• Journal of the Korean Society for Precision Engineering
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• v.20 no.8
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• pp.175-184
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• 2003

A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.

• Structural Engineering and Mechanics
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• v.41 no.5
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• pp.591-604
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• 2012

This paper provides an iteration approach for the solution of multiple notch problem, which is based on the complex variable boundary integral equation (CVBIE). The contours of notches are applied by some loadings. The source points are assumed on the boundary of individual notch and the displacements along the boundaries become unknowns to be investigated. After discretization of the BIE, many influence matrices are obtained. One does not need to assemble many influence matrices into a larger matrix. This will considerably reduce the work in the program. The displacements along the many boundaries can be obtained from an iteration. There is no limitation for the configuration of notches. Several numerical examples are provided to prove the efficiency of the suggested approach.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.915-918
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• 2005

Acoustic holography uses Kirchhoff·Helmholtz integral equation and Green's function which satisfies Dirichlet boundary condition Applications of acoustic holography have been taken to the sound field neglecting the effect of flow. The uniform flow, however, changes sound field and the governing equation, Green's function and so on. Thus the conventional method of acoustic holography should be changed. In this research, one possibility to apply acoustic holography to the sound field with uniform flow is introduced through checking for the plane wave in a duct. Change of Green's function due to uniform flow and one method to derive modified form of Kirchhoff·Heimholtz integral is suggested for 1-dimensional sound field. Derivation results show that using Green's function satisfying Dirichlet boundary condition, we can predict sound pressure in a duct using boundary value.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1001-1004
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• 1987

In this study mathematical properties of variational solution and solution of the boundary integral equation of the linear elasticity problem are studied. It is first reviewed that a variational solution for the three-dimensional linear elasticity problem exists in the Sobolev space [ $H^{1}$(.OMEGA.)]$^{3}$ and, then, it is shown that a unique solution of the boundary integral equation is identical to the variational solution in [ $H^{1}$(.OMEGA.)]$^{3}$. To represent the boundary integral equation, the Green's formula in the Sobolev space is utilized on the solution domain excluding a ball, with small radius .rho., centered at the point where the point load is applied. By letting .rho. tend to zero, it is shown that, for the linear elasticity problem, boundary integral equation is valid for the variational solution. From this fact, one can obtain a numerical approximatiion of the variational solution by the boundary element method even when the classical solution does not exist.exist.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.9
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• pp.2138-2144
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• 1993

An integral equation representation of cracks was presented which differs from well-known "dislocation layer" representation. In this new representation, the equations are written in terms of the displacement discontinuity across the crack surfaces rather than derivatives of the displacement-discontinuity. It was shown in that the new technique is well-suited to the treatment of kinked cracks. In the present paper, this integral equation representation is coupled to the direct boundary-element method for the treatment of finite bodies containing kinked cracks. The method is demonstrated for two-dimensional finite domains but extension to three-dimensional problems would appear to be possible. The resulting approach is shown to be simple, yet very accurate. accurate.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.111-129
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• 1998

An integral equation representation of cracks was presented, which differs from well-known "dislocation layer" representation. In this new representation, an integral equation representation of cracks was developed and coupled to the direct boundary-element method for treatment of cracks in plane finite bodies. The method was developed for in-plane(modes I and II) loadings only. In this paper, the method is formulated and applied to mode III problems involving smooth or kinked cracks in finite region. The results are compared to exact solutions where available and the method is shown to be very accurate despite of its simplicity.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1186-1193
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• 1996

The analytic solution of the stress field at creep crack in the presence of grain boundary caviation is to be obtained by solving the governing equation which was derived through the previous paper. The complex integral technique is used to slove the singular integral equation. under the help of the information about stress behaviors at the ends of integral region know by numerical solution. The resultant stress disstribution obtained shows the relaxed crack-tip singularity of $r^{1/2+\theta}$ due to the intervention of cavitation effect, otherwise, it should assumed to be $r^{1/2}$ singularity of linear elastic fracture mechanics with no cavitation.

• Proceedings of the KIEE Conference
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• 1999.11b
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• pp.101-103
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• 1999

This paper presents an analysis of 2-dimensional(2-D) multi-regions problem using boundary integral equation method(BIEM). When compared with finite element method(FEM), there are only a few unknown variables in BIEM because it implements numerical analysis only for the surface or boundary of a model. As a result, a lot of computational memory and time can be saved. Procedure to analyze 2-D multi-regions problem using potentials and its derivatives in a boundary as unknown variables, first, numerical analysis is performed for each of subregions. And then interface continuity condition is applied to the interface between them and Gauss Quadrature Formula are adopted to solve singular integral in a boundary in this paper.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.2 no.1
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• pp.11-17
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• 1990

Dirichlet boundary value problems originated from unsteady deep water wave propagation are transformed to Boundary Intergral Equation Methods by use of a free surface Green's function and the integral equations are discretized by a cubic spline element method. In order to enhance the stability of the numerical model based on the derived Fredholm integral equation of 1 st kind, the method by Hsiao and MacCamy (1973) is employed. The numerical model is tested against exact solutions for two cases and the model shows very good accuracy.

• Computational Structural Engineering
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• v.9 no.4
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• pp.127-134
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• 1996

This paper is about a progressive fracture analysis of concrete by boundary element method. From both displacement boundary integral equation and traction boundary integral equation of solids with cracks, a boundary integral equation for crack problem is derived. For the analysis of progressive fracture of concrete, fracture process zone is modelled based on Dugdale-Barenblatt model with linear tension-softening curve. By using the boundary element modeling, the progressive fractures of concrete beam and compact-tension specimens with various loading conditions are analyzed and compared with experiments. The analysis results show that the technique in this paper can predict the maximum strength and the nonlinear behavior of concrete including post-peak behavior.