Steel and Composite Structures

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A new higher order shear and normal deformation theory for functionally graded beams

  • Meradjah, Mustapha (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 (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • 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 : 2014.06.17
  • Accepted : 2014.09.28
  • Published : 2015.03.25
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Abstract

In this scientific work, constructing of a novel shear deformation beam model including the stretching effect is of concern for flexural and free vibration responses of functionally graded beams. The particularity of this model is that, in addition to considering the transverse shear deformation and the stretching effect, the zero transverse shear stress condition on the beam surface is assured without introducing the shear correction parameter. By employing the Hamilton's principle together with the concept of the neutral axe's position for such beams, the equations of motion are obtained. Some examples are performed to demonstrate the effects of changing gradients, thickness stretching, and thickness to length ratios on the bending and vibration of functionally graded beams.

Keywords

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  52. 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
  53. 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
  54. 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
  55. Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory vol.15, pp.6, 2019, https://doi.org/10.1108/mmms-03-2019-0057
  56. 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
  57. 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
  58. 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
  59. Buckling and stability analysis of sandwich beams subjected to varying axial loads vol.34, pp.2, 2015, https://doi.org/10.12989/scs.2020.34.2.241
  60. 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
  61. Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer vol.35, pp.3, 2015, https://doi.org/10.12989/scs.2020.35.3.343
  62. Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes vol.36, pp.6, 2015, https://doi.org/10.12989/scs.2020.36.6.643
  63. Three-point bending of beams with consideration of the shear effect vol.37, pp.6, 2015, https://doi.org/10.12989/scs.2020.37.6.733
  64. A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams vol.9, pp.12, 2015, https://doi.org/10.3390/math9121422