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A new simple shear and normal deformations theory for functionally graded beams
Mohamed Bourada,Abdelouahed Tounsi,Abdelhakim Kaci,Mohammed Sid Ahmed Houari 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.2
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 (εz= 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.
Buckling behavior of rectangular plates under uniaxial and biaxial compression
Mohamed Bourada,Abed Bouadi,Abdelmoumen Anis Bousahla,Amel Senouci,Fouad Bourada,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.70 No.1
In the classical stability investigation of rectangular plates the classical thin plate theory (CPT) is often employed, so omitting the transverse shear deformation effect. It seems quite clear that this procedure is not totally appropriate for the investigation of moderately thick plates, so that in the following the first shear deformation theory proposed by Meksi et al. (2015), that permits to consider the transverse shear deformation influences, is used for the stability investigation of simply supported isotropic rectangular plates subjected to uni-axial and bi-axial compression loading. The obtained results are compared with those of CPT and, for rectangular plates under uniaxial compression, a novel direct formula, similar to the conventional Bryan’s expression, is found for the Euler stability stress. The accuracy of the present model is also ascertained by comparing it, with model proposed by Piscopo (2010).
Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory
Fouad Bourada,Abdelmoumen Anis Bousahla,Mohamed Bourada,Abdelghani Azzaz,Amina Zinata,Abdelouahed Tounsi 한국풍공학회 2019 Wind and Structures, An International Journal (WAS Vol.28 No.1
This article present the free vibration analysis of simply supported perfect and imperfect (porous) FG beams using a high order trigonometric deformation theory. It is assumed that the material properties of the porous beam vary across the thickness. Unlike other theories, the number of unknown is only three. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton’s principle will be used herein to determine the equations of motion. Since, the beams are simply supported the Navier’s procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature.
Liani, Mohamed,Moulay, Noureddine,Bourada, Fouad,Addou, Farouk Yahia,Bourada, Mohamed,Tounsi, Abdelouahed,Hussain, Muzamal Techno-Press 2022 Advances in materials research Vol.11 No.1
In this paper, the nonlocal integral Timoshenko beam model is employed to study the free vibration characteristics of singled walled carbon nanotubes (SWCNTs) including the thermal effect. Based on the nonlocal continuum theory, the governing equations of motion are formulated by considering thermal effect. The influences of small scale parameter, the chirality of SWCNTs, the vibrational mode number, the aspect ratio of SWCNTs and temperature changes on the thermal vibration properties of single-walled nanotubes are examined and discussed. Results indicate significant dependence of natural frequencies on the nonlocal parameter, the temperature change, the aspect ratio and the chirality of SWCNTs. This work should be useful reference for the application and the design of nanoelectronics and nanoelectromechanical devices that make use of the thermal vibration properties of SWCNTs.
A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation
Zoulikha Boukhlif,Mohammed Bouremana,Fouad Bourada,Abdelmoumen Anis Bousahla,Mohamed Bourada,Abdelouahed Tounsi,Mohammed A. Al-Osta 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.31 No.5
This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (εz ≠ 0), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton‟s principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.
Bendaho, Boudjema,Belabed, Zakaria,Bourada, Mohamed,Benatta, Mohamed Atif,Bourada, Fouad,Tounsi, Abdelouahed Techno-Press 2019 Advances in nano research Vol.7 No.4
In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.
On the free vibration response of laminated composite plates via FEM
Mohammed Sehoul,Soumia Benguediab,Mohamed Benguediab,Mahmoud M. Selim,Fouad Bourada,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.2
In this research paper, the free vibrational response of laminated composite plates is investigated using a non-polynomial refined shear deformation theory (NP-RSDT). The most interesting feature of this theory is the parabolic distribution of transverse shear deformations while ensuring the conditions of nullity of shear stresses at the free surfaces of the plate without requiring the Shear correction factor “Ks”. A fourth-nodded isoparametric element with four degrees of freedom per node is employed for laminated composite plates. The numerical analysis of simply supported square anti-symmetric cross-ply and angle-ply laminated plate is carried out using a special discretization based on four-node finite element method which four degrees of freedom per node. Several numerical results are presented to show the effect of the coupling parameters of the plate such as the modulus ratios, the thickness ratio and the plate layers number on adimensional eigen frequencies. All numerical results presented using the current finite element method (FEM) is presented in 3D curve form.
Mohamed Mekerbi,Samir Benyoucef,Abdelkader Mahmoudi,Fouad Bourada,Abdelouahed Tounsi 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.72 No.4
The present article deals with thermal buckling of functionally graded plates with porosity and resting on elastic foundation. The basic formulation is based on quasi 3D theory. The present theory contains only four unknowns and also accommodates the thickness stretching effect. Porosity-dependent material coefficients of the plate are compositionally graded throughout the thickness according to a modified micromechanical model. Different patterns of porosity distributions are considered. The thermal loads are assumed to be uniform, linear and non-linear temperature rises through the thickness direction. The plate is assumed to be simply supported on all edges. Various numerical examples are given to check the accuracy and reliability of the present solution, in which both the present results and those reported in the literature are provided. In addition, several numerous new results for thick FG plates with porosity are also presented.
Mohammed Cherif Rahmani,Abdelhakim Kaci,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,E.A. Adda Bedia,S.R. Mahmoud,Kouider Halim Benrahou,Abdelouahed Tounsi 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.3
The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin’s approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.
Vibration analysis of different material distributions of functionally graded microbeam
Youcef Tlidji,Mohamed Zidour,Kadda Draiche,Abdelkader Safa,Mohamed Bourada,Abdelouahed Tounsi,Abdelmoumen Anis Bousahla,S. R. Mahmoud 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.69 No.6
In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton’s principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.