• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.91-98
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• 2005

The straight rectangular fin is analyzed using the one-dimensional analytic method and the finite difference method. For the finite difference method, the numbers of nodes vary from 20 to 100. The relative errors of heat loss and temperature between the analytic method and the finite difference method are represented as a function of Biot Number and dimensionless fin length. One of the results shows that the relative error between the analytic method and the finite difference method decreases as the numbers of nodes for finite difference method increase.

• 한국자동차공학회논문집
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• 제7권5호
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• pp.141-153
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• 1999

A finite element procedure for the analysis of rubber-like hyperelastic material is developed. The volumetric incompressiblity conditions of the rubber deformation is included in the formulation by using penalty method. In this paper, the behavior of the rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The principle of virtual work is used to derive nonlinear finite element equation for the large displacement problem and presented in total-Lagrangian description. The finite element procedure using analytic differentiation resulted in very close solution to the result of the well known commercial packages NISAII AND ABAQUS. Numerical tests show that the results from the numerical differentiation method coincide very well with those from the analytic method and the well known commercial packages in static analysis. The convergency of rubber usingν iteration method is also discussed.

• 전기학회논문지P
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• 제66권1호
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• pp.1-6
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• 2017

Recently, many motor analysis methods have been developed and studied. Among these methods, the finite element method(FEM) and the analytic method are most popular in field engineers because of the accuracy of FEM and the convenience and rapid analysis time of the analytic method. Contrary, the finite element method has a weakness in calculation time and it is not easy to obtain the instantaneous characteristics value of motor with the analytic method. In this paper, the authors proposes a novel method for calculating the instantaneous characteristics of motors with the magnetic slot equivalent circuit.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• 제3B권4호
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• pp.159-164
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• 2003

In this paper, a three-dimensional finite element method and construction of equivalent-circuit for a linear ultrasonic motor are presented. The validity of three-dimensional finite element routine in this paper is experimentally confirmed by analyzing impedance of a piezoelectric transducer. Using this confirmed finite element routine, impedance and vibration mode of a linear ultrasonic motor are calculated. Elliptical motion of contact point between vibrator and rail of the linear ultrasonic motor is shown for determination of contact points. By using the finite element method and analytic equations, characteristics of the linear ultrasonic motor, such as thrust force, speed, losses, powers and efficiency, are calculated. The results are confirmed by experiment. Finally, equivalent circuit parameters of the linear ultrasonic motor are obtained using the three-dimensional finite element method and analytic equations.

• Journal of Advanced Marine Engineering and Technology
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• 제15권4호
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• 대한토목학회논문집
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• 제13권3호
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• pp.129-138
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• 1993

본 연구는 Navier-Stokes 식의 모형방정식으로 이류 및 확산거동을 갖는 선형화된 Burgers 방정식과 비선형 형태의 Burgers 방정식을 선택하여, 이에 대한 유한차분법과 유한해석법의 수치해를 해석해와 비교하여 봄으로써, 유한해석법의 응용성에 대해 고찰한 것이다. 본 연구를 통하여 얻어진 성과를 요약하면 다음과 같다. Burgers 방정식 및 선형화된 Burgers 방정식의 정상상태의 해석해를 사용하여 두 수치기법에 따른 수치해를 비교해 본 결과, 해석해와의 근사정도를 동일 기준 하에서 살펴볼 때, 유한해석법이 유한차분법보다 우수한 것으로 나타났다. Burgers 방정식의 비정상상태의 해석해에 대한 정확성 또한 유한해석법이 보다 잘 일치하는 것으로 나타났다. 특히 유한해석법은 유한차분법의 사용시 격자 크기의 선택에 따라 해의 수렴과정에서 발생할 수 있는 위상오차에 기인한 진동현상이 전혀 발생하지 않는다는 것을 확인할 수 있었으며, 따라서 유한해석법은 수치기법상 위상오차로부터 자유로운 안정된 해석기법이라고 판단된다.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.131-136
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• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Journal of the Optical Society of Korea
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• 제18권2호
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• pp.134-145
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• 2014

The number of lens groups in modern zoom camera systems is increased above that of conventional systems in order to improve the speed of the auto focus with the high quality image. As a result, it is difficult to calculate zoom loci using the conventional analytic method, and even the recent one-step advanced numerical calculation method is not optimal because of the time-consuming problem generated by the iteration method. In this paper, in order to solve this problem, we suggest a new unified analytic method for zoom lens loci with finite object distance including infinite object distance. This method is induced by systematically analyzing various distances between the object and other groups including the first lens group, for various situations corresponding to zooming equations of the finite lens systems after using a spline interpolation for each lens group. And we confirm the justification of the new method by using various zoom lens examples. By using this method, we can easily and quickly obtain the zoom lens loci not only without any calculation process of iteration but also without any limit on the group number and the object distance in every zoom lens system.

• 설비공학논문집
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• 제16권8호
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• pp.683-690
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• 2004

A modified rectangular fin is analyzed by two-dimensional analytic method and finite difference method. Relative error of heat loss from the modified rectangular fin between analytic method and finite difference method is presented. Comparisons of fin effectiveness and heat loss between a modified rectangular fin and a plane rectangular fin are made as a function of the non-dimensional fin length and wing height for different positions of wings by using analytic method. The ratio of the incremental rate of heat loss to that of the area of a modified rectangular fin is shown as a function of the wing height. One of the results shows that performance of a modified fin is more improved as the wing approaches the fin root.

• 대한기계학회논문집
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• 제7권4호
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• pp.417-424
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• 1983

This paper presents two methods of obtaining approximate analytic solutions for the temperature distributions and heat flow to two-dimensional transient heat conduction problems in a finite strip with constant thermal properties using the Heat Balance Integral. The methods introduced in this study are as follows; one using the Heat Balance Integral only, and the other successively using the Heat Balance Integral and an exact analytic method. Both methods are applicable to a large number of the two-dimensional unsteady conduction problems in finite regions such as extended surfaces with uniform thickness, but in this paper only solutions for the unsteady problems in a finite strip with boundary condition at the base expressed in terms of step function are provided as an illustration. Results obtained by both methods are compared with those by the exact two-dimensional transient analysis. It is found that both approximate methods generate small time solutions, which can not be obtained easily by any exact analytic method for small values of Fourier numbers. In the case of applying the successive use of the Heat Balance Integral and Laplace transforms, the analysis shows good agreement with the exact solutions for any Fourier number in the range of Biot numbers less than 0.5.