Buckling and free vibration analysis of multi-directional functionally graded sandwich plates

Ali Alnujaie,Atteshamuddin S. Sayyad,Lazreg Hadji,Abdelouahed Tounsi 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.84 No.6

In this article, the buckling and free vibration of multi-directional FGM sandwich plates are investigated. The material properties of FGM sandwich plates are assumed to be varying continuously in the in the longitudinal, transverse and thickness directions. The material properties are evaluated based on Voigt’s micro-mechanical model considering power law distribution method with arbitrary power index. Equations of motion for the buckling and vibration analysis of multi-directional FGM sandwich plate are obtained based on refined shear deformation theory. Analytical solution for simply supported multidirectional FGM sandwich plate is carried out using Navier’s solution technique. The FGM sandwich plate considered in this work has a homogeneous ceramic core and two functionally graded face sheets. Influence of volume fraction index in the longitudinal, transverse and thickness direction, layer thickness, and geometrical parameter over natural frequency and critical buckling load of multi-directional FGM sandwich plate is investigated. The finding shows a multi-directional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters have been identified which will guide researchers in selecting fabrication routes for improving the performance of such structures.

Damped forced vibration analysis of layered functionally graded thick beams with porosity

Ali Alnujaie,Şeref D. Akbaş,Mohamed A Eltaher,Amr E. Assie 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.27 No.4

The following article presents the damped forced vibration of layered functionally graded thick beams including material porosities. In case of very thick beams, beam theories fail to satisfy boundary conditions and to predict the mechanical response accurately. So, the two-dimensional (2D) plane continuum model is exploited to model a thick functionally graded layered beam. The beam is composed from three- layers with functionally graded porous materials. The porosity is described by three different distribution models through the layer thickness. Applied forces to the functionally graded beam are assumed to be sinusoidal harmonic point load in time domain. The Kelvin—Voigt viscoelastic constitutive model is used to simulate damping effect. The governing equations are obtained by using Lagrange's equations. In frame of finite element analysis, twelve .node 2D plane element is exploited to discretize the space domain of thick beam. In the solution of the dynamic problem, the Newmark average acceleration method is used. Numerical studies illustrate effects of porosity distribution, stacking sequence, and graduation constant on the dynamic responses of layered functionally graded porous thick beams. The results show that the porosity function, stacking sequences and the damping ratio have a vital role in dynamic response of functionally graded beams. The proposed model can be used in nuclear, marine, and aerospace technologies.

A quasi-3D nonlocal theory for free vibration analysis of functionally graded sandwich nanobeams on elastic foundations

Mofareh Hassan Ghazwani,Ali Alnujaie,Pham Van Vinh,Abdelouahed Tounsi Techno-Press 2024 Advances in nano research Vol.16 No.3

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

Bending and buckling of porous multidirectional functionality graded sandwich plate

Lazreg Hadji,Fabrice Bernard,Royal Madan,Ali Alnujaie,Mofareh Hassan Ghazwani 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.2

Bending and buckling analysis of multi-directional porous functionally graded sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. The principle of virtual displacements was employed and the solution was obtained using Navier’s technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The validation of the present study has been performed with those available in the literature. The composition of metal-ceramic-based FGM changes in longitudinal and transverse directions according to the power law. Different porosity laws, such as uniform distribution, unevenly and logarithmically uneven distributions were used to mimic the imperfections in the functionally graded material that were introduced during the fabrication process. Several sandwich plates schemes were studied based on the plate's symmetry and the thickness of each layer. The effects of grading parameters and porosity laws on the bending and buckling of sandwich plates were examined.

Effect of porosity distribution on free vibration of functionally graded sandwich plate using the P-version of the finite element method

Hakim Bentrar,Sidi Mohammed Chorfi,Sid Ahmed Belalia,Abdelouahed Tounsi,Mofareh Hassan Ghazwani,Ali Alnujaie 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.88 No.6

In this work, the free vibration analysis of functionally graded material (FGM) sandwich plates with porosity is conducted using the p-version of the finite element method (FEM), which is based on the first-order shear deformation theory (FSDT). The sandwich plate consists of two face-sheet layers of FGM and a homogeneous core layer. The obtained results are validated using convergence and comparison studies with previously published results. Five porosities distribution models of FGM sandwich plates are assumed and analyzed. The effect of the thickness ratio, boundary conditions, volume fraction exponents, and porosity coefficients of the top and bottom layers of FGM sandwich plates on the natural frequency are addressed.

Buckling behaviors of FG porous sandwich plates with metallic foam cores resting on elastic foundation

Abdelkader Tamrabet,Belgacem Mamen,Abderrahmane Menasria,Abdelhakim Bouhadra,Abdelouahed Tounsi,Mofareh Hassan Ghazwani,Ali Alnujaie,S.R. Mahmoud 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.3

The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton’s principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.

A refined quasi-3D theory for stability and dynamic investigation of cross-ply laminated composite plates on Winkler-Pasternak foundation

Nasrine Belbachir,Fouad Bourada,Abdelmoumen Anis Bousahla,Abdelouahed Tounsi,Mohamed A. Al-Osta,Mofareh Hassan Ghazwani,Ali Alnujaie,Abdeldjebbar Tounsi 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.4

The current paper discusses the dynamic and stability responses of cross-ply composite laminated plates by employing a refined quasi-3D trigonometric shear deformation theory. The proposed theory takes into consideration shear deformation and thickness stretching by a trigonometric variation of in-plane and transverse displacements through the plate thickness and assures the vanished shear stresses conditions on the upper and lower surfaces of the plate. The strong point of the new formulation is that the displacements field contains only 4 unknowns, which is less than the other shear deformation theories. In addition, the present model considers the thickness extension effects (εz≠0). The presence of the Winkler-Pasternak elastic base is included in the mathematical formulation. The Hamilton’s principle is utilized in order to derive the four differentials’ equations of motion, which are solved via Navier’s technique of simply supported structures. The accuracy of the present 3-D theory is demonstrated by comparing fundamental frequencies and critical buckling loads numerical results with those provided using other models available in the open literature.

Investigation of the mechanical behavior of functionally graded sandwich thick beams

Fethi Mouaici,Abed Bouadi,Mohamed Bendaida,Kada Draiche,Abdelmoumen Anis Bousahla,Fouad Bourada,Abdelouahed Tounsi,Mofareh Hassan Ghazwani,Ali Alnujaie 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.5

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton’s principle and solved by means of the Navier’s technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

A mechanical behavior of composite plates using a simple three variable refined plate theory

Ahmed Bakoura,Ibrahim Klouche Djedid,Fouad Bourada,Abdelmoumen Anis Bousahla,S.R. Mahmoud,Abdelouahed Tounsi,Mofareh Hassan Ghazwani,Ali Alnujaie 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.83 No.5

A novel three variable refined plate theory (TVRPT) is developed in this article for laminated composite plates for the first time. The theory takes into account the nonlinear variation of transverse shear deformations, and satisfies the boundary conditions of zero traction on the plate surfaces without considering the “shear correction factor”. The important characteristic of this new kinematic is that the unknowns numbers is only 3 as is employed in “classical plate theory” (CPT). The numerical results of the current theory are compared with 3D-elasticity solutions and the calculations of “first order theories” and other higher order models found in the literature.