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
  344. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2015, https://doi.org/10.12989/was.2019.29.6.371
  345. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2015, https://doi.org/10.1140/epjp/s13360-020-00137-w
  346. Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method vol.34, pp.3, 2020, https://doi.org/10.12989/scs.2020.34.3.361
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  353. 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
  354. Vibration analysis of FGM beam: Effect of the micromechanical models vol.9, pp.3, 2015, https://doi.org/10.12989/csm.2020.9.3.265
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  357. Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures vol.36, pp.3, 2015, https://doi.org/10.1007/s00366-019-00742-z
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  361. Application of operational method to develop dynamic stiffness matrix for vibration analysis of thin beams vol.224, pp.None, 2015, https://doi.org/10.1016/j.engstruct.2020.111244
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  364. Parametric instability of functionally graded carbon nanotube-reinforced hybrid composite plates in thermal environments vol.17, pp.1, 2015, https://doi.org/10.1007/s10999-020-09522-w
  365. State of the art in functionally graded materials vol.262, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2021.113596
  366. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2015, https://doi.org/10.1080/17455030.2019.1607623
  367. Bending analysis of functionally graded sandwich plates using the refined finite strip method vol.24, pp.1, 2022, https://doi.org/10.1177/10996362211020448