Terzi, Merve; Öner, Erdal; Uzun Yaylacı, Ecren; Oktay, Mine Gül; Yaylacı, Murat

Contact problems which concern the stress distribution resulting from the interaction between two elastic bodies have long been a focus of research. In the field of solid mechanics, they hold particular importance because loads are generally transmitted to deformable bodies through their points of contact. This study investigates the contact problem of a layered medium containing a homogeneous orthotropic layer and an isotropic half-plane using a multi-method approach. A rigid flat indenter is applied to the orthotropic layer with frictional effects neglected, while the influence of body forces in the orthotropic layer is taken into account. Key contact parameters such as the contact stress under the indenter, the initial separation load, and the point of initial separation are determined as part of the analysis. The study is structured into three main sections. In the first section, the problem is analytically examined based on classical elasticity theory. Within this framework, a singular integral equation governing the contact problem is derived and solved numerically. The second section presents a finite element analysis using ANSYS software to simulate the contact interaction and evaluate the stress distribution. In the third and final section, the problem is addressed through artificial neural network (ANN) techniques, offering a data-driven perspective. Ultimately, the results obtained from the analytical, numerical (FEM), and ANN-based methods are compared, showing excellent agreement across all approaches.

AtıfScopus15·WoS10·OpenAlex16

İncele

Turan, Muhittin; Kahya, Volkan; Yaylacı, Ecren Uzun; Yaylacı, Murat

This paper introduces a highly accurate and computationally efficient shear deformable finite element model for the static analysis of bi-directional functionally graded beams (BD-FGBs) with various boundary conditions grounded in the first-order shear deformation theory (FSDT). The model, featuring ten degrees of freedom across five nodes, excels in capturing both axial and shear deformations with remarkable precision while maintaining a streamlined formulation. In a novel approach, Artificial Neural Network (ANN) methods are also employed alongside the finite element analysis, offering a dual-method investigation into the static behavior of BD-FGBs. This paper aims to further advance the understanding of BD-FGM beams by exploring their static behavior under diverse loading conditions and boundary constraints, employing advanced finite element methods and artificial neural network techniques. The material properties are modeled through power-law distributions, and the governing equations are derived from Lagrange’s principle. Displacements and stresses were computed under different boundary conditions (BCs), slenderness ratios (L/h), and power-law indices (px, pz). Comparative analysis with existing literature reveals the superior suitability of the proposed finite element model for static analysis, while the ANN approach further reinforces its potential as a robust, complementary tool. The innovative combination of these methods promises to offer significant contributions to the field and provides new insights into the behavior of BD-FGBs under static loads.

AtıfScopus20·WoS24·OpenAlex3

İncele

Öner, Erdal; Oktay, Mine Gül; Uzun Yaylacı, Ecren; Yaylacı, Murat; Mirzaloğlu, İrem

This study examines the contact mechanics of a homogeneous orthotropic layer resting on a homogeneous isotropic half-space without being bonded, subjected to loading by a rigid cylindrical punch. The effect of the orthotropic layer’s body force has been taken into account in the study. The study is conducted in three phases. In the first phase, the contact problem is analytically tackled using advanced methods such as elasticity theory, integral transform techniques, and Gauss–Chebyshev integration. The second phase utilizes finite element analysis through ANSYS software, accurately modeling the system. In the final phase, an artificial neural network is employed, allowing the system to learn and recognize intricate patterns in the data. The standout feature of this study is its thorough comparison of these three distinct methodologies, offering a comprehensive understanding of the contact mechanics between isotropic and orthotropic materials. The results reveal key insights into contact length, maximum contact stress, critical separation load, and separation distance, all as functions of critical dimensionless parameters. This study is significant in today’s advancing field of contact mechanics as it not only explores the combined impact of body forces and the interaction between orthotropic and isotropic materials but also uniquely compares the results using three distinct methods, offering comprehensive insights that address both theoretical and practical challenges.

AtıfScopus27·WoS27·OpenAlex22

İncele

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

Öner, Erdal; Uzun Yaylacı, Ecren; Yaylacı, Murat

Analyzing the behavior of intelligent unconventional materials under diverse contact scenarios, in comparison to conventional materials, is a critical step in the initial design of engineering systems. This paper presents the development of analytical and numerical approaches for analyzing contact mechanics in a system comprising an orthotropic layer resting on a rigid foundation. Parametric analyses include the consideration of cylindrical and flat punch profiles. Analytical formulation utilizes integral transform methods to convert planar elasticity equations into a Cauchy-type singular integral equation of the second kind. A detailed description of the solution technique for the integral equation is provided, encompassing both the analytical formulation and the required discretization for obtaining the solution. Subsequently, a finite element approach (FEA) is employed to approximate contact bodies using a collection of finite elements, while contact boundaries are approximated by utilizing a set of polygons. Alternatively, the problem is addressed using the Multilayer Perceptron approach, a form of artificial neural network frequently applied in diverse machine learning applications, including scenarios involving contact problems. Finally, the resolution to the problem is achieved by employing the multilayer perceptron (MLP) method. The study yields determinations of contact stresses under the punch, the critical separation load resulting in the detachment of the orthotropic layer from the rigid foundation, and the corresponding separation distance. This analysis considers a range of dimensionless parameters and explored the behavior of diverse orthotropic materials. Comparisons between the results of the analytical method and computations from FEA and MLP reveal the exceptional accuracy attained by all three approaches. As the pioneer study employing three distinct approaches to examine continuous contact mechanics within an orthotropic layer under the influence of gravity, this research constitutes a valuable point of reference for upcoming scholars in the field.

AtıfScopus50·WoS53·OpenAlex44

İncele

Yaylacı, Murat; Yaylacı, Ecren Uzun; Turan, Muhittin; Özdemir, Mehmet Emin; Öztürk, Şevval; Ay, Sevil

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.

AtıfScopus27·WoS30·OpenAlex6

İncele

Turan, Muhittin; Uzun Yaylacı, Ecren; Yaylacı, Murat

In this study, an analytical solution based on the first-order shear deformation theory was performed for free vibration and buckling analysis of functionally graded porous beams (FGM-P) subjected to various boundary conditions. Also, this problem is solved by using finite element (FEM) and artificial neural network (ANN) methods. Here a Ritz-based analytical solution is used, and different polynomial series functions are proposed for each boundary condition. Lagrange's principle was used while deriving the equations of motion. A power-law rule describes the variation of the beam's materials in volume. The normalized fundamental frequencies and critical buckling loads are obtained for various boundary conditions, power-law index (k), slenderness (L/h), porosity coefficient (e), and porosity distribution (FGM-P1, FGM-P2). The polynomial series functions used in this study were verified with the literature, and the numerical results obtained were compared with FEM and ANN. The results obtained are quite compatible with each other.

AtıfScopus140·WoS136·OpenAlex101

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

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

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