• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.81-95
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• 1998

The superconvergence of the Sloan iterate obtained from a Galerkin method for the approximate solution of the singular integral equation based on the use of two sets of orthogonal polynomials is investigated. The discrete Sloan iterate using Gaussian quadrature to evaluate the integrals in the equation becomes the Nystr$\ddot{o}$m approximation obtained by the same rules. Consequently, it is impossible to expect the faster convergence of the Sloan iterate than the discrete Galerkin approximation in practice.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.85-97
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• 2000

A quadrature rule for the solution of Cauchy singular integral equation is constructed and investigated. This method to calculate numerically singular integrals uses classical Jacobi quadratures adopting Hunter's method. The proposed method is convergent under a reasonable assumption on the smoothness of the solution.

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.279-296
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• 2008

This paper presents an exact integration for the hypersingular boundary integral equation of two-dimensional elastostatics. The boundary is discretized by straight segments and the physical variables are approximated by discontinuous quadratic elements. The integral for the hypersingular boundary integral equation analysis is given in a closed form. It is proven that using the exact integration for discontinuous boundary element, the singular integral in the Cauchy Principal Value and the hypersingular integral in the Hadamard Finite Part can be obtained straightforward without special treatment. Two numerical examples are implemented to verify the correctness of the derived exact integration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2524-2539
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• 1996

A design process and an axisymmetric boundary integral equation method for precise structural analysis of the aircraft gas turbine rotor disk were developed. This axisymmetric boundary integral equation method for stress and steady-state thermal analysis was improved in solution accuracy by appling an implicit technique for Cauchy principal value evaluation, a subelement technique for weak singular integral evaluation and a double exponentical integral technoque for internal point solution near boundary surfaces. Stresses, temperatures, low cycle fatigue lifes and critical speeds for the turbine rotor disk of the thrust 1421 N class turbojet engine were analysed in a pratical calculation model problem.

• Journal of Mechanical Science and Technology
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• v.17 no.2
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• pp.269-279
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• 2003

The anti-plane shear problem of bonded elastic materials containing a crack at an arbitrary angle to the graded interfacial zone is investigated in this paper The interfacial zone is modeled as a nonhomogeneous interlayer of finite thickness with the continuously varying shear modulus between the two dissimilar, homogeneous half-planes. Formulation of the crack problem is based upon the use of the Fourier integral transform method and the coordinate transformations of basic field variables. The resulting Cauchy-type singular integral equation is solved numerically to provide the values of mode 111 stress intensity factors. A comprehensive parametric study is then presented of the influence of crack obliquity on the stress intensity factors for different crack size and locations and for different material combinations, in conjunction with the material nonhomogeneity within the graded interfacial zone.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.5
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• pp.787-797
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• 1986

An implicit approach is employed to obtain a general boundary integral formulation of axisymmetric elastic problems in terms of a pair of singular integral equations. The corresponding kernel functions from the solutions of Navier's equation are derived by applying a three dimensional integral and a direct axisymmetrical approach. A numerical discretization schem including the evaluation of Cauchy principal values of the singular integral is described. Finally the typical axisymmetric elastic models are analyzed, i.e. the hollow sphere, the constant thickness and the V-notched round bar.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.9
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• pp.151-157
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• 2000

Stress intensity factors for the circumferential surface crack of a long composite cylinder under torsion is investigated. The problem is formulated as a singular integral equation of the first kind with a Cauchy type kernel using the integral transform technique. The mode III stress intensity factors at the crack tips are presented when (a) the inner crack tip is away from the interface and (b) the inner crack tip is at the interface.

• Journal of Aerospace System Engineering
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• v.1 no.1
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• pp.25-35
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• 2007

In this paper, the interlaminar crack problems of a fiber metal laminate (FML) under generalized plane deformation are studied using the theory of anisotropic elasticity. The crack is considered to be embedded in the matrix interlaminar region (including adhesive zone and resin rich zone) of the FML. Based on Fourier integral transformation and the stress matrix formulation, the current mixed boundary value problem is reduced to solving a system of Cauchy-type singular integral equations of the 1st kind. Within the theory of linear fracture mechanics, the stress intensity factors are defined on terms of the solutions of integral equations and numerical results are obtained for in-plane normal (mode I) crack surface loading. The effects of location and length of crack in the 3/2 and 2/1 ARALL, GLARE or CARE type FML's on the stress intensity factors are illustrated.

• Journal of Mechanical Science and Technology
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• v.15 no.10
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• pp.1386-1397
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• 2001

In this paper, the plane elasticity equations are used to investigate the in-plane normal (mode I) and shear (mode II) behavior of a crack perpendicular to and terminating at the interface in bonded media with a graded interfacial zone. The interfacial Bone is treated as a nonhomogeneous interlayer with the continuously varying elastic modulus between the two dissimilar, homogeneous semi-infinite constituents. For each of the individual loading modes, based on the Fourier integral transform technique, a singular integral equation with a Cauchy kernel is derived in a separate but parallel manner. In the numerical results, the values of corresponding modes of stress intensity factors are illustrated for various combinations of material and geometric parameters of the bonded media in conjunction with the effect of the material nonhomogeneity within the graded interfacial zone.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.329-341
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• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.