Yaylacı, Murat; Öner, Erdal; Adıyaman, Gökhan; Öztürk, Şevval; Uzun Yaylacı, Ecren; Birinci, Ahmet

Contact mechanics analysis is crucial because such problems often arise in engineering practice. When examining contact mechanics, the material property of the contacting components is a crucially significant aspect. It is more complex to solve the contact mechanics of systems that are composed of materials that do not have a homogenous structure compared to materials that have homogeneous qualities throughout. While many studies on contact problems with homogeneous materials exist, those involving non-homogeneous materials are scarce in the literature. As material technology improves fast, there will be a greater need to solve such problems. In this respect, analytical and finite element method (FEM) solutions of the continuous and discontinuous contact problems of a functionally graded (FG) layer are carried out in this article. The FG layer in the problem rests on a rigid foundation and is pressed with a rigid punch. From the solutions, the contact length, contact stress, initial separation distance, and beginning and ending points of separation were determined, and the results were compared. It has been concluded that the FEM findings are consistent with the analytical results to a satisfactory degree. This study analyzes contact problem using different approaches and accounts for the influence of body force in a contact geometry that has yet to be reported.

AtıfScopus79·WoS83·OpenAlex68

İncele

Adiyaman, Gökhan; Öner, Erdal; Yaylaci, Murat; Birinci, Ahmet

One of the most important components of the early design process for layered systems is gaining a knowledge of the behavior of materials under varied contact situations. Functionally graded materials (FGMs) have grown in popularity in layered systems as a result of their numerous benefits, such as permitting the reduction of local stress concentrations and thermal stresses often experienced in traditional composites. This paper suggests an analytical approach to solving the continuous and discontinuous contact problems of a functionally graded (FG) layer subjected to a distributed load. Elasticity theory and integral transform methods provide the basis of the aforementioned analytical approach. The FG layer rests on a half-plane that is homogeneous, and there is no adhesion or bonding at the contact surface. For this problem, we assume an exponentially varying shear modulus and mass density in the FG layer. In the solution, the body force of the FG layer is considered. The problem is solved analytically by applying boundary conditions for both continuous and discontinuous contact cases. The presented results show the effects of load factor, amplitude of distributed load, inhomogeneity parameters, and interface material property mismatch on contact stress distributions, initial separation load (critical load), initial separation distance, starting and end point of separation, and separation interval.

AtıfScopus39·WoS40·OpenAlex30

İncele

Adiyaman, Gokhan; Oner, Erdal; Yaylaci, Murat; Birinci, Ahmet

This paper considers the continuous and discontinuous contact problems of a functionally graded (FG) layer under the effect of gravity. A finite distributed load is applied to the beam from the top and the beam is placed to the top of a rigid foundation. It is assumed that the shear modulus and mass density of the beam vary exponentially whereas Poisson's ratio remains constant. The problem is solved for both continuous and discontinuous cases. In each case, the governing equations and boundary conditions of the problem are reduced to an integral equation by the help of Fourier integral transform. In the continuous contact, the integral equation solved analytically and critical load that causes initial separation between the layer and the rigid foundation, separation distance and contact pressures are investigated for various non-homogeneity parameters that presents the change in the shear modulus and density and loadings. The singular integral equation in case of discontinuous contact is numerically solved by using corresponding Gauss–Chebyshev quadrature and an iterative scheme. The effect of non-homogeneity parameters and loading on the separation distance between the layer and the foundation and contact pressures are analyzed. All the results are shown in tables and figures. It is seen that increasing stiffness and decreasing density at the top of the layer reduce maximum pressures but increase separation distances. This study aims to fill the deficiency in the mechanical behavior of the coatings under gravity.

AtıfScopus19·WoS20·OpenAlex17

İncele

Öner, Erdal; Şengül Şabano, Bahar; Uzun Yaylacı, Ecren; Adıyaman, Gökhan; Yaylacı, Murat; Birinci, Ahmet

The frictionless double receding contact problem for two functionally graded (FG) layers pressed by a uniformly distributed load is addressed in this paper. The gradation in the layers is assumed to follow an exponential variation through the height with constant Poisson's ratios. The lower layer rests on a homogeneous half-plane (HP). There is no adhesion between the FG layers or between the lower layer and the HP. The body forces of the FG layers and HP are ignored. First, the governing equations are reduced to a system of two singular integral equations with contact pressures and contact lengths as unknowns using Fourier transform techniques and boundary conditions. The integral equations are solved numerically using the Gauss-Chebyshev integration formula. Then, a parametric finite element analysis is performed using the augmented contact method. Finally, the problem was extended based on the multilayer perceptron (MLP), an artificial neural network used for different problem parameters. The effects of stiffness parameters, the normalized load length, the ratio of shear moduli, the ratio of FG layer heights to the normalized contact lengths, and normalized maximum contact pressures are explored. The results of finite element analysis and the MLP approach are used to validate the normalized maximum contact pressures and contact lengths obtained from an analytical method based on elasticity theory, and finally, good agreement between these three methods results is obtained. The obtained results could help in designing multibody indentation systems with FGMs.

AtıfScopus85·WoS84·OpenAlex48

İncele

Yaylacı, Ecren Uzun; Öner, Erdal; Yaylacı, Murat; Özdemir, Mehmet Emin; Abushattal, Ahmad; Birinci, Ahmet

This paper investigates the artificial neural network (ANN) to predict the dimensionless parameters for contact pressures and contact lengths under the rigid punch, the initial separation loads, and the initial separation distances of a contact problem. The problem consisted of two elastic infinitely layers (EL) loaded by means of a rigid cylindrical punch and resting on a half-infinite plane (HP). Firstly, the problem was formulated and solved theoretically using the Theory of Elasticity (ET). Secondly, the contact problem was extended based on the ANN. External load, the radius of punch, layer heights, and material properties were created by giving examples of different values used at the training and test stages of ANN. Finally, the accuracy of the trained neural networks for the case was tested using 134 new data, generated via ET solutions to determine the best network model. ANN results were compared with ET results, and well agreements were achieved.

AtıfScopus62·WoS60·OpenAlex13

İncele

Yaylacı, Murat; Adıyaman, Gökhan; Öner, Erdal; Birinci, Ahmet

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress–strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

AtıfScopus78·WoS78·OpenAlex21

İncele

Yaylacı, Murat; Eyüboğlu, Ayşegül; Adıyaman, Gökhan; Yaylacı, Ecren Uzun; Öner, Erdal; Birinci, Ahmet

This paper presents a comparative study of different methods, such as the analytical method, finite element method (FEM), and multilayer perceptron (MLP) for analyzing a frictionless receding contact problem. The problem consists of two layers resting on a Winkler foundation. The top layer is functionally graded (FG) along the depth and pressed using a rigid cylindrical stamp, whereas the bottom layer is homogeneous. We assumed that the contact between the two layers, and that between the FG layer and the rigid cylindrical stamp are frictionless; additionally, compressive normal tractions can be transmitted through the interface. First, the problem was solved analytically using the theory of elasticity and integral transform techniques. Second, the finite element solution of the problem was obtained using ANSYS software. Finally, the problem was extended based on the MLP, which an artificial neural network used for different problem parameters. The results of this study showed that the variations in the contact lengths at the interface between the rigid cylindrical stamp and the FG layer, those between the homogeneous layer and the FG layer, and the maximum contact pressures at these interfaces depended on various dimensionless quantities such as the stamp radius, stiffness parameter, shear modulus ratio, and elastic spring constant ratio. We observed that the results obtained with the three different methods, namely the analytical method, FEM, and MLP, are extremely compatible with each other, thus proving the accuracy of these results.

AtıfScopus87·WoS86·OpenAlex40

İncele

Yaylacı, Murat; Adıyaman, Gökhan; Öner, Erdal; Birinci, Ahmet

In this study, the continuous and discontinuous contact problems of functionally graded (FG) layer resting on a rigid foundation were considered. The top of the FG layer was loaded by a distributed load. It was assumed that the shear modulus and the density of the layer varied according to exponential functions along the depth whereas the the Poisson ratio remained constant. The problem first was solved analytically and the results were verified with the ones obtained from finite element (FE) solution. In analytical solution, the stress and displacement components for FG layer were obtained by the help of Fourier integral transform. Critical load expression and integral equation for continuous and discontinuous contact, respectively, using corresponding boundary conditions in each case. The finite element solution of the problem was carried out using ANSYS software program. In continuous contact case, initial separation distance and contact stresses along the contact surface between the FG layer and the rigid foundation were examined. Separation distances and contact stresses were obtained in case of discontinuous contact. The effect of material properties and loading were investigated using both analytical and FE solutions. It was shown that obtained results were compatible with each other.

AtıfScopus71·WoS72·OpenAlex22

İncele

Öner, Erdal; Birinci, Ahmet

kUnfortunately, Figs. 5, 6, 8 and 10 have been processed incorrectly. Correct figures are provided in this correction article. The Original article has also been corrected.

AtıfScopus2·WoS2·OpenAlex2

İncele

Öner, Erdal; Birinci, Ahmet

In this study, the discontinuous contact problem between a functionally graded (FG) layer, which is loaded symmetrically with point load P through a rigid block, and a homogeneous half-space was solved using the theory of elasticity and integral transform techniques. The shear modulus and density of the layer addressed in the problem vary with an exponential function along with its height. The half-space is homogeneous, and no binder exists on the contact surface containing the FG layer. In the solution, the body force of the FG layer was considered, whereas that of the homogeneous half-space was neglected. The Poisson’s ratios of both the FG layer and homogeneous half-space were assumed to remain constant. Additionally, all the surfaces addressed in the problem were assumed to be frictionless. Using the theory of elasticity and integral transform techniques, the discontinuous contact problem was reduced to two integral equations, wherein the contact stress under the rigid block and the slope of the separation, which occurred at the interface of the FG layer and homogeneous half-space, are unknown. These integral equations were solved numerically for the flat condition of the rigid block profile using the Gauss–Chebyshev integration formula. Consequently, the stress distributions, start–end points of the separation region, and separation displacements between the FG layer and homogeneous half-space were obtained for various dimensionless quantities.

AtıfScopus24·WoS25·OpenAlex23

İncele

Adiyaman, Gokhan; Öner, Erdal; Birinci, Ahmet

In this study, the general solution of a receding contact problem of layered medium resting on rigid foundation is considered. The layered medium consists of N homogeneous layer with varying material properties and heights. The contact surfaces can be receding or attached. The problem may include M receding contact surfaces. The layered medium is loaded with n concentrated loads transmitted by circular stamps and r distributed loads. The problem is reduced to integral equation system using elasticity theory and Fourier integral transform. The numerical solution of the system is done by using Matlab. A program is written to solve the problem given by the user with any geometry and loading. The program is tested with two studies from the literature and it was shown that the results are compatible.

AtıfWoS3

İncele

Adıyaman, Gökhan; Öner, Erdal; Birinci, Ahmet

In this study, the continuous and discontinuous contact problem of a functionally graded (FG) layer resting on a rigid foundation is considered. The top of the FG layer is subjected to normal tractions over a finite segment. The graded layer is modeled as a non-homogenous medium with a constant Poissons’ ratio and exponentially varying shear modules and density. For continuous contact, the problem was solved analytically using plane elasticity and integral transform techniques. The critical load that causes first separation and contact pressures is investigated for various material properties and loadings. The problem reduced to a singular integral equation using plane elasticity and integral transform techniques in case of discontinuous contact. The obtained singular integral equation is solved numerically using Gauss–Jacobi integral formulation, and an iterative scheme is employed to obtain the correct separation distance. The separation distance and contact pressures between the FG layer and the foundation are analyzed for various material properties and loading. The results are shown in Tables and Figures. It is seen that decreasing stiffness and density at the top of the layer result in an increment in both critical load in case of continuous contact and separation distance in case of discontinuous contact.

AtıfScopus24·WoS24·OpenAlex26

İncele

Yaylaci, Murat; Birinci, Ahmet; Adiyaman, Gokhan; Öner, Erdal

This paper presents the elastostatic plane problem of a long strip containing an internal or edge crack perpendicular to its boundaries. The plane problem consists of an infinitely long strip of thickness h. The infinitely long strip is loaded by uniformly distributed load and rests on two simple supports. It is assumed that the effect of gravity is neglected. The finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. Normalized stress-intensity factors for the cases with internal and edge crack, and normal stress (sigma(x)) for uncracked layer case are obtained for various dimensionless quantities. Finally, the results obtained from the finite element analysis are verified by comparing with analytical ones and it is seen that the results from finite element analysis indicate a good agreement with the analytical solution.

AtıfWoS4

İncele

Adıyaman, Gökhan; Birinci, Ahmet; Öner, Erdal; Yaylacı, Murat

In this paper, the plane problem of a frictionless receding contact between an elastic functionally graded layer and two homogeneous quarter planes is considered when the graded layer is pressed against the quarter planes. The top of the layer is subjected to normal tractions over a finite segment. The graded layer is modeled as a non-homogeneous medium with a constant Poisson’s ratio and exponentially varying shear modules. The problem is converted into the solution of a Cauchy-type singular integral equation in which the contact pressure and the receding contact half-length are the unknowns using integral transforms. The singular integral equation is solved numerically using Gauss–Jacobi integration. The corresponding receding contact half-length that satisfies the global equilibrium condition is obtained using an iterative procedure. The effect of the material non-homogeneity parameter on the contact pressure and on the length of the receding contact is investigated.

AtıfScopus58·WoS55·OpenAlex42

İncele

Birinci, Ahmet; Adıyaman, Gökhan; Yaylacı, Murat; Öner, Erdal

In this paper, continuous and discontinuous cases of a contact problem for two elastic layers supported by a Winkler foundation are analyzed using both analytical method and finite element method. In the analyses, it is assumed that all surfaces are frictionless, and only compressive normal tractions can be transmitted through the contact areas. Moreover, body forces are taken into consideration only for layers. Firstly, the problem is solved analytically using theory of elasticity and integral transform techniques. Then, the finite element analysis of the problem is carried out using ANSYS software program. Initial separation distances between layers for continuous contact case and the size of the separation areas for discontinuous contact case are obtained for various dimensionless quantities using both solutions. In addition, the normalized contact pressure distributions are calculated for both cases. The analytic results are verified by comparison with finite element results. Finally, conclusions are presented.

AtıfScopus38·WoS39·OpenAlex36

İncele

Öner, Erdal; Yaylaci, Murat; Birinci, Ahmet

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

AtıfScopus84·WoS84·OpenAlex35

İncele

Yaylaci, Murat; Öner, Erdal; Birinci, Ahmet

This paper considers a receding contact problem for two elastic layers (with different elastic constants and heights) supported by two elastic quarter planes. The lower layer is supported by two elastic quarter planes, and the upper elastic layer is subjected to a symmetrical distributed load whose length is 2a on its top surface. It is assumed that contact between all surfaces is frictionless, and the effect of gravity force is neglected. First, the problem is formulated and solved using the theory of elasticity and integral transform technique. Using the integral transform technique and boundary conditions of the problem, the problem is reduced to a system of singular integral equations in which contact pressures and contact areas are unknown. The system of singular integral equations is solved numerically by using the Gauss-Jacobi integration formulation. Second, the receding contact problem has been developed based on the FEM ANSYS software. Two-dimensional analysis of the problem is carried out. The ANSYS and analytical results for the contact pressures, contact areas, and normal stresses (sigma(x) and sigma(y)) along the axis of symmetry are given for various dimensionless quantities. The ANSYS results are verified by comparison with analytical results. (C) 2014 American Society of Civil Engineers.

AtıfWoS50·OpenAlex35

İncele

Öner, Erdal; Birinci, Ahmet

The continuous contact problem for two elastic layers resting on an elastic half-infinite plane and loaded by means of a rigid stamp is presented. The elastic layers have different heights and elastic constants. An external load is applied to the upper elastic layer by means of a rigid stamp. The problem is solved under the assumptions that all surfaces are frictionless, body forces of elastic layers are taken into account, and only compressive normal tractions can be transmitted through the interfaces. General expressions of stresses and displacements are obtained by using the fundamental equations of the theory of elasticity and the integral transform technique. Substituting the stress and the displacement expressions into the boundary conditions, the problem is reduced to a singular integral equation, in which the function of contact stresses under the rigid stamp is unknown. The integral equation is solved numerically by making use of the appropriate Gauss-Chebyshev integration formula for circular and rectangular stamp profiles. The contact stresses under the rigid stamp, contact areas, initial separation loads, and initial separation distances between the two elastic layers and the lower-layer elastic half-infinite plane are obtained numerically for various dimensionless quantities and shown in graphics and tables.

AtıfScopus24·WoS25·OpenAlex26

İncele

Öner, Erdal; Yaylaci, Murat; Birinci, Ahmet

In this study, a receding contact problem for two elastic layers supported by a Winkler foundation is handled using two different methods such as an analytical method and a finite element method. Firstly, the problem is solved analytically using linear elasticity theory. Then, in order to solve the same problem in a different way, a finite element model of the problem is created by ANSYS software, and finite element analysis of the problem is performed. The contact stresses and the contact areas at the interfaces between punch-Layer 2 and Layer 1-Layer 2 are obtained for both solutions, and it is shown that the finite element method indicates a good agreement with the analytical method.

AtıfScopus36·WoS37·OpenAlex25

İncele