Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory

Kaci, Abdelhakim,Houari, Mohammed Sid Ahmed,Bousahla, Abdelmoumen Anis,Tounsi, Abdelouahed,Mahmoud, S.R. Techno-Press 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.5

In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory

Abdelhakim Kaci,Mohammed Sid Ahmed Houari,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,S. R. Mahmoud 국제구조공학회 2018 Structural Engineering and Mechanics, An Int'l Jou Vol.65 No.5

In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

Nonlinear cylindrical bending analysis of E-FGM plateswith variable thickness

Abdelhakim Kaci,Khalil Belakhdar,Abdelouahed Tounsi,El Abbes Adda Bedia 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.4

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates

Abdelhakim Kaci,Abdelouahed Tounsi,Karima Bakhti,El Abbas Adda Bedia 국제구조공학회 2012 Steel and Composite Structures, An International J Vol.12 No.6

In this paper, the nonlinear cylindrical bending of simply supported, functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs), is studied. The plates are subjected to uniform pressure loading in thermal environments and their geometric nonlinearity is introduced in the strain–displacement equations based on Von-Karman assumptions. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are reduced to linear differential equation with nonlinear boundary conditions yielding a simple solution procedure. Numerical results are presented to show the effect of the material distribution on the deflections and stresses.

A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams

Khadra Bouafia,Abdelhakim Kaci,Mohammed Sid Ahmed Houari,Abdelnour Benzair,Abdelouahed Tounsi 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.19 No.2

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

A four variable refined plate theory for nonlinear cylindrical bending analysis of functionally graded plates under thermomechanical loadings

Bouazza Fahsi,Abdelhakim Kaci,Abdelouahed Tounsi,El Abbas Adda Bedia 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.12

In this paper we present a new application for a four variable refined plate theory to analyse the nonlinear cylindrical bending behavior of functionally graded plates subjected to thermomechanical loadings. This recent theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and,likewise, the shear components do not contribute toward bending moments. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. The non-linear strain–displacement relations in the von Karman sense are used to study the effect of geometric non-linearity. The solutions are achieved by minimizing the total potential energy and the results are compared to the classical and the first-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the nonlinear cylindrical bending behavior of functionally graded plates.

An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core

Djilali Kouider,Abdelhakim Kaci,Mahmoud M. Selim,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,Abdelouahed Tounsi,Muzamal Hussain 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.41 No.2

This paper presents an original high-order shear and normal deformation theory for the static and free vibration of sandwich plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. New types of functionally graded materials (FGMs) sandwich plates are considered, namely, both FG face sheets which the properties vary according to power-law function and exponentially graded hard core. The equations of motion for the present problem are derived from Hamilton’s principle. For simply-supported boundary conditions, Navier’s approach is utilized to solve the motion equations. The accuracy of the present theory is verified by comparing the obtained results with three-dimensional elasticity solutions and other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending and free vibration responses of the FGM sandwich plates are studied. It can be concluded that present formulation which takes into account both the transverse shear and normal deformation, predicts the natural frequencies with the same degree of accuracy as that of 3D elasticity solutions and gives a good results of displacements and stress compared with others Quasi-3D theories. It can be also deduced that the central deflection is in direct correlation relation with inhomogeneity parameter and the natural frequency is in inverse relation with this parameter.

A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and free vibration analysis

Miloud Kaddari,Abdelhakim Kaci,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,Fouad Bourada,AbdeldjebbarTounsi,E.A. Adda Bedia,Mohammed A. Al-Osta 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.1

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions

Abderrahmane Menasria,Abdelhakim Kaci,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdeldjebbar Tounsi,Kouider Halim Benrahou,Abdelouahed Tounsi,E.A. Adda Bedia,S.R. Mahmoud 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.36 No.3

The current work, present dynamic analysis of the FG-sandwich plate seated on elastic foundation with various kinds of support using refined shear deformation theory. The present analytical model is simplified which the unknowns number are reduced. The zero-shear stresses at the free surfaces of the FG-sandwich plate are ensured without introducing any correction factors. The four equations of motion are determined via Hamilton’s principle and solved by Galerkin’s approach for FG-sandwich plate with three kinds of the support. The proposed analytical model is verified by comparing the results with those obtained by other theories existing in the literature. The parametric studies are presented to detect the various parameters influencing the fundamental frequencies of the symmetric and non-symmetric FG-sandwich plate with various boundary conditions.

A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations

Houari Hachemi,Abdelhakim Kaci,Mohammed Sid Ahmed Houari,Mohamed Bourada,Abdelouahed Tounsi,S.R. Mahmoud 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.25 No.6

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, sideto- thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.