• Title, Summary, Keyword: Boundary Integral Equation

### Exact integration for the hypersingular boundary integral equation of two-dimensional elastostatics

• Zhang, Xiaosong;Zhang, Xiaoxian
• 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.

### Properties of integral operators in complex variable boundary integral equation in plane elasticity

• Chen, Y.Z.;Wang, Z.X.
• 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.

### A boundary-volume integral equation method for the analysis of wave scattering

• Touhei, Terumi
• Coupled systems mechanics
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• v.1 no.2
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• pp.183-204
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• 2012
• A method for the analysis of wave scattering in 3-D elastic full space is developed by means of the coupled boundary-volume integral equation, which takes into account the effects of both the boundary of inclusions and the uctuation of the wave field. The wavenumber domain formulation is used to construct the Krylov subspace by means of FFT. In order to achieve the wavenumber domain formulation, the boundary-volume integral equation is transformed into the volume integral equation. The formulation is also focused on this transform and its numerical implementation. Several numerical results clarify the accuracy and effectiveness of the present method for scattering analysis.

### A Study on Structural Analysis for Aircraft Gas Turbine Rotor Disks Using the Axisymmetric Boundary Integral Equation Method (축대칭 경계적분법에 의한 항공기 가스터빈 로터디스크 구조해석에 관한 연구)

• Kong, Chang-Duk;Chung, Suk-Choo
• 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.

### REMOVAL OF HYPERSINGULARITY IN A DIRECT BEM FORMULATION

• Lee, BongJu
• 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.

### Integral Transforms in Electromagnetic Formulation

• Eom, Hyo Joon
• Journal of electromagnetic engineering and science
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• v.14 no.3
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• pp.273-277
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• 2014
• In this research, integral transform technique for electromagnetic scattering formulation is reviewed. Electromagnetic boundary-value problems are presented to demonstrate how the integral transforms are utilized in electromagnetic propagation, antennas, and electromagnetic interference/compatibility. Various canonical structures of slotted conductors are used for illustration; moreover, Fourier transform, Hankel transform, Mellin transform, Kontorovich-Lebedev transform, and Weber transform are presented. Starting from each integral transform definition, the general procedures for solving Helmholtz's equation or Laplace's equation for the potentials in the unbounded region are reviewed. The boundary conditions of field continuity are incorporated into particular formulations. Salient features of each integral transform technique are discussed.

### Elastic Analysis of a Half-Plane Containing an Inclusion and a Void Using Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한, 함유체와 공동을 포함한 반무한 고체에서의 탄성해석)

• Lee, Jung-Ki;Yoon, Koo-Young
• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.12
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• pp.1072-1087
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• 2008
• A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

### Calculation of Stress Intensity Factors Using the Mixed Volume and Boundary Integral Equation Method (혼합 체적-경계 적분방정식법을 이용한 응력확대계수 계산)

• Lee, Jung-Ki;Lee, Hyeong-Min
• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1120-1131
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• 2003
• A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

### MULTIPLE POSITIVE SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

• Liu, Xiping;Jin, Jingfu;Jia, Mei
• 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.

### Development of the Direct Boundary Element Method for Thin Bodies with General bBundary Conditions (일반 경계 조건을 가진 얇은 물체에 대한 직접 경계 요소법의 개발)

• 이강덕;이덕주
• Journal of KSNVE
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• v.7 no.6
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• pp.975-984
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• 1997
• A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.