Papers by Keyword: Singular Integral Equation

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Authors: Hichème Ferdjani
Abstract: The elastostatic antiplane problem of a Dugdale crack at the interface of two different materials is considered. Using integral transform, the problem is reduced to a single integral equation. The integral equation is solved numerically. The evolution of the crack for different values of the physical and geometrical parameters of the problem is studied. A comparison between the results obtained with the Griffith and Dugdale models is presented.
Authors: Naoaki Noda, Chun Hui Xu
Abstract: In this study, a rectangular interfacial crack in three dimensional bimaterials is analyzed. First, the problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express a two-dimensional interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factor along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. It is found that the stress intensity factors K1 and K2 are determined by bimaterials constant e alone, independent of elastic modulus ratio and Poisson's ratio.
Authors: Aysegul Kucuksucu, Mehmet A. Guler, Ahmet Avci
Abstract: In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.
Authors: Jian Mei Chang, Wen Jie Feng
Abstract: Mode III fracture failure of a through crack in an orthotropic functionally graded strip is investigated. The shear moduli in two directions of the material are respectively assumed to vary proportionately as a definite gradient. Fourier cosine transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function. Energy density factor criterion is applied to obtain the maximum of the minimum energy density and direction of crack initiation. Numerical results are given graphically to illustrate the effects of the material property parameters and geometry criterion on the energy density factor.
Authors: Naoaki Noda, Yasushi Takase, Ryohji Shirao, Jun Li, Jun Suke Sugimoto
Abstract: In this study, singular stress fields at the ends of fibers are discussed by the use of models of rectangular and cylindrical inclusions in a semi-infinite body under pull-out force.The body force method is used to formulate those problems as a system of singular integral equations where the unknown functions are densities of the body forces distributed in a semi-infinite body having the same elastic constants as those of the matrix and inclusions.Then generalized stress intensity factors at the corner of rectangular and cylindrical inclusions are systematically calculated with varying the elastic ratio, length, and spacing of the location from edge to inner of the body. The effects of elastic modulus ratio and aspect ratio of inclusion upon the stress intensity factors are discussed.
Authors: Li Fang Guo, Xing Li, You Zheng Yang
Abstract: In this paper, the Fourier integral transform-singular integral equation method is presented for the Mode I crack problem of the functionally graded orthotropic coating-substrate structure. The elastic property of the material is assumed vary continuously along the thickness direction. The principal directions of orthotropy are parallel and perpendicular to the boundaries of the strip. Numerical examples are presented to illustrate the effects of the crack length, the material nonhomogeneity and the thickness of coating on the stress intensity factors.
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