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Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory

  • Beldjelili, Youcef (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) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.01.19
  • Accepted : 2016.04.26
  • Published : 2016.10.25
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Abstract

The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

Keywords

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  138. 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
  139. 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
  140. 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
  141. Hygrothermal effects on the behavior of reinforced-concrete beams strengthened by bonded composite laminate plates vol.69, pp.3, 2016, https://doi.org/10.12989/sem.2019.69.3.327
  142. 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
  143. Dynamic analysis of concrete column reinforced with Sio2 nanoparticles subjected to blast load vol.7, pp.1, 2016, https://doi.org/10.12989/acc.2019.7.1.051
  144. Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory vol.16, pp.2, 2019, https://doi.org/10.12989/eas.2019.16.2.177
  145. 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
  146. 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
  147. 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
  148. 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
  149. 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
  150. 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
  151. Dynamic response of metal foam FG porous cylindrical micro-shells due to moving loads with strain gradient size-dependency vol.134, pp.5, 2016, https://doi.org/10.1140/epjp/i2019-12540-3
  152. 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
  153. Improved analytical method for adhesive stresses in plated beam: Effect of shear deformation vol.7, pp.3, 2016, https://doi.org/10.12989/acc.2019.7.3.151
  154. 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
  155. 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
  156. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2016, https://doi.org/10.12989/sem.2019.70.4.407
  157. 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
  158. 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
  159. 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
  160. 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
  161. 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
  162. Dynamic analysis of multi-layered composite beams reinforced with graphene platelets resting on two-parameter viscoelastic foundation vol.134, pp.7, 2016, https://doi.org/10.1140/epjp/i2019-12739-2
  163. 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
  164. Bending, buckling and vibration of shear deformable beams made of three-dimensional graphene foam material vol.41, pp.10, 2016, https://doi.org/10.1007/s40430-019-1926-1
  165. Assessment of porosity influence on dynamic characteristics of smart heterogeneous magneto-electro-elastic plates vol.72, pp.1, 2019, https://doi.org/10.12989/sem.2019.72.1.113
  166. 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
  167. 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
  168. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2016, https://doi.org/10.12989/eas.2019.17.5.447
  169. Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution vol.72, pp.4, 2016, https://doi.org/10.12989/sem.2019.72.4.513
  170. Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation vol.12, pp.24, 2019, https://doi.org/10.1007/s12517-019-4871-5
  171. 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
  172. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2016, https://doi.org/10.12989/scs.2019.33.5.699
  173. 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
  174. Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model vol.33, pp.6, 2016, https://doi.org/10.12989/scs.2019.33.6.805
  175. 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
  176. Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method vol.26, pp.1, 2020, https://doi.org/10.1177/1077546319876389
  177. Variational approximate for high order bending analysis of laminated composite plates vol.73, pp.1, 2016, https://doi.org/10.12989/sem.2020.73.1.097
  178. Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle vol.73, pp.2, 2016, https://doi.org/10.12989/sem.2020.73.2.209
  179. Nonlinear Vibration Analysis of Sigmoid Functionally Graded Sandwich Plate with Ceramic-FGM-Metal Layers vol.8, pp.1, 2016, https://doi.org/10.1007/s42417-018-0058-8
  180. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  181. Effect of Microstructure and Surface Energy on the Static and Dynamic Characteristics of FG Timoshenko Nanobeam Embedded in an Elastic Medium vol.61, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/jnanor.61.97
  182. Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle vol.8, pp.2, 2016, https://doi.org/10.12989/anr.2020.8.2.135
  183. 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
  184. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  185. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105
  186. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2016, https://doi.org/10.12989/anr.2020.8.3.203
  187. 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
  188. 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
  189. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2016, https://doi.org/10.12989/csm.2020.9.3.281
  190. Active vibration control of nonlinear stiffened FG cylindrical shell under periodic loads vol.25, pp.6, 2016, https://doi.org/10.12989/sss.2020.25.6.643
  191. Dynamic behavior of axially functionally graded simply supported beams vol.25, pp.6, 2016, https://doi.org/10.12989/sss.2020.25.6.669
  192. Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00742-z
  193. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633
  194. 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
  195. 2D magnetic field effect on the thermal buckling of metal foam nanoplates reinforced with FG-GPLs lying on Pasternak foundation in humid environment vol.135, pp.11, 2016, https://doi.org/10.1140/epjp/s13360-020-00905-8
  196. Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory vol.23, pp.3, 2016, https://doi.org/10.1177/1099636219845841
  197. Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions vol.23, pp.3, 2016, https://doi.org/10.1177/1099636219851281
  198. Stress Distribution on the Cracked Sandwich Plate with Non Linear Thermal and Moisture Concentration vol.32, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.32.45
  199. Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’ vol.23, pp.5, 2021, https://doi.org/10.1177/1099636220904340
  200. Modeling of memory-dependent derivative in a functionally graded plate vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1606962
  201. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1607623
  202. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2016, https://doi.org/10.12989/scs.2021.40.3.355