• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 춘계학술대회 논문집
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• pp.194-199
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• 2013

Using moving support finite elements, seismic analysis of statically-determinate beams subjected to support motions is performed to show its accuracy and its ease of use. Examples of cantilever and simply-supported beam subjected to support motions are illustrated and the numerical results are compared with the analytical solutions. The examples show the elements facilitate modeling beams with the conventional 2-noded, Hermitian, Euler-Bernoulli beam element. The comparisons of the results with analytical solutions show good agreements with high accuracy.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.220-226
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• 2002

A general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system. Particularly, are proposed the analytical solutions of major and minor axis radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system, having a bull-pinion speed increasing gear. The bumps of unbalance responses have been observed at the first torsional natural frequency due to the coupling of lateral and torsional dynamics by the gear meshing. Further, the proposed analytical solutions have been validated with results obtained by a full numerical approach.

• 한국시뮬레이션학회논문지
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• 제11권3호
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• pp.13-22
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• 2002

This paper describes an automated evaluation of electrostatic field for micro motors whose sizes range 10 to 103um. Electric field modeling in micro motors has been generally restricted to in-plane two-dimensional finite element analysis (FEA). In this paper, the actual three-dimensional geometry of the micro motor is considered. An automatic FE mesh generation technique, which is based on the fuzzy knowledge processing and computational geometry techniques, is incorporated in the system, together with one of commercial FE analysis codes and one of commercial solid modelers. The system allows a geometry model of concern to be automatically converted to different FE models, depending on physical phenomena to be analyzed, electrostatic analysis and stress analysis and so on. The FE models are then exported to the FE analysis code, and then analyses are peformed. Then, analytical analysis and FE analysis about the torque generated by electrostatic micro motor are performed. The starting torque is proportional to $V^2$, the calculated starting torque from the two-dimensional analytical solutions are three times larger than those from the three-dimensional FE solutions.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1995년도 춘계학술발표회논문집(2)
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• pp.643-650
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• 1995

A numerical method for treating transient diffusion Involving change of phase is presented. In other methods of dealing with this class of problems, the mass flux balance at the moving phase boundary requires explicit treatment of two distinct phases. The technique, originating from the apparent heat capacity method in transient heat conduction with the phase change, avoids the difficulty by transferring the concentration discontinuity at the boundary to smoothed physical property variations near the moving front. This technique accomodates the nonlinearities which preclude use of analytical solutions. It was tested against known analytical solutions for simple cases and turned out to be quite accurate.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.1033-1049
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• 2014

The free vibration of functionally graded material (FGM) beams on an elastic foundation and spring supports is investigated. Young's modulus, mass density and width of the beam are assumed to vary in thickness and axial directions respectively following the exponential law. The spring supports are also taken into account at both ends of the beam. An analytical formulation is suggested to obtain eigen solutions of the FGM beams. Numerical analyses, based on finite element method by using a beam finite element developed in this study, are performed in order to show the legitimacy of the analytical solutions. Some results for the natural frequencies of the FGM beams are given considering the effect of various structural parameters. It is also shown that the spring supports show the greatest effect on the natural frequencies of FGM beams.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.497-512
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• 2021

In this paper, we study the analytical and approximate solutions for a fractional quadratic integral equation involving Katugampola fractional integral operator. The existence and uniqueness results obtained in the given arrangement are not only new but also yield some new particular results corresponding to special values of the parameters 𝜌 and ϑ. The main results are obtained by using Banach fixed point theorem, Picard Method, and Adomian decomposition method. An illustrative example is given to justify the main results.

• Structural Engineering and Mechanics
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• 제83권6호
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• pp.825-834
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• 2022

The effectiveness and accuracy of the strain-based approach applied for analysis of two kinds of heterogeneous hollow cylinders subjected to thermal and mechanical loads are examined in this study. One is a multilayer cylinder in which the material in each layer is assumed to be linearly elastic, homogeneous and isotropic. Another is a hollow cylinder made of functionally graded materials with arbitrary gradient. The steady state condition without heat generation is considered. A sector in-plane finite element in the polar coordinate system based on strain approach is used. This element has only three degrees of freedom at each corner node. Analytical solutions available in the literature are presented to illustrate the accuracy of the sector element used. The obtained results for displacements and stresses are shown to be in good agreement with the analytical solutions.

• 대한설비공학회지:설비저널
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• 제11권3호
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• pp.9-17
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• 1982

In this paper, temperature distributions in radial fin of hyperbolic profile for steady -state with no heat generation are obtained by one-dimensional analytical method, finite difference method and experiment respectively. Heat flow rate and fin efficiency from the fin model are obtained by analytical method. To compare the exact solutions obtained by theoretical analysis with the results obtained by finite difference method, cylindrical shape is selected. Particularly, equations of finite difference method for cylindrical shape with irregular boundary are rearranged and formulated. Consequently, temperature distributions in radial fin can certify that are similar to exact solutions. From theoretical analysis, the effects according to heat flow rate and fin efficiency are related to variation of parameters which are fin thickness ${\delta}_o$, fin base temperature $T_o$, thermal conductivity K with same basic dimensions and the fleets are studied and compared.

• 한국강구조학회 논문집
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• 제14권3호
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• pp.423-432
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• 2002

비대칭 박벽단면을 갖는 곡선보의 자유진동해석을 수행할 수 있는 엄밀해 및 유한요소 이론을 제시한다. 단순지지된 일축대칭 박벽단면을 갖는 곡선보의 면내 자유진동 모드에 대응하는 엄밀해를 산정하였으며, 곡섬보를 유한요소로 분할하여 요소의 변위장을 요소의 변위벡터의 대하여 축방향 신장조건에서는 3차 그리고 비신장조건에서는 5차의 Hermitian 다항식으로 나타내고, 이를 운동방정식에 대입함으로써 탄성강성행렬과 질량행렬을 유도한다. 또한 본 연구에서 얻어진 엄밀해와 곡선보요소를 이용한 유한요소 해석결과를 ABAQUS 쉘요소를 이용하여 얻어진 결과와 비교 검토함으로써 본 연구의 타당성을 입증한다. 특히 곡선보의 축방향 비신장조건과 두께-곡률효과가 동적거동에 미치는 영향을 조사한다.