• 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.

• Structural Engineering and Mechanics
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• v.45 no.4
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• pp.495-519
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• 2013

This paper investigates properties of integral operators in complex variable boundary integral equation in plane elasticity, which is derived from the Somigliana identity in the complex variable form. The generalized Sokhotski-Plemelj's formulae are used to obtain the BIE in complex variable. The properties of some integral operators in the interior problem are studied in detail. The Neumann and Dirichlet problems are analyzed. The prior condition for solution is studied. The solvability of the formulated problems is addressed. Similar analysis is carried out for the exterior problem. It is found that the properties of some integral operators in the exterior boundary value problem (BVP) are quite different from their counterparts in the interior BVP.

• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.97-119
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• 2008

Electrical impedance tomography (EIT) problem with anisotropic anomalous region is formulated in a few different ways using boundary integral operators. The Frechet derivative of Neumann-to-Dirichlet map is computed also by using boundary integral operators and the boundary of the anomalous region is approximated by trigonometric expansion with Lagrangian basis. The numerical reconstruction is done in case that the conductivity of the anomalous region is isotropic.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.425-440
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• 2010

Using Green's theorem, elliptic boundary value problems can be converted to boundary integral equations. A numerical methods for boundary integral equations are boundary elementary method(BEM). BEM has advantages over finite element method(FEM) whenever the fundamental solutions are known. Helmholtz type equations arise naturally in many physical applications. In a boundary integral formulation for the exterior Neumann there occurs a hypersingular operator which exhibits a strong singularity like $\frac{1}{|x-y|^3}$ and hence is not an integrable function. In this paper we are going to remove this hypersingularity by reducing the regularity of test functions.

• Bulletin of the Society of Naval Architects of Korea
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• v.24 no.4
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• pp.19-36
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• 1987

In this research the coupling problem between the elastic structure and the fluid, specially the hydroelastic harmonic vibration problem, is studied. In order to couple the domains, i.e., the structural domain and the fluid domain, the boundary integral method(direct boundary integral formulation) is used in the fluid domain in combination with the finite element method for the structure. The boundary integral method has been widely developed to apply it to the hydroelastic vibration problem. The hybrid boundary integral method using eigenfunctions on the radiation boundaries and the boundary integral method using the series form image-functions to replace the even bottom and free surface boundaries in case of high frequencies have been developed and tested. According to the boundary conditions and the frequency ranges the different boundary integral methods with the different idealizations of the fluid boundaries have been studied. Using the same interpolation functions for the pressure distribution and the displacement the two domains have been coupled and using Hamilton principle the solution of the hydroelastic have been obtained through the direct minimizing process. It has become evident that the finite-boundary element method combining with the eigenfunction or the image-function method give good results in comparison with the experimental ones and the other numerical results by the finite element method.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.913-930
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• 2002

For curved crack problems in plane elasticity, subjected to the traction conditions on the crack faces, we present a system of boundary integral equations. The procedure is based on the indirect boundary integral method in terms of real variables. For efficient mathematical analysis, we decompose the singular kernel into the Cauchy singular part and the regular one. As a result, solvability of the presented system is proved and availability of the present approach is shown by the numerical example of a circular arc crack.

• East Asian mathematical journal
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• v.40 no.1
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.11
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• pp.777-782
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• 1987

A new composite method of finite element and boundary integral methods is presented to solve the two dimensional magnetostatic field problems with open boundary. The method can deal with the current source of the boundary integral regin where the boundary integral method is applied, and also Neumann and Dirichlet boundary conditions at the interfacial boundary between the boundary integral region and the finite element region where the finite element method is applied. The new approach has been applied to a simple linear problem to verify the usefulness. It is shown that the proposed algorithm gives more accurate results than the finite element methed under the same elementdiscretization.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.305-320
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• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.