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Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory

Belarbi Mohamed-Ouejdi, Daikh Ahmed Amine, Garg Aman, Hirane Hicham, Houari Mohammed Sid Ahmed, Civalek Ömer, Chalak H. D.

Archives of Civil and Mechanical Engineering

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2023

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Vol. 23, no. 1

art. no. e15, 2023

EN

In this paper, for the first time, the bending and free vibration analysis of porous functionally graded sandwich plates with various porosity distributions is investigated using an efficient layerwise model. The present model, proposed recently by the authors, supposes a first-order displacement field for the two face sheets and a higher-order displacement field for the core, thereby ensuring the displacement continuity at the layer's interface. Unlike the conventional layerwise models, the number of degrees of freedom is fixed and does not increase when increasing the number of layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Three different types of porosity distribution including even, logarithmic-uneven, and linear-uneven porosities are considered. The material properties of the FGM sandwich porous plate are graded continuously through the thickness direction according to a power-law function. The numerical analysis is carried out by using an efficient C0 continuous eight-node quadrilateral isoparametric element developed for this purpose. The governing equations are derived according to Hamilton’s principle and solved by employing the finite element method. The robustness and accuracy of the proposed formulation are ascertained by comparing its results with those available by other researchers in the existing literature. Further, a comprehensive parametric study is examined in detail to show the effects of material distribution, aspect ratios, porosity coefficient, side-to-thickness ratio, porosity distribution, core-to-face thickness ratio, boundary conditions, volume fraction index, modes shapes on the bending and free vibration behaviors of symmetric and non-symmetric FGM porous sandwich plate. The numerical results show that these parameters play significant roles in the bending and free vibration behaviors of the FGM sandwich porous plates. Many new results are also reported, which will serve as a benchmark for future analysis of FGM sandwich plates with porosity.

2

Two-dimensional analysis of functionally graded thermoelastic microelongated solid

Sharma Anchal, Ailawalia Praveen

International Journal of Applied Mechanics and Engineering

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2022

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Vol. 27, no. 4

155--169

EN

The present research focuses on two-dimensional deformation in a functionally graded thermoelastic micro-elongated medium. It is supposed that the non-homogeneous properties (thermal and mechanical) of FGM are in the x-direction. The normal mode technique is used to acquire the analytic expression for displacement components, stress, micro-elongation and temperature. The cause and effect relationship of non-homogeneity and physical quantities is shown through graphical results.

3

Buckling analysis of composite conical shells reinforced by agglomerated functionally graded carbon nanotube

Eskandary K., Shishesaz Mohammad, Moradi Shapour

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 3

art. no. e132

EN

This study primary objective is to analyze the effect of agglomeration of carbon nanotubes on the buckling behavior of functionally graded carbon nanotube-reinforced composite conical shells (FG-CNTCS). Considering the first-order shear deformation theory, the differential equations of buckling behavior are obtained. Subsequently, the buckling load was derived utilizing Galerkin methods. A parametric study is established to consider the influence of characteristic parameters on the buckling behavior of the FG-CNTCS. The results reveal that agglomeration of CNTs substantially reduces the buckling load. Considering that, the effect of high volume fractions of carbon nanotubes on increasing buckling load is overly inconsiderable, it is suggested to use low volume fractions of nanoparticles in producing this type of nanocomposites, which reduces the probability of agglomeration phenomenon and also cut down the manufacturing costs.

4

Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment

Zenkour A. M., Radwan A. F.

Archives of Civil and Mechanical Engineering

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2020

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Vol. 20, no. 4

198--220

EN

The present paper deals with the effect of exponential temperature and moisture concentration on the bending and buckling analysis of functionally graded plates resting on two-parameter elastic foundations via a four-variable exponential shear deformation theory. The mechanical properties of the plates are assumed to vary through the thickness. The equations of equilibrium are derived using Hamilton’s principle. The present solutions are derived using Navier’s method. Using Navier’s solution the numerical results are presented and compared well with those available in the literature. Discussions are made to show how the foundation stiffness, hygrothermal loading and other parameters have a significant influence on the bending and buckling analysis of FG plates under hygrothermal and mechanical loading.

5

Exact thermomechanical analysis of functionally graded (FG) thick-walled spheres

Yildirim V.

Mechanics and Mechanical Engineering

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2018

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Vol. 22, nr 4

1197--1221

EN

The present study aims to provide a deeper understanding for the thermo-mechanical analysis of spheres made of non-homogeneous isotropic materials. To this end, Navier equations are solved analytically based on the spherically-symmetric plain-strain assumptions and closed-form formulas are proposed for the elastic fields in a simple-power-law graded spheres subjected to steady-state thermal and internal/external pressure loads. A comprehensive parametric study is then performed with both functionally-graded hypothetical and physical materials. Two benchmark examples are reconsidered with hypothetically chosen inhomogeneity indexes. Effects of inhomogeneity indexes are reviewed in these examples. Differently from the literature, thickness effects are also examined under separate and combined loads together with the thermo-mechanical behavioral differences in spheres and cylinders. Finally three physical metal-ceramic pairs are studied originally with appropriate inhomogeneity indexes which are deffned as the inner surface is full ceramic and the outer surface is full metal. Results are presented in graphical and tabular forms.

6

Thermoelastic stresses in functionally graded rotating annular disks with variable thickness

Allam M. N. M., Tantawy R., Zenkour A. M.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 4

1029--1041

EN

This article presents semi-analytical solutions for stress distributions in exponentially and functionally graded rotating annular disks with arbitrary thickness variations. The disk is under pressure on its boundary surfaces and exposed to temperature distribution varying linearly across thickness. Material properties are supposed to be graded in the radial direction of the disk and obeying to two different forms of distribution of volume fraction of constituents. Different conditions at boundaries for stresses and displacement are discussed. Accurate and efficient solutions for displacement and stresses in rotating annular disks are determined using infinitesimal theory. Numerical results are carried out and discussed for different cases. It can be deduced that the gradient of material properties and thickness variation as well as the change of temperature sources have a specific effect in modern applications.

7

Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation

Alipour M. M.

Archives of Civil and Mechanical Engineering

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2016

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Vol. 16, no. 4

678--694

EN

In practical applications, sandwich plates are often connected to other members, supported by damaged clamped/simply supported boundary conditions or supported by elastic restraints. Therefore, the mentioned structures may not always be simulated by the classical boundary conditions, i.e., ideal simply supported, clamped and free edges. Also, these structures may be subjected to various loads. In this study, for the first time, a novel economical analytical solution procedure is presented for axisymmetric static analysis of sandwich annular plates, by using the layerwise and 3D elasticity theories. Based on the proposed approach, functionally graded sandwich annular plates with various elastically restrained edges under arbitrary distributed loads may be analyzed and all of the displacements and stresses components may be exactly achieved. Also, imposed loads at the boundaries may be evaluated. Transverse shear and normal stresses boundary conditions on the top and bottom of the sandwich plate and the interlaminar continuity conditions of the in-plane displacement, transverse shear and normal stresses are exactly satisfied. Accuracy and efficiency of the presented solution procedure are demonstrated by comparing the obtained results for sandwich plates with the classical edge conditions as some special cases of the elastic supports with results of the three-dimensional theory of elasticity.