Frictionless Contact of a Functionally Graded Half-Space and a rigid Base with an Axially Symmetric Recess
TL;DR: In this paper, an axially symmetric frictionless contact between an elastically transversely isptropic functionally graded half-space and a rigid base that has a small axisymmetric surface recess is considered.
Abstract: This paper is concerned with an axially symmetric frictionless contact between an elastically transversely isptropic functionally graded half-space and a rigid base that has a small axisymmetric surface recess. The graded half-space is modeled as a nonhomogeneous medium. We reduce the problem to solving Fredholm integral equations, solve these equations numerically and establish a relationship between the applied pressure and gap radius. The effects of anisotropy and nonhomogeneity parameter of the graded half-space on the normal pressure as well as on the critical pressure have been shown graphically.
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01 Aug 1992
TL;DR: In this article, the axisymmetric crack problem for a nonhomogeneous medium is considered and the main results given are the stress intensity factors as a function of the nonhomogeneity parameter alpha for various loading conditions.
Abstract: : In this paper the axisymmetric crack problem for a nonhomogeneous medium is considered. It is assumed that the shear modulus is a function of z approximated by mu = mu (sub 0) e to the alpha z power. This is a simple simulation of materials and interfacial zones with intentionally or naturally graded properties. The problem is a mixed mode problem and is formulated in terms of a pair of singular integral equations. With fracture mechanics applications in mind, the main results given are the stress intensity factors as a functions of the nonhomogeneity parameter alpha for various loading conditions. Also given are some sample results showing the crack opening displacements.
56 citations
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.
9 citations
TL;DR: In this article, the relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order, and numerical results have been presented to assess the effects of functional grading of the non-homogeneous medium and the application load on the stress distribution in the layer as well as on the relationship of applied load and the area of contact.
Abstract: Abstract This article is concerned with the study of frictionless contact between a rigid punch and a transversely isotropic functionally graded layer. The rigid punch is assumed to be axially symmetric and is supposed to be pressing the layer by an applied concentrated load. The layer is resting on a rigid base and is assumed to be sufficiently thick in comparison with the amount of indentation by the rigid punch. The graded layer is modeled as a non-homogeneous medium. The relationship between the applied load P and the contact area is obtained by solving the mathematically formulated problem through using the Hankel transform of different order. Numerical results have been presented to assess the effects of functional grading of the medium and the applied load on the stress distribution in the layer as well as on the relationship between the applied load and the area of contact.
4 citations
15 Oct 2018
TL;DR: In this paper, the receding contact problem of functionally graded (FG) layer resting on a Winkler foundation is considered and a general formulation is obtained using elasticity theory and Fourier integral transform.
Abstract: In this paper, the receding contact problem of functionally graded (FG) layer resting on a Winkler foundation is considered. It is assumed that the shear modulus of the layer change functionally along the depth whereas Poisson ratio remains constant. Arbitrary concentrated loads by means of arbitrary rigid punches are applied to the top of the layer. The problem is considered as a plain strain problem. A general formulation is obtained using elasticity theory and Fourier integral transform. Obtained formulation is valid for both symmetric and asymmetric systems. A parametric study is carried out to investigate the effect of material properties and loading on contact distances and contact pressures. It is found that, increasing rigidity of the bottom of the FG layer compared to the top of the FG layer, the contact distances between the circular punch and FG layer contact surface decreases whereas maximum contact pressure increases. In addition, placement of the rigid punches has an effect on the contact distances and contact pressures.
2 citations
Cites background from "Frictionless Contact of a Functiona..."
...[21] studied the stationary plane contact of a functionally graded heat conducting punch and a rigid insulated half-space....
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TL;DR: In this article, a boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements is presented, which guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacement without changing the initial discretization of the boundary of the bodies.
Abstract: A new algorithm is presented for the boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements. The contact constraints are not applied node-on-node but node-on-element, using the element shape functions to distribute the geometry, displacements and tractions on each element in the contact zone. Thus, the discretizations performed along the two surfaces in contact need not necessarily be the same. The solution procedure is based on the updated Lagrangian approach and the resulting method is incremental. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements without it being necessary to change the initial discretization of the boundary of the bodies. Only the frictionless static problem is dealt with, and the proposed algorithm is applied to the most representative receding contact problem: a layer pressed against an elastic foundation. The results obtained when the displacements are small are in good agreement with the analytical solution. When large displacements are considered, another nonlinearity appears and its influence will be shown in this paper.
28 citations
26 citations
TL;DR: In this paper, an incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis for joints subjected to cyclic loading.
18 citations
TL;DR: In this article, the frictionless contact between a rounded or flat-ended rigid stamp and an elastic layered composite is considered according to theory of elasticity and the problem is formulated in terms of a singular integral equation for the contact pressure.
Abstract: The frictionless contact between a rounded or flat-ended rigid stamp and an elastic layered composite is considered according to theory of Elasticity. The elastic layered composite consisted of two materials with different elastic constants and heights is rested on simple supports. It is assumed that the layered composite is subjected to a concentrated load with a magnitude of 2P by means of a rigid stamp on its top surface and the effect of gravity is neglected. Stresses and displacements are expressed depending on the contact pressure using Fourier transforms technique and the problem is formulated in terms of a singular integral equation for the contact pressure. The singular integral equation is solved numerically by using appropriate Gauss- Chebyshev integration. Numerical results obtained for various dimensionless quantities for the contact pressure are presented in graphical form.
14 citations
Journal Article•
TL;DR: In this paper, the authors considered the problem of smooth receding contact between an orthotropic layer and a orthotropic half-space and showed that finding the extent of contact in the loaded configuration can be reduced to an eigenvalue problem of a homogenous Fredholm integral equation.
Abstract: THE PROBLEM of smooth receding contact between an orthotropic layer and an orthotropic half-space has been considered in this papaer. The paper includes a generalization of the results of the paper by L. M. KEER, J. DUNDURS, K. C. TSAI [4] concerning receding contact between an isotropic layer and an isotropic half-space. It is observed that the task of finding the extent of contact in the loaded configuration can be reduced to an eigenvalue problem of a homogenous Fredholm integral equation. The kernel of the Fredholm integral equation is found to be dependent on the elastic constants of the layer but is independent of the elastic constants of the half-space below, which is in contrast to the study for the isotropic materials, where the kernel is independent of the elastic constants. Finally some numerical results have been presented in graphs in order to compare the results of interest for isotropic and orthotropic materials.
9 citations