Structural Engineering and Mechanics

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On thermal stability of plates with functionally graded coefficient of thermal expansion

  • Bousahla, Abdelmoumen Anis (Centre Universitaire de Relizane) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2016.03.15
  • Accepted : 2016.07.19
  • Published : 2016.10.25
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Abstract

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

Keywords

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  57. 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
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  61. 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
  62. 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
  63. Dynamic characteristics of curved inhomogeneous nonlocal porous beams in thermal environment vol.64, pp.1, 2016, https://doi.org/10.12989/sem.2017.64.1.121
  64. 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
  65. 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
  66. 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
  67. 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
  68. 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
  69. 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
  70. 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
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  72. 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
  73. 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
  74. 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
  75. 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
  76. 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
  77. 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
  78. Post-buckling responses of a laminated composite beam vol.26, pp.6, 2016, https://doi.org/10.12989/scs.2018.26.6.733
  79. 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
  80. 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
  81. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.027
  82. 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
  83. 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
  84. 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
  85. 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
  86. 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
  87. 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
  88. 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
  89. 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
  90. A unified formulation for modeling of inhomogeneous nonlocal beams vol.66, pp.3, 2016, https://doi.org/10.12989/sem.2018.66.3.369
  91. Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory vol.15, pp.1, 2016, https://doi.org/10.12989/gae.2018.15.1.711
  92. 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
  93. Mathematical modeling of smart nanoparticles-reinforced concrete foundations: Vibration analysis vol.27, pp.4, 2016, https://doi.org/10.12989/scs.2018.27.4.465
  94. 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
  95. 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
  96. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  97. 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
  98. Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials vol.27, pp.6, 2016, https://doi.org/10.12989/scs.2018.27.6.777
  99. Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations vol.66, pp.6, 2016, https://doi.org/10.12989/sem.2018.66.6.729
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  101. 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
  102. 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
  103. Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field vol.67, pp.1, 2016, https://doi.org/10.12989/sem.2018.67.1.021
  104. 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
  105. The critical buckling load of reinforced nanocomposite porous plates vol.67, pp.2, 2016, https://doi.org/10.12989/sem.2018.67.2.115
  106. 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
  107. 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
  108. Forced vibration response in nanocomposite cylindrical shells - Based on strain gradient beam theory vol.28, pp.3, 2016, https://doi.org/10.12989/scs.2018.28.3.381
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  110. 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
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  115. Seismic analysis of AL2O3 nanoparticles-reinforced concrete plates based on sinusoidal shear deformation theory vol.15, pp.3, 2016, https://doi.org/10.12989/eas.2018.15.3.285
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  117. Dynamic analysis of immersion concrete pipes in water subjected to earthquake load using mathematical methods vol.15, pp.4, 2016, https://doi.org/10.12989/eas.2018.15.4.361
  118. 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
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  121. 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
  122. Size-dependent forced vibration response of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory vol.22, pp.5, 2016, https://doi.org/10.12989/sss.2018.22.5.527
  123. 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
  124. Thermal stress induced by electric current in the vicinity of an elliptic inclusion in an infinite plate vol.42, pp.8, 2016, https://doi.org/10.1080/01495739.2019.1607789
  125. Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory vol.6, pp.1, 2019, https://doi.org/10.12989/aas.2019.6.1.001
  126. Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel vol.16, pp.1, 2016, https://doi.org/10.12989/eas.2019.16.1.055
  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
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  130. 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
  131. 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
  132. 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
  133. 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
  134. Experimental method for obtaining the elastic properties of components of a laminated composite vol.12, pp.None, 2019, https://doi.org/10.1016/j.rinp.2019.01.016
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  136. 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
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  138. 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
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  144. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  145. Nonlinear bending and thermal post-buckling behavior of functionally graded piezoelectric nanosize beams using a refined model vol.6, pp.6, 2016, https://doi.org/10.1088/2053-1591/ab0f78
  146. 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
  147. 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
  148. 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
  149. Robust quasi 3D computational model for mechanical response of FG thick sandwich plate vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.571
  150. Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities vol.6, pp.2, 2016, https://doi.org/10.12989/smm.2019.6.2.147
  151. 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
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  153. 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
  154. 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
  155. 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
  156. 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
  157. 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
  158. 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
  159. 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
  160. Interaction Between Thermal Field and Two-Dimensional Functionally Graded Materials: A Structural Mechanical Example vol.11, pp.10, 2016, https://doi.org/10.1142/s1758825119500996
  161. 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
  162. 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
  163. 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
  164. 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
  165. 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
  166. 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
  167. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  168. 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
  169. 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
  170. Buckling response of functionally graded nanoplates under combined thermal and mechanical loadings vol.22, pp.4, 2020, https://doi.org/10.1007/s11051-020-04815-9
  171. 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
  172. 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
  173. 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
  174. 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
  175. Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer vol.35, pp.3, 2016, https://doi.org/10.12989/scs.2020.35.3.343
  176. 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
  177. Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates vol.36, pp.3, 2016, https://doi.org/10.1007/s00366-019-00737-w
  178. 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
  179. 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
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