Turan, Muhittin; Adiyaman, Gokhan

A new type of functionally graded material (FGM) with material properties varying in two or three directions is needed to obtain materials with better mechanical properties and high-temperature resistance for use in the military, aerospace, automotive, and engineering structures. Considering the porosity that occurs during the production of these materials, it has become necessary to examine the free vibration and buckling behaviors. Therefore, this study investigated free vibration and buckling analysis of porous two-directional functionally graded (2D FG) beams subject to various boundary conditions. A high-order finite element based on parabolic shear deformation theory (PSDT) is proposed to solve this problem. Three types of porosity distributions were used in the study (FGP-1, FGP-2, and FGP-3). The governing equations are derived from Lagrange’s principle. The material change in the beam volume in both directions is defined by a power-law rule. The dimensionless fundamental frequencies and critical buckling loads are obtained for various boundary conditions, gradation exponents (px, pz), porosity coefficient (e), porosity distribution, and slenderness (L/h). The numerical results obtained with the proposed higher-order finite element are compatible with the literature.

AtıfScopus47·WoS44·OpenAlex40

İncele

Turan, Muhittin; Adiyaman, Gokhan

A new higher-order finite element for the static analysis of two-directional functionally graded (2D FG) porous beams subjected to various boundary conditions based on parabolic shear deformation theory (PSDT) is presented. The main purpose of this study is to predict the deflections and stresses of 2D FG porous and non-porous beams with the help of the proposed finite element. Since a higher-order finite element with a third order polynomial is used, the deflections and stresses can be accurately and rapidly obtained even for short beams. In addition, the new higher-order element is free of shear locking phenomenon without requiring any shear correction factors. Three types of distribution functions were used for porosity in this study. To the author's knowledge, the sinusoidal uneven distribution function (FGP-3) is presented for the first time. The governing equations are derived by Lagrange’s principle using a parabolic shear deformation theory that considers normal and shear deformations. According to a power-law rule, the material change in the beam volume in both directions is defined. The dimensionless maximum transverse deflections, normal stresses, and shear stresses are obtained for various boundary conditions, gradation exponents (px, pz) in the x- and z-directions, porosity coefficient (e), porosity distribution (FGP-1, FGP-2, FGP-3), and the slenderness (L/h). This study's new higher-order finite element gives results compatible with the literature and it can be used to accurately find the deflections and stresses for the 2D FG non-porous or porous beams subjected to various boundary conditions.

AtıfScopus30·WoS28·OpenAlex26

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

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

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