Effect of nonhomogeneity on the contact of an isotropic half-space and a rigid base with an axially symmetric recess
11 Mar 2008-Journal of Mechanics of Materials and Structures (Mathematical Sciences Publishers)-Vol. 3, Iss: 1, pp 1-18
TL;DR: In this paper, an axially symmetric frictionless contact problem between a nonhomogeneous elastic halfspace and a rigid base that has a small axisymmetric surface recess was studied.
Abstract: We study an axially symmetric frictionless contact problem between a nonhomogeneous elastic halfspace and a rigid base that has a small axisymmetric surface recess. We reduce the problem to solving Fredholm integral equations, solve these equations numerically, and establish a relationship between the applied pressure and the gap radius. We find and graph the effects of nonhomogeneity on the normal pressure, critical pressure and on the surface displacement.
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15 Aug 1977
TL;DR: In this paper, the authors have developed methods for solving integral equations which work well in spite of the presence of singularities, in which the new approximation methods which were developed do work well for singularities.
Abstract: : One encounters difficulties in the solution of integral equations, namely, the occurrence of singularities in the kernel, and the occurence of unknown-type singularities in the solution of the integral equation. Standard methods of approximation based on exactness for polynomials up to a certain degree are very poor, and frequently fail for functions having such singularities. The purpose of this contract was to develop methods for solving integral equations which work well in spite of the presence of singularities. This goal has been accomplished, in that the new approximation methods which were developed do work well in the presence of singularities. (Author)
205 citations
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
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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
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TL;DR: In this article, the authors apply density functional theory and for the first time with the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation, study the electronic, elastic, and mechanical properties of aluminium and silicon carbide.
2 citations
References
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01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
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01 Jan 1917
TL;DR: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + bdx = 1 a ln|ax + b| (4) Integrals of Rational Functions
Abstract: Basic Forms x n dx = 1 n + 1 x n+1 (1) 1 x dx = ln |x| (2) udv = uv − vdu (3) 1 ax + b dx = 1 a ln |ax + b| (4) Integrals of Rational Functions 1 (x + a) 2 dx = −
11,190 citations
"Effect of nonhomogeneity on the con..." refers background in this paper
...[Gradshteyn and Ryzhik 1963] I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, Academic Press, New York, 1963....
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4,700 citations
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TL;DR: In this paper, a pair of Gauss-Chebyshev integration formulas for singular integrals are developed and a simple numerical method for solving a system of singular integral equations is described.
Abstract: In this paper a pair of Gauss-Chebyshev integration formulas for singular integrals are developed. Using these formulas a simple numerical method for solving a system of singular integral equations is described. To demonstrate the effectiveness of the method, a numerical example is given. In order to have a basis of comparison, the example problem is solved also by using an alternate method.
1,300 citations