An Efficient Shear Deformation Beam Theory Based on Neutral Surface Position for Bending and Free Vibration of Functionally Graded Beams#

By Latifa Ould Larbi, Abdelhakim Kaci, Mohammed Sid Ahmed Houari, Abdelouahed Tounsi. 2013

200 citations recorded by the source corpus.

In this article, an efficient shear deformation beam theory based on neutral surface position is developed for bending and frees vibration analysis of functionally graded beams. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The neutral surface position for a functionally graded beam in which its material properties vary in the thickness direction is determined. Based on the present higher order shear deformation beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3db4cb260cc4984ee2d3459355b0c11a5141706c

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position (2015, unknown): “[20], Bousahla et al.”
Parametric study of three-dimensional bending and frequency of FG-GPLRC porous circular and annular plates on different boundary conditions (2019, background): “…many advantages and superior properties, including high temperature resistance and high strength (Yuda and Xiaoguang 2011; Demirhan and Kanber 2013; Larbi et al. 2013; Sofiyev et al. 2016; Tufekci, Eroglu, and Aya 2016; Li 2017; Wang, Liang, and Jin 2017; Arefi and Soltan Arani 2018; Ding et al.…”
Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept (2016, background): “…of the neutral surface of the FG nanobeam is determined 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…”
Nonlinear vibration analysis of functionally graded beams considering the influences of the rotary inertia of the cross section and neutral surface position (2018, unknown): “On the other hand, in the above studies the physical neutral surface was coincided with the geometric mid-surface (Yaghoobi and Fereidoon, 2010; Larbi et al., 2013; Bellifa et al., 2016).”
On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model (2015, methodology): “…ρ is given by the rule of mixtures as (Natarajan et al. 2011, Benachour et al. 2011, Bessaim et al. 2013, Yaghoobi and Torabi 2013, Tounsi et al. 2013d, Ould Larbi et al. 2013, Bouremana et al. 2013, Hebali et al. 2014) mmCC VV (5) 1066 On vibration properties of functionally graded nano-plate…”
A new simple shear and normal deformations theory for functionally graded beams (2015, methodology): “Some researchers (Bousahla et al. 2014, Ould Larbi et al. 2013, Yahoobi and Feraidoon 2010, Morimoto et al. 2006) have shown that there is no stretching-bending coupling in constitutive equations if the reference surface is properly selected.”
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation (2016, background): “…engineering applications (El Meiche et al. 2011, Bourada et al. 2012, Tounsi et al. 2013c, Bouderba et al. 2013, Yaghoobi and Torabi 2013, Ould Larbi et al. 2013, Chakraverty and Pradhan 2014, Liang et al. 2014, Zidi et al. 2014, Khalfi et al. 2014, Fekrar et al. 2014, Bousahla et al. 2014,…”
Static and free vibration analysis of graphene platelets reinforced composite truncated conical shell, cylindrical shell, and annular plate using theory of elasticity and DQM (2020, background): “2019 Taylor & Francis Group, LLC properties, including high temperature resistance and high strength (C. Li 2017; Ding et al. 2018; Larbi et al. 2013; A. Sofiyev et al. 2016; Tufekci, Eroglu, and Aya 2016; X. Wang, Liang, and Jin 2017; Yuda and Xiaoguang 2011; Mao et al. 2018).”