• Structural Engineering and Mechanics
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• 제82권3호
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• pp.401-416
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• 2022

The aim of this study is to examine the frictionless double receding contact problem for two functionally graded (FG) layers pressed with a uniformly distributed load and resting on a homogeneous half plane (HP) using analytical and numerical methods. The FG layers are made of a non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layers and FG layer-HP interface is frictionless. The body force of the FG layers and homogeneous HP are ignored in the study. Firstly, an analytical solution for the contact problem has been realized using the theory of elasticity and the Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using the ANSYS package program based on FEM. Numerical results for contact lengths and contact pressures between FG layers and FG layer-HP were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio, and the heights of the FG layers for both methods. The results obtained using FEM were compared with the results found using the analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

• Steel and Composite Structures
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• 제50권1호
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• pp.77-87
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• 2024

In this study, the two-dimensional crack problem was investigated by using the finite element method (FEM)-based ANSYS package program and the artificial neural network (ANN)-based multilayer perceptron (MLP) method. For this purpose, a half-infinite functionally graded (FG) layer with a crack pressed through two rigid blocks was analyzed using FEM and ANN. Mass forces and friction were neglected in the solution. To control the validity of the crack problem model exercised, the acquired results were compared with a study in the literature. In addition, FEM and ANN results were checked using Root Mean Square Error (RMSE) and coefficient of determination (R²), and a well agreement was found. Numerical solutions were made considering different geometric parameters and material properties. The stress intensity factor (SIF) was examined for these values, and the results were presented. Consequently, it is concluded that the considered non-dimensional quantities have a noteworthy influence on the SIF. Also FEM and ANN can be logical alternative methods to time-consuming analytical solutions if used correctly.

• Structural Engineering and Mechanics
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• 제64권1호
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• pp.71-79
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• 2017

In this study, interaction of several interface cracks located between a functionally graded material (FGM) layer and an elastic layer under anti-plane deformation based on the distributed dislocation technique (DDT) is analyzed. The variation of the shear modulus of the functionally graded coating is modeled by an exponential and linear function along the thickness of the layer. The complex Fourier transform is applied to governing equation to derive a system of singular integral equations with Cauchy type kernel. These equations are solved by a numerical method to obtain the stress intensity factors (SIFs) at the crack tips. The effects of non-homogeneity parameters for exponentially and linearly form of shear modulus, the thickness of the layers and the length of crack on the SIFs for several interface cracks are investigated. The results reveal that the magnitude of SIFs decrease with increasing of FG parameter and thickness of FGM layer. The values of SIFs for FGM layer with exponential form is less than the linear form.

• Structural Engineering and Mechanics
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• 제59권2호
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• pp.227-241
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• 2016

A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.

• Steel and Composite Structures
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• 제18권2호
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• pp.443-465
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• 2015

In this paper, an efficient and simple trigonometric shear deformation theory is presented for thermal buckling analysis of functionally graded plates. It is assumed that the plate is in contact with elastic foundation during deformation. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the proposed sinusoidal shear deformation theory contains only four unknowns. It is assumed that the mechanical and thermal non-homogeneous properties of functionally graded plate vary smoothly by distribution of power law across the plate thickness. Using the non-linear strain-displacement relations, the equilibrium and stability equations of plates made of functionally graded materials are derived. The boundary conditions for the plate are assumed to be simply supported on all edges. The elastic foundation is modelled by two-parameters Pasternak model, which is obtained by adding a shear layer to the Winkler model. The effects of thermal loading types and variations of power of functionally graded material, aspect ratio, and thickness ratio on the critical buckling temperature of functionally graded plates are investigated and discussed.

• 한국분말재료학회지
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• 제29권4호
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• pp.309-313
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• 2022

In this study, additive manufacturing of a functionally graded material (FGM) as an alternative to joining dissimilar metals is investigated using directed energy deposition (DED). FGM consists of five different layers, which are mixtures of austenitic stainless steel (type 316 L) and low-alloy steel (LAS, ferritic steel) at ratios of 100:0 (A layer), 75:25 (B layer), 50:50 (C layer), 25:75 (D layer), and 0:100 (E layer), respectively, in each deposition layer. The FGM samples are successfully fabricated without cracks or delamination using the DED method, and specimens are characterized using optical and scanning electron microscopy to monitor their microstructures. In layers C and D of the sample, the tensile strength is determined to be very high owing to the formation of ferrite and martensite structures. However, the elongation is high in layers A and B, which contain a large fraction of austenite.

• 대한금속재료학회지
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• 제48권8호
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• pp.775-779
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• 2010

Functionally graded materials (FGM) of PSZ/NiCrAlY on Inconel substrate were fabricated by detonation gun spraying method. A thick ceramic layer generally has a high thermal barrier effect however, because failure often occurs, the use of an FGM layer gives an advantage in thermal property. During the thermal shock test, micro fracture processes were detected by the AE method. Also, the thermal shock test was performed for NFGM, FGM and the changed FGM in the layered composition profile. It was found through AE testing and the observation of fracture surface that FGM was superior to NFGM in thermal shock properties. The linear or metal-rich type FGM in composition profile had the best resisting property among the FGM. It was found that the controlled composition profile of the graded layers had better thermal properties.

• Steel and Composite Structures
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• 제25권2호
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.

• Coupled systems mechanics
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• 제8권1호
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• pp.1-17
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• 2019

The present paper deals with delamination fracture analyses of the multilayered functionally graded non-linear elastic Symmetric Split Beam (SSB) configurations. The material is functionally graded in both width and height directions in each layer. It is assumed that the material properties are distributed non-symmetrically with respect to the centroidal axes of the beam cross-section. Sine laws are used to describe the continuous variation of the material properties in the cross-sections of the layers. The delamination fracture is analyzed in terms of the strain energy release rate by considering the balance of the energy. A comparison with the J-integral is performed for verification. The solution derived is used for parametric analyses of the delamination fracture behavior of the multilayered functionally graded SSB in order to evaluate the effects of the sine gradients of the three material properties in the width and height directions of the layers and the location of the crack along the beam width on the strain energy release rate. The solution obtained is valid for two-dimensional functionally graded non-linear elastic SSB configurations which are made of an arbitrary number of lengthwise vertical layers. A delamination crack is located arbitrary between layers. Thus, the two crack arms have different widths. Besides, the layers have individual widths and material properties.

• Geomechanics and Engineering
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• 제24권6호
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• pp.545-557
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• 2021

Since the functionally graded materials (FGMs) are used extensively as thermal barriers in many of applications. Therefore, the current article focuses on studying and presenting dynamic responses of multilayer functionally graded (FG) deep beams placed in a thermal environment that is not addressed elsewhere. The material properties of each layer are proposed to be temperature-dependent and vary continuously through the height direction based on the Power-Law function. The deep layered beam is exposed to harmonic sinusoidal load and temperature rising. In the modelling of the multilayered FG deep beam, the two-dimensional (2D) plane stress continuum model is used. Equations of motion of deep composite beam with the associated boundary conditions are presented. In the frame of finite element method (FEM), the 2D twelve-node plane element is exploited to discretize the space domain through the length-thickness plane of the beam. In the solution of the dynamic problem, Newmark average acceleration method is used to solve the time domain incrementally. The developed procedure is verified and compared, and an excellent agreement is observed. In numerical examples, effects of graduation parameter, geometrical dimension and stacking sequence of layers on the time response of deep multilayer FG beams are investigated with temperature effects.