Hichem Bellifa

Bio: Hichem Bellifa is an academic researcher from SIDI. The author has contributed to research in topics: Plate theory & Neutral plane. The author has an hindex of 4, co-authored 6 publications receiving 325 citations.

Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position

Abstract: A new first-order shear deformation theory is developed for bending and dynamic behaviors of functionally graded plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The equations governing the axial and transverse deformations of functionally graded plates are derived based on the present first-order shear deformation plate theory and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. To examine accuracy of the present formulation, several comparison studies are investigated. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams

Abstract: In this work, a nonlocal zeroth-order shear deformation theory is developed for the nonlinear postbuckling behavior of nanoscale beams. The beauty of this formulation is that, in addition to including the nonlocal effect according to the nonlocal elasticity theory of Eringen, the shear deformation effect is considered in the axial displacement within the use of shear forces instead of rotational displacement like in existing shear deformation theories. The principle of virtual work together of the nonlocal differential constitutive relations of Eringen, are considered to obtain the equations of equilibrium. Closed-form solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state for simply supported and clamped clamped nanoscale beams are determined.

An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates

Abstract: In this article, an efficient and simple refined theory is proposed for buckling analysis of functionally graded plates by using a new displacement field which includes undetermined integral variables. This theory contains only four unknowns, with is even less than the first shear deformation theory (FSDT). Governing equations are obtained from the principle of virtual works. The closed-form solutions of rectangular plates are determined. Comparison studies are carried out to check the validity of obtained results. The influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are examined and discussed.

Influence of porosity on thermal buckling behavior of functionally graded beams

Abstract: The interest of this work is the analysis of the effect of porosity on the nonlinear thermal stability response of power law functionally graded beam with various boundary conditions. The modelling was done according to the Euler-Bernoulli beam model where the distribution of material properties is imitated polynomial function. The thermal loads are assumed to be not only uniform but linear as well non-linear and the temperature rises through the thickness direction. The effects of the porosity parameter, slenderness ratio and power law index on the thermal buckling of P-FG beam are discussed.

Une nouvelle théorie quasi-3D pour l'étude de la flexion thermomécanique des plaques fonctionnellement graduées épaisses

Abstract: The aim of this research is to study the thermomechanical bending analysis of functionally graded thick plates by proposing a new quasi-3D theory of shear deformation. The mathematical model used proposes only 5 variables as in the case of the theory of deformation at first order shear (FSDT). Unlike high order theories (HSDT) this theory presents a new field of displacement that includes indeterminate integral variables. The mechanical properties of the functionally graduated plate are assumed to change in the thickness direction according to a power law (P-FGM). The governing equations for the thermomechanical bending study are obtained by the principle of virtual work and solved by a Navier method. Interesting results are determined and compared with the results found by the HSDT and 2D theories. The influence of the thickness of the plate and of the index of power law on the arrow and the stresses of the thick FGM plates will be represented. Mots clefs : Matériaux fonctionnellement gradués, Etude de la flexion thermomécanique, Les plaques épaisses, Théorie quasi 3-D, L’effet d’étirement

Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures

Abstract: This research develops a nonlocal couple stress theory to investigate static stability and free vibration characteristics of functionally graded (FG) nanobeams. The theory introduces two parameters based on nonlocal elasticity theory and modified couple stress theory to capture the size effects much accurately. Therefore, a nonlocal stress field parameter and a material length scale parameter are used to involve both stiffness-softening and stiffness-hardening effects on responses of FG nanobeams. The FG nanobeam is modeled via a higher order refined beam theory in which shear deformation effect is verified needless of shear correction factor. A power-law distribution is used to describe the graded material properties. The governing equations and the related boundary conditions are derived by Hamilton’s principle and they are solved applying Chebyshev–Ritz method which satisfies various boundary conditions. A comparison study is performed to verify the present formulation with the provided data in the literature and a good agreement is observed. The parametric study covered in this paper includes several parameters such as nonlocal and length scale parameters, power-law exponent, slenderness ratio, shear deformation and various boundary conditions on natural frequencies and buckling loads of FG nanobeams in detail.

Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory

Abstract: The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.