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CONTENTS
Volume 8, Number 3, September 2019
 

Abstract
In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.

Key Words
functionally graded materials; sandwich plates; refined plate theory; bending; Navier solution; porosity

Address
(1) Ahemd Keddouri:
Department of Earth Sciences and Universe, Ziane Achour University, BP 3117, 17000 Djelfa, Algeria;
(2) Ahemd Keddouri, Abdelouahed Tounsi:
Material and Hydrology Laboratory, University of Sidi Bel Abbes 22000, Algeria;
(3) Lazreg Hadji:
Department of Mechanical Engineering, Ibn Khaldoun University, BP 78 Zaaroura, 14000 Tiaret, Algeria;
(4) Lazreg Hadji:
Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret, Algeria.

Abstract
This paper researches static and dynamic bending behaviors of a crystalline nano-size shell having pores and grains in the framework of strain gradient elasticity. Thus, the nanoshell is made of a multi-phase porous material for which all material properties on dependent on the size of grains. Also, in order to take into account small size effects much accurately, the surface energies related to grains and pores have been considered. In order to take into account all aforementioned factors, a micro-mechanical procedure has been applied for describing material properties of the nanoshell. A numerical trend is implemented to solve the governing equations and derive static and dynamic deflections. It will be proved that the static and dynamic deflections of the crystalline nanoshell rely on pore size, grain size, pore percentage, load location and strain gradient coefficient.

Key Words
crystalline material; static bending; porous nanoshell; strain gradient; Mori-Tanaka scheme

Address
Al-Mustansiriah University, Engineering Collage P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq.


Abstract
In this study, the interfacial stresses in RC beams strengthened by externally bonded prestressed GFRP laminate are evaluated using an analytical approach, based on the equilibrium equations and boundary conditions. A comparison of the interfacial stresses obtained from the present analytical model and other existing models is undertaken. Otherwise, a parametric study is conducted to investigate the effects of geometrical and material properties on the variation of interfacial stresses in damaged RC beams strengthened by externally bonded prestressed GFRP laminate. The results obtained indicate that the damage degree has little effect on the maximum shear stress, with a variation less than 5% between the damaged and undamaged RC beams. However, the results also reveal that the prestressing level has a significant effect on the interfacial stresses; hence the damaged RC beam strengthened with an initial prestressing force of 100 kN gives 110% higher maximum shear stress than the damaged RC beam strengthened with an initial prestressing force of 50 kN. The values of shear stress obtained by the analytical approach are approximately equal to 44% of those obtained from the numerical solution, while the interfacial normal stresses predicted by the numerical study are approximately 26% higher than those calculated by the analytical solution.

Key Words
damaged beam; interfacial stresses; strengthening; prestressed GFRP laminate; analytical solution

Address
(1) Selma Chergui, Mostefa Hamrat, Bensaid Boulekbache, Abdelkader Bougara:
Hassiba Benbouali University of Chlef, Algeria;
(2) Tahar Hassaine Daouadji:
Laboratory of Geomatics and sustainable development, University of Tiaret, Algeria;
(3) Boussad Abbes:
GRESPI Laboratory, University of Reims, France;
(4) Sofiane Amziane:
Université Clermont Auvergne, Institut Pascal, Clermont-Ferrand, France.

Abstract
This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

Key Words
nonlinear buckling; graphene platelets; geometric imperfection; thermal loading; modified couple stress theory

Address
Al-Mustansiriah University, Engineering Collage P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq.


Abstract
The present article researches large-amplitude thermal free vibration characteristics of nonlocal two-phase piezo-magnetic nano-size beams having geometric imperfections by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All previous studies on vibrations of piezoelectric-magnetic nano-size beams ignore the influences of geometric imperfections which are crucial since a nanobeam is not always ideal or perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtain nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric phase in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam is dependent on the magnitude of exerted electric voltage, magnetic imperfection amplitude and substrate constants.

Key Words
piezo-magnetic nanobeam; geometrical imperfection; thermal vibration; piezoelectric reinforcement; electric voltage

Address
Al-Mustansiriah University, Engineering Collage P.O. Box 46049, Bab-Muadum, Baghdad 10001, Iraq.



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