• Journal of Magnetics
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• 제18권2호
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• 대한토목학회논문집
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• 제28권4B호
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• pp.413-419
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• 2008

본 연구에서는, 바닥의 수심이 반경의 임의 차수의 제곱 꼴로 표현되는 다양한 형태의 축 대칭 지형 위를 통과하는 장파의 해석해를 유도하였다. 첫 번째 지형은 둔덕 위에 원기둥 모양의 섬이 있는 경우이며 두 번째는 원형의 섬이 있는 경우이다. 해를 구하기 위하여 변수 분리법, Taylor 급수전개법 및 Frobenius 급수법을 사용하였다. 유도된 해석해를 기존에 유도된 해석해와 비교를 하여 그 정확성을 검증 하였다. 또한, 입사파의 주기, 둔덕의 반지름 및 차수를 가지는 경우에 대하여 분석하였다.

• 전기학회논문지P
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• 제55권3호
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• pp.141-145
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• 2006

The line current problem(2-dimensional space : point source) is not easy to analyze the magnetic field using the standard finite element method(FEM), such as overhead trolley line or transmission line. To supplement such a defect this paper is proposed the coupling scheme of analytical solution and FEM. In analysis of the magnetic field using the standard FEM. If the current region is a relatively small compared to the whole region. Therefore the current region must be finely divided using a large number of elements. And the large number of elements increase the number of unknown variables and the use of computer memories. In this paper, an analytical solution is suggested to supplement this weak points. When source is line current and the part of interest is far from line current, the analytical solution can be coupling with FEM at the boundary. Analytical solution can be described by the multiplication of two functions. One is power function of radius, the other is a trigonometric function of angle in the cylindrical coordinate system. There are integral constants of two types which can be established by fourier series expansion. Also fourier series is represented as the factor to apply the continuity of the magnetic vector potential and magnetic field intensity with tangential component at the boundary. To verify the proposed algorithm, we chose simplified model existing magnetic material in FE region. The results are compared with standard FE solution. And it is good agreed by increasing harmonic order.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.315-320
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• 2007

An analytical solution has been developed for the impact response of delaminated composite plates. The analysis is based on an expansion of loads, displacements, and rotations in a Fourier series which satisfies the end boundary conditions of simply-supported. The analytical formulation adopts the Laplace transformation technique, requiring a linearization of contact deformation. In this paper, the nonlinear contact stiffness is replaced by a linearized stiffness, to provide an estimate of the additional compliance due to contact area deformation effects. It has been shown that defects such as delaminations may be modeled as spring stiffness. The change in the impact characteristics as this spring stiffness has been investigated theoretically. Predicted impact responses using analytical solution are compared with the numerical ones from the 3-D non-linear finite element model. From the results, it is shown that analytical solution was found to be reliable for predicting the impact response.

• Journal of Advanced Research in Ocean Engineering
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• 제1권3호
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.583-593
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• 2022

Lienard's equations are important nonlinear differential equations with application in many areas of applied mathematics. In the present article, a new approach known as the modified fractional Taylor series method (MFTSM) is proposed to solve the nonlinear fractional Lienard equations with Caputo fractional derivatives, and the convergence of this method is established. Numerical examples are given to verify our theoretical results and to illustrate the accuracy and effectiveness of the method. The results obtained show the reliability and efficiency of the MFTSM, suggesting that it can be used to solve other types of nonlinear fractional differential equations that arise in modeling different physical problems.

• 한국강구조학회 논문집
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• 제22권3호
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• pp.241-251
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• 2010

본 논문에서는 등분포 하중을 받는 등방성 환형 섹터판의 지배방정식에 대한 새로운 해석적 해가 3차원 극좌표계에서 개발된다. 4차의 편미분방정식 형태를 가지는 지배방정식은 레비 타입 시리즈 해에 대한 가정과 그 후속적인 수학적 처리를 통해 4차의 상미분방정식으로 전환된다. 전환된 상미분방정식의 특성방정식에 대한 실수 영역 및 복소수 영역의 해를 해석적으로 구한 후 제차 및 비제차 방정식의 각 해의 조합으로 최종적인 지배방정식의 해가 완성된다. 개발된 해의 수렴성 및 정확성을 보여주기 위해 다양한 경계조건 및 내부 중심 각도를 가지는 판에 대한 예제 해석을 수행하였고 그 결과를 다른 해석적 연구결과와 비교하였다. 또한 개발된 해의 정확성을 확인하기 위하여 유한요소 프로그램인 ABAQUS를 이용한 탄성해석을 추가로 수행하여 그 결과를 비교하였다. 제안된 해로부터 결정된 환형 섹터판의 변위 및 모멘트 값은 여타의 해석적 및 수치적 접근방법으로 구한 값들과 비교해 본 결과 매우 높은 수준에서 일치하고 있음이 확인되었다.

• Coupled systems mechanics
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• 제1권2호
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• 한국방재학회 논문집
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• 제8권1호
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• pp.133-138
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• 2008

외해에서 내습하는 파랑 자료를 분석하는 일은 연안에서 발생하는 문제를 해결함에 있어 기본이 되기 때문에 매우 중요하다. 파랑을 해석하는 방법에는 크게 수치 모델을 이용하는 방법과 해석 해를 이용하는 방법이 있다. 수치 모델의 경우, 다양한 지형과 파랑 조건에 대해 적용할 수 있다는 장점이 있지만 수치 오차를 고려해야 하는 번거로움이 있다. 반면, 해석 해의 경우 수치 오차 없이 빠르고 정확하게 해를 구할 수 있다는 장점이 있지만 특정한 지형 및 파랑 조건에서만 성립한다는 단점이 있다. 본 연구에서는 수치적인 기법과 해석적인 접근을 혼합하여 수치 오차를 최소화시키면서 다양한 조건에 적용이 가능한 완경사 방정식의 해를 유도하였다. 유도된 해를 기존의 수치 해와 비교한 결과 매우 잘 일치한다는 알 수 있었다.