Axisymmetric analysis of a functionally graded layer resting on elastic substrate
TL;DR: In this paper, a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading is considered, where the shear modulus of the FG layer is assumed to vary in an exponential form through the thickness.
Abstract: This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel\'s transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.
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TL;DR: In this article, the receding contact between a homogeneous elastic layer and a halfplane substrate reinforced by a functionally graded coating was examined and the material properties of the coating were investigated.
Abstract: In this work, we examine the receding contact between a homogeneous elastic layer and a half-plane substrate reinforced by a functionally graded coating. The material properties of the coating are ...
18 citations
TL;DR: In this article, the receding contact mechanics of an elastic layer reinforced by a functionally graded coating, pressed against a half-plane substrate as an integral assembly, are analyzed using both an analytical and a finite element method.
Abstract: We aim to analyze the receding contact mechanics of an elastic layer reinforced by a functionally graded coating, pressed against a half-plane substrate as an integral assembly. The graded reinforcement is modeled by an inhomogeneous medium whose shear modulus is allowed to vary exponentially. A smooth receding contact is arisen due to the normal tractions applied over a finite segment of the reinforcement surface. The primary goal of this study is the determination of both the receding contact pressure and the extent of receding contact along the assembly and substrate interface. Using both an analytical and a finite element method solves the problem. In the former approach, Fourier integral transforms help convert the problem into a singular integral equation of Cauchy type, which is numerically integrated with Gauss-Chebyshev quadrature. In the numerical approach, multiple homogeneous layers approximate the graded coating. The stresses at those nodes lying on sublayer interfaces are averaged over their surrounding elements for guaranteeing the continuity in stress field. Very good agreements are found between the results obtained from the two methods. Extensive parametric case studies reveal that material properties, loading configuration, and geometric parameters all play important roles in the determination of both the contact pressure distribution and the length of contact. These receding contact properties can therefore be optimized as desired by appropriately varying the influential parameters. Both the solution methodologies and the numerical results presented in this work can provide some useful guidelines on the better design of multilayered functionally graded structures.
7 citations
Dissertation•
06 Dec 2017
4 citations
TL;DR: In this paper, the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter was solved, and the Poisson's ratio was kept as a constant.
Abstract: This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, ...
3 citations
30 Mar 2019
TL;DR: In this article, a frictionless contact problem for a functionally graded (FG) layer is considered and the problem is reduced to a singular integral equation using plane elasticity and integral transform techniques.
Abstract: In this study, frictionless contact problem for a functionally graded (FG) layer is considered. The FG layer is subjected to load with a rigid stamp and the FG layer is bonded on a rigid foundation. The graded layer is modeled as a non-homogenous medium with a constant Poisson’s ratio and exponentially varying shear modules. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is solved analytically using plane elasticity and integral transform techniques. The problem is reduced to a singular integral equation using plane elasticity and integral transform techniques. Obtained singular integral equation is solved numerically using Gauss-Jacobi integration formulation and obtain the contact pressure and contact length. The contact length and contact pressures between the FG layer and the rigid stamp are analyzed for various material properties and loading. Aim of the paper is to investigate the effect of the non-homogeneity parameter of the graded layer on the contact pressures and lengths.
2 citations
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TL;DR: In this article, the exact solution of the problem of a pinned-end laminate composed of N layers, each of which possesses only a single plane of elastic symmetry, under cylindrical bending is investigated.
Abstract: Investigation of the success of classical lamination theory in predicting the response of composite laminates under static bending is extended by consideration of the influence of shear coupling. Specifically, we treat the exact solution of the problem of a pinned-end laminate composed of N layers, each of which possesses only a single plane of elastic symmetry, under cylindrical bending. Several example problems, involving unidirectional and angle-ply composites, are solved and the detailed results compared to corresponding approximate solutions. Some observations are offered in regard to the general range of validity of classical laminated plate theory.
245 citations
TL;DR: In this paper, a formal solution based on integral transforms and matrix analysis is proposed to evaluate the exact state of stress and displacement for a multilayered medium, where the problem is reduced to the evaluation of some basic matrices and thus the calculation takes place in a clearly arranged way.
Abstract: Though the basic equations of the linear theory of elasticity are well known, it is rather cumbersome to evaluate the exact state of stress and displacement for a multilayered medium. In this paper we discuss a formal solution based on integral transforms and matrix analysis. Essentially the problem is reduced to the evaluation of some basic matrices and thus the calculation takes place in a clearly arranged way. Here we restrict ourselves to plane elastic and isotropic layers and use cartesian coordinates.
181 citations
IBM1
TL;DR: In this paper, the exact analysis of stresses and displacements in a linear elastic half-space composed of one or two layers bonded to another homogeneous half space is presented, in a form suitable for numerical computation.
141 citations
TL;DR: In this paper, an exact finite-layer flexibility matrix is introduced for the analysis of a horizontally layered elastic material and it is shown that this matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite.
Abstract: It is well known that the analysis of a horizontally layered elastic material can be considerably simplified by the introduction of a Fourier or Hankel transform and the application of the finite layer approach. The conventional finite layer (and finite element) stiffness approach breaks down when applied to incompressible materials. In this paper these difficulties are overcome by the introduction of an exact finite layer flexibility matrix. This flexibility matrix can be assembled in much the same way as the stiffness matrix and does not suffer from the disadvantage of becoming infinite for an incompressible material. The method is illustrated by a series of examples drawn from the geotechnical area, where it is observed that many natural and man-made deposits are horizontally layered and where it is necessary to consider incompressible behaviour for undrained conditions. For abstract of part 2 see TRIS no. 378330. (Author/TRRL)
79 citations
TL;DR: In this paper, a method is presented to study the three-dimensional quasi-static response of a multi-layered poroelastic half-space with compressible constituents.
74 citations