Influence of the porosities on the free vibration of FGM beams

Hadji, L.,Adda Bedia, E.A. Techno-Press 2015 Wind and Structures, An International Journal (WAS Vol.21 No.3

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

Vibration analysis of nonlocal porous nanobeams made of functionally graded material

Berghouti, Hana,Adda Bedia, E.A.,Benkhedda, Amina,Tounsi, Abdelouahed Techno-Press 2019 Advances in nano research Vol.7 No.5

In this work, dynamic behavior of functionally graded (FG) porous nano-beams is studied based on nonlocal nth-order shear deformation theory which takes into the effect of shear deformation without considering shear correction factors. It has been observed that during the manufacture of "functionally graded materials" (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the dynamic analysis of FG beams taking into account the influence of these imperfections is established. Material characteristics of the FG beam are supposed to be vary continuously within thickness direction according to a "power-law scheme" which is modified to approximate material characteristics for considering the influence of porosities. A comparative study with the known results in the literature confirms the accuracy and efficiency of the current nonlocal nth-order shear deformation theory.

Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory

Abderrahmane Mouffoki,E.A. Adda Bedia,Mohammed Sid Ahmed Houari,Abdelouahed Tounsi,S.R. Mahmoud 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.20 No.3

In this work, the effects of moisture and temperature on free vibration characteristics of functionally graded (FG) nanobeams resting on elastic foundation is studied by proposing a novel simple trigonometric shear deformation theory. The main advantage of this theory is that, in addition to including the shear deformation influence, the displacement field is modeled with only 2 unknowns as the case of the classical beam theory (CBT) and which is even less than the Timoshenko beam theory (TBT). Three types of environmental condition namely uniform, linear, and sinusoidal hygrothermal loading are studied. Material properties of FG beams are assumed to vary according to a power law distribution of the volume fraction of the constituents. Equations of motion are derived from Hamilton’s principle. Numerical examples are presented to show the validity and accuracy of present shear deformation theories. The effects of hygro-thermal environments, power law index, nonlocality and elastic foundation on the free vibration responses of FG beams under hygro-thermal effect are investigated.

A New Higher Order Shear Deformation Model for Functionally Graded Beams

Lazreg Hadji,Zoubida Khelifa,Adda Bedia El Abbes 대한토목학회 2016 KSCE JOURNAL OF CIVIL ENGINEERING Vol.20 No.5

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton’s principle. Navier type solution method was used to obtain frequencies. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Influence of the porosities on the free vibration of FGM beams

L. Hadji,E.A. Adda Bedia 한국풍공학회 2015 Wind and Structures, An International Journal (WAS Vol.21 No.3

In this paper, a free vibration analysis of functionally graded beam made of porous material is presented. The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton’s principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

Analyse of the behavior of functionally graded beams based on neutral surface position

Lazreg Hadji,El Abbes Adda Bedia 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.55 No.4

In this paper, a simple n-order refined theory based on neutral surface position is developed for bending and frees vibration analyses of functionally graded beams. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, 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. The governing equations are derived by employing the Hamilton’s principle and the physical neutral surface concept. The accuracy of the present solutions is verified by comparing the obtained results with available published ones.

Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes

Tounsi, Abdelouahed,Benguediab, Soumia,Adda Bedia, El Abbas,Semmah, Abdelwahed,Zidour, Mohamed Techno-Press 2013 Advances in nano research Vol.1 No.1

The thermal buckling properties of double-walled carbon nanotubes (DWCNTs) are studied using nonlocal Timoshenko beam model, including the effects of transverse shear deformation and rotary inertia. The DWCNTs are considered as two nanotube shells coupled through the van der Waals interaction between them. The geometric nonlinearity is taken into account, which arises from the mid-plane stretching. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling temperatures under uniform temperature rise are obtained. The results show that the critical buckling temperature can be overestimated by the local beam model if the nonlocal effect is overlooked for long nanotubes. In addition, the effect of shear deformation and rotary inertia on the buckling temperature is more obvious for the higher-order modes. The investigation of the thermal buckling properties of DWCNTs may be used as a useful reference for the application and the design of nanostructures in which DWCNTs act as basic elements.

Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory

Bouiadjra, Rabbab Bachir,Bedia, E.A. Adda,Tounsi, Abdelouahed Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.4

Nonlinear behavior of functionally graded material (FGM) plates under thermal loads is investigated here using an efficient sinusoidal shear deformation theory. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the sinusoidal distribution of transverse shear stress through the thickness in such a way that shear stresses vanish on the plate surfaces. Therefore, there is no need to use shear correction factor. Unlike the conventional sinusoidal shear deformation theory, the proposed efficient sinusoidal shear deformation theory contains only four unknowns. The material is graded in the thickness direction and a simple power law based on the rule of mixture is used to estimate the effective material properties. The neutral surface position for such FGM plates is determined and the sinusoidal shear deformation theory based on exact neutral surface position is employed here. 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. The non-linear strain-displacement relations are also taken into consideration. The thermal loads are assumed as uniform, linear and non-linear temperature rises across the thickness direction. Closed-form solutions are presented to calculate the critical buckling temperature, which are useful for engineers in design. Numerical results are presented for the present efficient sinusoidal shear deformation theory, demonstrating its importance and accuracy in comparison to other theories.

Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams

Berrabah, H.M.,Tounsi, Abdelouahed,Semmah, Abdelwahed,Adda Bedia, E.A. Techno-Press 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.3

In this paper, unified nonlocal shear deformation theory is proposed to study bending, buckling and free vibration of nanobeams. This theory is based on the assumption that the in-plane and 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. In addition, this present model is capable of capturing both small scale effect and transverse shear deformation effects of nanobeams, and does not require shear correction factors. The equations of motion are derived from Hamilton's principle. Analytical solutions for the deflection, buckling load, and natural frequency are presented for a simply supported nanobeam, and the obtained results are compared with those predicted by the nonlocal Timoshenko beam theory and Reddy beam theories.

Hygrothermal effect on the moisture absorption in composite laminates with transverse cracks and delamination

Kesba, Mohamed Khodjet,Benkhedda, A.,Adda bedia, E.A.,Boukert, B. Techno-Press 2019 Advances in aircraft and spacecraft science Vol.6 No.4

The stiffness degradation of the cross-ply composite laminates containing a transverse cracking and delamination in $90^{\circ}$ layer is predicted by using a modified shear-lag model by introducing the stress perturbation function. The prediction shows better agreement with the experimental results published by Ogihara and Takeda 1995, especially for laminates with thicker $90^{\circ}$ plies in which extensive delamination occurs. A homogenised analytic model for average transient moisture uptake in composite laminates containing periodically distributed matrix cracks and delamination is presented. It is shown that the model well describes the moisture absorption in a cross-ply composite laminate containing periodically distributed transverse matrix cracks in the $90^{\circ}$ plies. The obtained results represent well the dependence of the stiffness degradation on the crack density, thickness ratio and moisture absorption. The present study has proved to be important to the understanding of the degradation of the material propertiesin the failure process when the laminates in which the delamination grows extensively.