• Journal of Mechanical Science and Technology
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• 제14권2호
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• 한국전산구조공학회논문집
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• 제21권4호
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• pp.375-382
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• 2008

본 연구는 2차원 및 3차원 동적 탄소성 응력 해석을 위한 특수 적분해 경계요소법의 공식 개발을 제시한다 정적 탄성에 대한 기본식이 일반해를 구하는데 이용되었으며, 전체형상함수 개념을 이용하여, 변위율과 traction rate의 특수 적분해를 구함으로써 지배 방정식의 가속도 부분을 근사화시켰다. 시간 적분을 위하여 Houbolt 시적분 방법을 이용하였으며, Newton-Raphson 알고리즘을 이용하여 수치 연산을 행하였다. 제시된 공식에 따른 예제 해석을 통하여 그 방법의 유효성과 정확성을 설명하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.1032-1037
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• 2003

Although the holes on the shell case are very important fer the acoustic performance, it is difficult to solve the problem because the case includes thin bodies. Hence, in the past, only the method of trial and error, which depends on the engineer's intuition and experience, was available fur the design of holes. Many researchers have tried to solve the thin-body acoustic problems, since the conventional boundary element method (BEM ) using the Helmholtz integral equation fails to yield a reliable solution fer the numerical modelling of radiation anti scattering of sound from thin bodies. In the area of the analysis of thin-body acoustic problem, three approaches are generally used; the multi-domain BEM, the indirect variational BEM, and the normal derivative integral equation And there has been just a f9w study reported on the design optimization for the acoustic radiation problems by using only the conventional BEM. For the thin-body acoustics, however, no further study in the optimization fields has been reported. In this research, the normal derivative integral equation is adopted as an analysis formulation in the thin-body acoustics, and then used fur the optimization. The analytical approaches for the design of holes are proposed by using a topology optimization technique and a genetic algorithm. The proposed approaches are implemented and validated using numerical examples.

• ETRI Journal
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• 제29권1호
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• pp.8-17
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• 2007

In this paper, we present a time domain combined field integral equation formulation (TD-CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.

• 대한조선학회지
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• 제24권4호
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• pp.9-18
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• 1987

The hydrodynamic radiation forces acting on a ship travelling in waves have been conventionally treated by strip theories or by direct three dimensional approaches, most of which have been formulated in frequency domain. If the forward speed of a ship varies with time, or if its path is not a straight line, conventional frequency domain analysis can no more be used, and for these cases time domain analysis may be used. In this paper, formulations are made in time domain with applications to some problems the results of which are known in frequency domain. And the results of both domains are compared to show the characteristics and validity of time domain solutions. The radiation forces acting on a three dimensional body within the framework of a linear theory. If the linearity of entire system is assumed, radiation forces due to arbitrary ship motions can be expressed by the convolution integral of the arbitrary motion velocity and the so called impulse response function. Numerical calculations are done for some bodies of simple shapes and Series-60[$C_B=0.7$] ship model. For all cases, integral equation techniques with transient Green's function are used, and velocity or acceleration potentials are obtained as the solution of the integral equations. In liner systems, time domain solutions are related with frequency domain solutions by Fourier transform. Therefore time domain solutions are Fourier transformed by suitable relations and the results are compared with various frequency domain solutions, which show good agreements.

• Structural Engineering and Mechanics
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• 제63권5호
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• pp.647-657
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• 2017

To achieve this goal, two four-span concrete box-girder bridges with typical configurations of California highway bridges are selected as representative bridges: an integral abutment bridge and a seat-type abutment bridge. A detailed numerical model of the representative bridges is created in OpenSees to perform dynamic analyses. To examine the effect of earthquake incidence angle on the fragility of skewed bridges, the representative bridge models are modified with different skew angles. Dynamic analyses for all bridge models are performed for all earthquake incidence angles examined. Simulated results are used to develop demand models and component and system fragility curves for the skewed bridges. The fragility characteristics are compared with regard to earthquake incidence angle. The results suggest that the earthquake incidence angle more significantly affects the seismic demand and fragilities of the integral abutment bridge than the skewed abutment bridge. Finally, a recommendation to account for the randomness due to the ground motion directionality in the fragility assessment is made in the absence of the predetermined earthquake incidence angle.

• 한국전자파학회논문지
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• 제12권7호
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• pp.1122-1130
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• 2001

본 논문에서는 방사 적분방정식의 해를 구하기 위하여 파수영역 웨이블릿 변환개념에 기반을 둔 윈도우 그린 함수를 사용하여 파수영역에서 고속으로 산란필드를 계산하는 방법을 제안하였다. 그린함수에 적용된 파수영역 웨이블릿 변환은 공간영역에서 동일한 Q를 갖는 윈도우를 사용하여 필터링함으로써 등가적으로 구현하였다. 고유함수를 이용하여 관찰점을 중심으로 전개된 그린함수를 푸리에 변환한 후 파수영역에서 방사 적분을 계산함으로써 계산효율을 얻을 수 있음을 확인하였다. 관찰영역에서만 정확한 값을 갖는 고유함수로 전개된 그린함수는 그린함수에 윈도우 함수를 씌운 형태로 방사 적분방정식의 파수영역 표현에 적용하면 기존의 고속멀티폴 법과 동일한 산란필드 공식을 얻을 수 있다.

• Structural Engineering and Mechanics
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• 제85권5호
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• pp.621-633
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• 2023

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.73-91
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• 2005

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.