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 paper, the authors considered the elastostatic plane problem of a layered composite containing an internal or edge crack perpendicular to its boundaries in its lower layer, and solved the problem numerically by making use of Gauss-Chebyshev integration.
Abstract: The elastostatic plane problem of a layered composite containing an internal or edge crack perpendicular to its boundaries in its lower layer is considered. The layered composite consists of two elastic layers having different elastic constants and heights and rests on two simple supports. Solution of the problem is obtained by superposition of solutions for the following two problems: The layered composite subjected to a concentrated load through a rigid rectangular stamp without a crack and the layered composite having a crack whose surface is subjected to the opposite of the stress distribution obtained from the solution of the first problem. Using theory of Elasticity and Fourier transform technique, the problem is formulated in terms of two singular integral equations. Solving these integral equations numerically by making use of Gauss–Chebyshev integration, numerical results related to the normal stress σ x ( 0 , y ) , the stress-intensity factors, and the crack opening displacements are presented and shown graphically for various dimensionless quantities.
7 citations
TL;DR: In this article, a rigid smooth indentor is treated as a superposition of contact-triggered infinitesimal deformations superposed upon finite deformations due to pre-stress.
Abstract: A rigid smooth indentor slides at a constant speed on a compressible isotropic neo-Hookean half-space that is subjected to pre-stress aligned with the surface and sliding direction. A dynamic steady-sliding situation of plane strain is treated as the superposition of contact-triggered infinitesimal deformations superposed upon finite deformations due to pre-stress. The neo-Hookean material behaves for small strains as a linear elastic solid with Poisson's ratio 1 : 4. Exact solutions are presented for both deformations and, for a range of acceptable pre-stress values, the infinitesimal component exhibits the typical non-isotropy induced by pre-stress, and several critical speeds. In view of the unilateral constraints of contact, these speeds serve to define the sliding speed ranges for which physically acceptable solutions arise. A Rayleigh speed is the upper bound for subsonic sliding, and transonic sliding can occur only at a single speed. For the generic parabolic indentor, contact zone traction continuity is lost at the zone leading edge for trans- and supersonic sliding. For pre-stress levels that fall outside the acceptable range, either a negative Poisson effect occurs, or a Rayleigh speed does not exist and the unilateral constraints cannot be satisfied for any subsonic sliding speed.
7 citations
TL;DR: In this article, the authors examined the problem of the unilateral interaction between two precompressed transversely isotropic elastic halfspaces which are subjected to localized body forces and developed an exact solution for the radius of the axisymmetric separation region.
Abstract: The present paper examines the problem of the unilateral interaction between two precompressed transversely isotropic elastic halfspaces which are subjected to localized body forces. The interface is assumed to be frictionless and the body forces are directed away from the interface. The unilateral nature of the contact leads to the development of a zone of separation between the halfspace regions. An exact solution is developed for the radius of the axisymmetric separation region.
7 citations
TL;DR: In this article, an axially symmetric problem of frictionless contact interaction of an elastic half-space and a rigid base that has a small surface recess is considered, and the problem is solved by the method of double integral equations.
Abstract: An axially symmetric problem of frictionless contact interaction of an elastic half-space and a rigid base that has a small surface recess is considered. A corresponding problem of elasticity theory is formulated. The problem is solved by the method of double integral equations. The contact pressure, the surface shape of the half-space after compression, and the size of the gap are found in closed form.
4 citations
TL;DR: In this article, the authors used matched asymptotic expansions to study a contact problem for a system consisting of a large number of small punches situated along a given curve on the boundary of an elastic half-space.
2 citations