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1
Content available Generalized characteristic singular integral equation with Hilbert kernel
100%
Karczmarek P.
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2008
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tom Vol. 28, no. 3
287-294
EN
In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.
2
Content available remote Singular integral equations with multiplicative Cauchy-type kernels
100%
Kaczmarek P. , Pylak D. , Wójcik P.
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tom Nr 50
77--90
EN
In this paper we consider singular integral equations of the first kind with multiplicative Cauchy-type kernels defined on n-dimensional domains. We give their general solutions in the class of Holder continuous functions and propose the statements of uniqueness problem.
3
Content available remote Solution of the plane contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-profile
100%
Arslan O.
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2019
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tom Vol. 71, nr 6
531--565
EN
A singular integral equation (SIE) approach and a finite element method are developed for the solution of the frictional sliding contact problem between a finite-thickness laterally graded solid and a rigid stamp of an arbitrary tip-shape considering the plane strain assumption. An exponential shear modulus variation is introduced through the lateral direction. The field variables are obtained applying the Fourier transformation techniques on the governing partial differential equations. A surface displacement gradient is then utilized to derive a SIE of the second kind. A numerical solution of the SIE is performed by using a collation method and the Gauss quadrature integration techniques for the flat, triangular and circular stamp profiles. Finite element analyses (FEA) of the same contact problems are also performed upon selection of the augmented Lagrange contact-solver in ANSYS. For the incomplete (triangular and circular) stamp problems, an iterative algorithm is developed in order to obtain practically computational solutions for any desired contact lengths. Successful convergence of the SIE results and excellent consistency between the SIE and FEA results are attained, that indicate the reliability of both methods. The change in the thickness is shown to alter the contact behavior of the laterally graded solid significantly.
4
Content available Singular integral equation with a multiplicative Cauchy kernel in the half-plane
100%
Karczmarek P.
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2008
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tom Vol. 28, no. 1
63-72
EN
In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.
5
Content available remote Continuous contact problem of a functionally graded layer resting on an elastic half‐plane
88%
Öner E. , Adiyaman G. , Birinci A.
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tom Vol. 69, nr 1
53--73
EN
In this study, the continuous contact problem of a functionally graded layer resting on an elastic half-plane and loaded by a rigid rectangular stamp is examined. The problem is solved assuming that the functionally graded (FG) layer is isotropic and the shear modulus and mass density vary exponentially throughout the layer’s thickness. However, the body force of the elastic half-plane is neglected. In addition, it is assumed that all surfaces are frictionless and only compressive stress is transferred along the contact surfaces. The mathematical problem is reduced to a singular integral equation in which the contact stress under the rigid stamp is unknown using the Fourier integral transform and boundary conditions related to the problem. This singular integral equation is solved numerically using the Gauss–Chebyshev integration formula. The dimensionless contact stress under the rigid stamp, the initial separation loads and the initial separation distances between the FG layer and the elastic half-plane are obtained for various dimensionless quantities.
6
Content available remote Plane receding contact problem for a functionally graded layer supported by two quarter-planes
88%
Çömez İ. , Kahya V. , Erdöl R.
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2018
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tom Vol. 70, nr 6
485--504
EN
In this study, the plane receding contact problem for a functionally graded (FG) layer resting on two quarter-planes is considered by using the theory of linear elasticity. The layer is indented by a rigid cylindrical punch that applies a concentrated force in the normal direction. While the Poisson’s ratio is kept constant, the shear modulus is assumed to vary exponentially through-the-thickness of the layer. It is assumed that the contact at the layer-punch interface and the layer-substrate interface is frictionless, and only the normal tractions can be transmitted along the contact regions. Applying the Fourier integral transform, the plane elasticity equations are converted to a system of two singular integral equations, in which the contact stresses and the contact widths are unknowns. The singular integral equations are solved numerically by Gauss–Jacobi integration formula. Effects of the material inhomogeneity, the distance between quarter-planes and the punch radius on the contact stresses, the contact widths, and the stress intensity factors at the sharp edges are shown. Although the theoretical analysis is formulated with respect to elastic quarter planes, the numerical studies are carried out only for rigid ones.
7
Content available On 3D anticrack problem of thermoelectroelasticity
88%
Kaczyński A.
Acta Mechanica et Automatica
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2018
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tom Vol. 12, no. 2
109--114
EN
A solution is presented for the static problem of thermoelectroelasticity involving a transversely isotropic space with a heat-insulated rigid sheet-like inclusion (anticrack) located in the isotropy plane. It is assumed that far from this defect the body is in a uniform heat flow perpendicular to the inclusion plane. Besides, considered is the case where the electric potential on the anticrack faces is equal to zero. Accurate results are obtained by constructing suitable potential solutions and reducing the thermoelectromechanical problem to its thermomechanical counterpart. The governing boundary integral equation for a planar anticrack of arbitrary shape is obtained in terms of a normal stress discontinuity. As an illustration, a closed-form solution is given and discussed for a circular rigid inclusion.
8
Content available Doubly periodic cracks in the anisotropic medium with the account of contact of their faces
75%
Maksymovych O. , Pasternak I. , Sulym H. , Kutsyk S.
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tom Vol. 8, no. 3
160--164
EN
The paper presents complex variable integral formulae and singular boundary integral equations for doubly periodic cracks in anisotropic elastic medium. It utilizes the numerical solution procedure, which accounts for the contact of crack faces and produce accurate results for SIF evaluation. It is shown that the account of contact effects significantly influence the SIF of doubly periodic curvilinear cracks both for isotropic and anisotropic materials.
9
Content available An Analysis Of Stress Intensity Factor Due To Normal Stress For A Cracked Plate Reinforced With A Sheet By Seam Welding
75%
Kim O.-H. , Kim Y. C.
Archives of Metallurgy and Materials
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2015
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tom Vol. 60, iss. 2B
1441--1444
EN
It is essential in damage tolerance design to determine the stress intensity factor theoretically. The stress intensity factor for a cracked plate that is reinforced with a sheet by seam welding is determined theoretically and plotted as function of the seam welding location and stiffness ratio. The singular integral equation is derived based on the compatibility condition between the cracked plate and the reinforcement plate, and it is solved by means of Erdogan and Gupta‘s method. The theory is verified by comparing the results of the present analysis with those of a numerical analysis. The results from the present analysis show that the reinforcement effect improves as the welding line is situated closer to the crack and as the stiffness ratio of the cracked plate and the reinforcement plate increases.
10
A boundary-value problem for the equation of mixed type with generalized operators of fractional differentiation in the boundary conditions
51%
Repin O. A. , Kumykova S. K.
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2016
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tom Vol. 22, nr 1
27--36
EN
The paper is devoted to the study of a boundary-value problem for an equation of mixed type with generalized operators of fractional differentiation in boundary conditions. We prove uniqueness of solutions under some restrictions on the known functions and on the different orders of the operators of generalized fractional differentiation appearing in the boundary conditions. Existence of solutions is proved by reduction to a Fredholm equation of the second kind, for which solvability follows from the uniqueness of the solution of our original problem.
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