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Bouderba B.,University Djilali Liabes | Houari M.S.A.,University Djilali Liabes | Tounsi A.,University Djilali Liabes | Tounsi A.,Algerian National Thematic Agency of Research in Science and Technology ATRST | And 2 more authors.
Structural Engineering and Mechanics | Year: 2016

In the present work, a simple first-order shear deformation theory is developed and validated for a variety of numerical examples of the thermal buckling response of functionally graded sandwich plates with various boundary conditions. Contrary to the conventional first-order shear deformation theory, the present first-order shear deformation theory involves only four unknowns and has strong similarities with the classical plate theory in many aspects such as governing equations of motion, and stress resultant expressions. Material properties and thermal expansion coefficient of the sandwich plate faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. The thermal loads are considered as uniform, linear and non-linear temperature rises within the thickness direction. The results reveal that the volume fraction index, loading type and functionally graded layers thickness have significant influence on the thermal buckling of functionally graded sandwich plates. Moreover, numerical results prove that the present simple first-order shear deformation theory can achieve the same accuracy of the existing conventional first-order shear deformation theory which has more number of unknowns. Copyright © 2016 Techno-Press, Ltd. Source


Bounouara F.,University Djilali Liabes | Benrahou K.H.,University Djilali Liabes | Belkorissat I.,University Djilali Liabes | Tounsi A.,University Djilali Liabes | Tounsi A.,Algerian National Thematic Agency of Research in Science and Technology ATRST
Steel and Composite Structures | Year: 2016

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated. Copyright © 2016 Techno-Press, Ltd. Source


Bellifa H.,University Djilali Liabes | Benrahou K.H.,University Djilali Liabes | Hadji L.,University Djilali Liabes | Hadji L.,Universite Ibn Khaldoun | And 4 more authors.
Journal of the Brazilian Society of Mechanical Sciences and Engineering | Year: 2016

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. © 2015, The Brazilian Society of Mechanical Sciences and Engineering. Source


Aissani K.,University Djilali Liabes | Bachir Bouiadjra M.,University Djilali Liabes | Bachir Bouiadjra M.,Algerian National Thematic Agency of Research in Science and Technology ATRST | Ahouel M.,University Djilali Liabes | And 2 more authors.
Structural Engineering and Mechanics | Year: 2015

This work presents a new nonlocal hyperbolic shear deformation beam theory for the static, buckling and vibration of nanoscale-beams embedded in an elastic medium. The present model is able to capture both the nonlocal parameter and the shear deformation effect without employing shear correction factor. The nonlocal parameter accounts for the small size effects when dealing with nanosize structures such as nanobeams. Based on the nonlocal differential constitutive relations of Eringen, the equations of motion of the nanoscale-beam are obtained using Hamilton's principle. The effect of the surrounding elastic medium on the deflections, critical buckling loads and frequencies of the nanobeam is investigated. Both Winklertype and Pasternak-type foundation models are used to simulate the interaction of the nanobeam with the surrounding elastic medium. Analytical solutions are presented for a simply supported nanoscale-beam, and the obtained results compare well with those predicted by the other nonlocal theories available in literature. Copyright © 2015 Techno-Press, Ltd. Source


Chikh A.,University Djilali Liabes | Bakora A.,University Djilali Liabes | Heireche H.,University Djilali Liabes | Houari M.S.A.,University Djilali Liabes | And 5 more authors.
Structural Engineering and Mechanics | Year: 2016

In this work, an analytical formulation based on both hyperbolic shear deformation theory and stress function, is presented to study the nonlinear post-buckling response of symmetric functionally graded plates supported by elastic foundations and subjected to in-plane compressive, thermal and thermomechanical loads. Elastic properties of material are based on sigmoid power law and varying across the thickness of the plate (S-FGM). In the present formulation, Von Karman nonlinearity and initial geometrical imperfection of plate are also taken into account. By utilizing Galerkin procedure, closed-form expressions of buckling loads and post-buckling equilibrium paths for simply supported plates are obtained. The effects of different parameters such as material and geometrical characteristics, temperature, boundary conditions, foundation stiffness and imperfection on the mechanical and thermal buckling and post-buckling loading capacity of the S-FGM plates are investigated. Copyright © 2016 Techno-Press, Ltd. Source

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