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

By M. Bourada, Abdelhakim Kaci, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi. Steel and composite structures, 2015

377 citations recorded by the source corpus.

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 (ez ≠ 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.

Subfields: Civil and Structural Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/442b1affea068901ac0f83c89bd78348dcc8378c

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Citations in the corpus

Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory (2016, background): “So, it is also possible to extend these theories accounting for thickness stretching effect [36–38].”
Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams (2017, background): “Hosseini and SadeghiGoughari [29] studied vibration and instability of nanotubes conveying fluid subjected to a longitudinal magnetic field based on DTM.”
Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams (2016, methodology): “An appropriate shear correction factor is needed in the formulations due to the zero transverse shear stress and strain condition at the upper and lower surfaces of the beam [32].”
Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT (2019, neutral): “2014, Bourada et al .”
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation (2016, background): “…form, this principle can be stated by (Reddy 2007, Draiche et al. 2014, Ait Amar Meziane et al. 2014, Nedri et al. 2014, Mahi et al. 2015, Bourada et al. 2015, Al-Basyouni et al. 2015) t fp dtKUU 0 ) (0 (10) where δUp and δUf are the variations of strain energy of the plate and…”
Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept (2016, background): “…to satisfy the first moment with respect to Young‟s modulus being zero as follows (Ould Larbi et al. 2013, Bousahla et al. 2014, Fekrar et al. 2014, Bourada et al. 2015) 0)( 2/ 2/ h h msmsms dzCzzE (3) Consequently, the position of neutral surface can be obtained as 966 Size-dependent…”