Geomechanics and Engineering

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A refined theory with stretching effect for the flexure analysis of laminated composite plates

  • Draiche, Kada (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret) ;
  • 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 : 2015.07.16
  • Accepted : 2016.07.03
  • Published : 2016.11.25
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Abstract

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

Keywords

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  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory vol.16, pp.2, 2016, https://doi.org/10.12989/gae.2018.16.2.141
  47. 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
  48. Post-buckling responses of a laminated composite beam vol.26, pp.6, 2016, https://doi.org/10.12989/scs.2018.26.6.733
  49. 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
  50. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.027
  51. 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
  52. 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
  53. 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
  54. 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
  55. 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
  56. 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
  57. 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
  58. 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
  59. 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
  60. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.567
  61. 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
  62. 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
  63. 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
  64. 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
  65. 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
  66. 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
  67. 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
  68. 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
  69. 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
  70. 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
  71. 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
  72. Nonlinear analysis of damaged RC beams strengthened with glass fiber reinforced polymer plate under symmetric loads vol.15, pp.2, 2016, https://doi.org/10.12989/eas.2018.15.2.113
  73. 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
  74. 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
  75. 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
  76. 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
  77. Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure vol.67, pp.6, 2018, https://doi.org/10.12989/sem.2018.67.6.565
  78. A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates vol.22, pp.3, 2016, https://doi.org/10.12989/sss.2018.22.3.303
  79. Dynamic buckling of smart sandwich beam subjected to electric field based on hyperbolic piezoelasticity theory vol.22, pp.3, 2016, https://doi.org/10.12989/sss.2018.22.3.327
  80. 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
  81. 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
  82. 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
  83. 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
  84. 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
  85. 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
  86. 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
  87. 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
  88. 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
  89. 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
  90. 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
  91. 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
  92. 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
  93. 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
  94. 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
  95. 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
  96. 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
  97. 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
  98. 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
  99. 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
  100. 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
  101. 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
  102. 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
  103. 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
  104. 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
  105. 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
  106. 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
  107. Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory vol.24, pp.4, 2019, https://doi.org/10.12989/cac.2019.24.4.369
  108. Effect of porosity in interfacial stress analysis of perfect FGM beams reinforced with a porous functionally graded materials plate vol.72, pp.3, 2016, https://doi.org/10.12989/sem.2019.72.3.293
  109. 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
  110. 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
  111. Theoretical and experimental modal responses of adhesive bonded T-joints vol.29, pp.5, 2016, https://doi.org/10.12989/was.2019.29.5.361
  112. Free vibration analysis of angle-ply laminated composite and soft core sandwich plates vol.33, pp.5, 2019, https://doi.org/10.12989/scs.2019.33.5.663
  113. 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
  114. 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
  115. 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
  116. 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
  117. 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
  118. Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect vol.34, pp.2, 2016, https://doi.org/10.12989/scs.2020.34.2.279
  119. 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
  120. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2016, https://doi.org/10.1140/epjp/s13360-020-00137-w
  121. Application of semi-analytical method to vibration analysis of multi-edge crack laminated composite beams with elastic constraint vol.135, pp.2, 2020, https://doi.org/10.1140/epjp/s13360-020-00140-1
  122. 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
  123. 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
  124. A study of fracture of a fibrous composite vol.73, pp.5, 2016, https://doi.org/10.12989/sem.2020.73.5.585
  125. Analysis of Laminated Plates Subjected to Mechanical and Hygrothermal Environmental Loads Using Fifth-Order Shear and Normal Deformation Theory vol.12, pp.3, 2020, https://doi.org/10.1142/s1758825120500283
  126. 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
  127. 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
  128. 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
  129. 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
  130. 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
  131. 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
  132. Static stability analysis of smart nonlocal thermo-piezo-magnetic plates via a quasi-3D formulation vol.26, pp.1, 2020, https://doi.org/10.12989/sss.2020.26.1.077
  133. Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects vol.234, pp.18, 2016, https://doi.org/10.1177/0954406220916481
  134. Forced vibration of a functionally graded porous beam resting on viscoelastic foundation vol.24, pp.1, 2016, https://doi.org/10.12989/gae.2021.24.1.091
  135. The effect of micro-architecture on the failure response of multi-layered lattice sandwich panels under three-point loading vol.23, pp.2, 2016, https://doi.org/10.1177/1099636219842163
  136. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2016, https://doi.org/10.1080/17455030.2019.1607623
  137. Quasi-static compressive strength of polymethacrylimide foam-filled square carbon fiber reinforced composite honeycombs vol.23, pp.6, 2021, https://doi.org/10.1177/1099636220909819