Öner, Erdal; Al-Qado, Ahmed Wasfi Hasan

Contact mechanics is a complex and advanced field of engineering, with continuous research dedicated to modeling and examining contact problems in multilayered and multibody systems. Given that fatigue and fracture failures often result from contact loads, precise determination of subsurface stresses is crucial for the design of mechanical components. This study provides an exact analytical solution for the frictionless indentation of a functionally graded (FG) orthotropic layer by a rigid cylindrical punch. The FG orthotropic layer, which rests on a rigid, non-adhesive substrate, is treated as a nonhomogeneous medium with an orthotropic stress–strain relationship. Part of its top surface experiences normal tractions, while the rest remains traction-free. The analysis also incorporates the gravitational force affecting the FG orthotropic layer. Five distinct real orthotropic materials are used, each with individually graded stiffness constants in their principal directions, to define the FG orthotropic behavior of the material. The governing equations are formulated using the singular integral equation method and transformed into algebraic systems via the Gauss–Chebyshev integration technique. A comprehensive parametric study examines how variations in dimensionless punch radius, compressive force, inhomogeneity parameters, and body force influence contact widths, contact pressures, normal and shear stresses, critical load factor, and the initial point of interface separation.

AtıfScopus9·WoS9

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

Turan, Muhittin

A new analytical solution based on the Ritz method is presented in this paper for analyzing the free vibration and buckling behavior of porous bi-directional functionally graded (2D-FG) beams under various boundary conditions. The solution is based on first-order shear deformation theory (FSDT). The selection of solution functions used in Ritz methods distinguishes the methods from each other and determines the accuracy of the analytical solution. To accurately capture the system's behavior and achieve the desired results, these functions have been carefully selected as a combination of polynomial and trigonometric expressions tailored as mixed series functions for each boundary condition. The study considers three types of porosity, namely PFG-1, PFG-2, and PFG-3. The equations of motion are derived using Lagrange's principle, taking into account the power-law variation of the beam material components throughout the volume. The non-dimensional fundamental frequencies and critical buckling loads are calculated for different boundary conditions, gradation exponents in the x and z directions (px, pz), slenderness (L/h), porosity coefficient (e), and porosity types. Initially, the accuracy of the mixed series functions is investigated for non-porous bi-directional functionally graded beams, and the numerical results are compared with existing literature to validate the proposed solution. Subsequently, the paper focuses on analyzing the influence of porosity on the free vibration and buckling behavior of bi-directional functionally graded beams using the developed solution method.

AtıfScopus21·WoS22·OpenAlex18

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

Turan, Muhittin

In the present paper, Navier’s method based on the first-order shear deformation theory for bending analysis of two-directional functionally graded beams subjected to various sets of boundary conditions is presented. In Navier's method, different trigonometric series functions are proposed for each boundary condition. The accuracy of these proposed functions was investigated and compared with the literature. It is also presented in a parametric study. The governing equations are derived according to Lagrange’s principle. The variation of the components of the beam material in the volume is defined by a power-law rule. The normalized maximum transverse deflections, the normalized axial and transverse shear stresses are obtained for various boundary conditions, gradation exponents (px, pz) in the x- and z-directions, and the slenderness (L/h). The trigonometric series functions used in this study give results that are quite compatible with the literature. In addition, the parametric study contributes to the literature.

AtıfScopus31·WoS31·OpenAlex27

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

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