• 제목/요약/키워드: Exact solution

검색결과 871건 처리시간 0.024초

수평평판의 층류 막응축에서 압력의 영향 (The Effect of Pressure on Laminar Film Condensation along a Horizontal Plate)

  • 이억수;이승홍
    • 대한기계학회논문집B
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    • 제32권12호
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    • pp.945-953
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    • 2008
  • Laminar film condensation of saturated vapor in forced flow over a flat plate is analysed. The problem is formulated as exact boundary-layer solution and integral approximate solution. From numerical solutions of the governing equations, it is found that the energy transfer by convection and the effect of inertia term in the momentum equation in negligibly small for low pressure but quite important for high pressure. The condensate rate, liquid-vapor interfacial shear stress and local heat transfer are strongly dependent on the reduced pressure $P_r$ and the modified Jacob number Ja/Pr.

均一두께의 環狀흰에서 週期的 過渡應答 特性에 관한 硏究 (A Study on the Periodic Transient Response Characteristics in Annular Fin with Uniform Thickness)

  • 김광수
    • 대한기계학회논문집
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    • 제12권2호
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    • pp.338-348
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    • 1988
  • 본 연구는 환상휜에서 휜 바탕의 온도가 조기적으로 변화할 때, 휜 바탕의 온도가 주기적으로 변화할 때, 휜 주변 뿐만 아니라 휜 선단에서의 대류현상을 고려한 과도 전열에 대한 해석이다.

유한요소-전달강성계수법에 의한 2차원 곡선 보 구조물의 정적해석 (Static Analysis of Two Dimensional Curbed Beam Structure by Finite Element-Transfer Stiffness Coefficent Method)

  • 최명수
    • 동력기계공학회지
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    • 제21권6호
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    • pp.40-45
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    • 2017
  • The objective of this study is the finite element-transfer stiffness coefficient method, which is the combination of the modeling technique of finite element method and the transfer technique of transfer stiffness coefficient method, is applied in the static analyses of two dimensional curved beam structures. To confirm the effectiveness of the applied method, two computational models are selected and analyzed by using finite element method, finite element-transfer stiffness coefficient method and exact solution. The computational results of the static analyses for two computational models using finite element-transfer stiffness coefficient method are equal to those using finite element method. When the element partition number of curved beam structure is increased, the computational results of the static analyses using both methods approach the exact solution. We confirmed that the finite element-transfer stiffness coefficient method is superior to finite element method when the number of the curved beam elements is increased from the viewpoints of the computational speed and the utility of computer memory.

유화중합의 모델연구 1. Pseudo-homopolymerization (Study on Model of Emulsion Polymeration 1. Pseudo-homopolymerization)

  • 박상보;서차수
    • 공업화학
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    • 제9권2호
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    • pp.294-299
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    • 1998
  • 입자당 한 개 이상의 성장라디칼이 있는 일반계에서 근사적인 psedo-homopolymerization (PHP)방법의 신뢰성을 간접적으로 증명하기 위하여, 벌크중합의 Mayo-Lewis식이 Interval II 동안 유화중합의 순간공중합조성식으로부터 확률적으로 유도됨을 보였다. Ballard등에 의하여 제안된 유화공중합의 확장된 Smith-Ewart식으로부터 0-1계(입자당 1개 이하의 성장라디칼이 있는 계)에 대하여 완전해를 얻었다. 이 해를 사용하여 입자당 평균라디칼수와 순간공중합조성이 몇 분 이내에 정상상태에 도달함을 예측할 수 있었다. 따라서 0-1계에 국한하여 PHP근사방법의 신뢰성을 직접 증명할 수 있었다. 모델계산의 목적으로 Styrene-butadiene(St-Bu)과 Styrene-methyl methacrylate(St-MMA)계를 예로 들었다.

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FDM에 의한 응고해석시 계산시간 단축을 위한 음적해법의 적용과 잠열처리방법 (Reduction of Computing Time through FDM using Implicit Method and Latent Heat Treatment in Solidification Analysis)

  • 김태규;최정길;홍준표;이진형
    • 한국주조공학회지
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    • 제13권4호
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    • pp.323-332
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    • 1993
  • An implicit finite difference formulation with three methods of latent heat treatment, such as equivalent specific heat method, temperature recovery method and enthalpy method, was applied to solidification analysis. The Neumann problem was solved to compare the numerical results with the exact solution. The implicit solutions with the equivalent specific heat method and the temperature recovery method were comparatively consistent with the Neumann exact solution for smaller time steps, but its error increased with increasing time step, especially in predicting the solidification beginning time. Although the computing time to solve energy equation using temperature recovery method was shorter than using enthalpy method, the method of releasing latent heat is not realistic and causes error. The implicit formulation of phase change problem requires enthalpy method to treat the release of latent heat reasonably. We have modified the enthalpy formulation in such a way that the enthalpy gradient term is not needed, and as a result of this modification, the computation stability and the computing time were improved.

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미분구적법(DQM)을 이용한 곡선보의 내평면 비신장 및 신장 진동해석 (In-Plane Inextensional and Extensional Vibration Analysis of Curved Beams Using DQM)

  • 강기준
    • 한국산학기술학회논문지
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    • 제16권11호
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    • pp.8064-8073
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    • 2015
  • 편미분방정식 해를 위한 효율적인 방법 중의 하나는 미분구적법이다. 이방법은 복잡한 구조 및 하중에 따른 컴퓨터 용량의 과도한 사용뿐만 아니라, 컴퓨터 프로그래밍의 복합알고리즘 해석상의 어려움 피하기 위해 많은 분야에 적용되어왔다. 아크축의 비신장 및 신장을 고려한 곡선보의 내평면 진동을, 미분구적법 (DQM)을 이용하여 해석하였다. 다양한 경계조건과 열림각에 따른 진동수을 계산하였다. DQM의 해석결과는, 비교 가능한 정확한 수학적 해법을 다른 수치해석결과와 비교하였다. DQM은 적은 격자점을 사용하고도 정확한 해석을 보여주었고, 다양한 변화에 따른 새로운 결과를 제시하였다.

모든 3차 수차를 제거하여 얻은 극자외선 Lithography용 4-반사경 Holosymmetric System(배율=1) (Holosymmetric 4-Mirror Optical System(Unit Maginification) for Deep Ultraviolet Lithography Obtained from the Exact Solution of All Zero Third Order Aberrations)

  • 조영민
    • 한국광학회지
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    • 제4권3호
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    • pp.252-259
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    • 1993
  • 극자외선 과장을 사용하는 micro-lithography를 위해 등배율을 갖는 4-반사경 holosymmetric system을 설계하였다. Holosymmetric system에서는 모든 차수의 코마와 왜곡수차가 영이 된다. 이 원리를 4-구명경계에 적용하여 등배율을 갖고 5개의 3차 수차가 모두 제거된 4-구면 반사경 holosymmetric system에 대해 유일한 해를 완전히 해석적인 표현으로 구하였다. 이 4-구면경계에 남아있는 고차 수차들을 보정하기 위해 holosymmetric 성질을 유지하면서 비구면을 채용하였고 그결과 개구수 0.33과 image field diameter 7.6mm 이내에서 극자외선 파장 $0.248{\mu}m$(KrF 엑시머 레이저 빔)에 대해 거의 회절한계의 수차성능을 갖는 비구면 4-반사경 holosymmetric system를 얻었다.

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Exact solution for dynamic response of size dependent torsional vibration of CNT subjected to linear and harmonic loadings

  • Hosseini, Seyyed A.H.;Khosravi, Farshad
    • Advances in nano research
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    • 제8권1호
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    • pp.25-36
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    • 2020
  • Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

Improved analytical solution for slip and interfacial stress in composite steel-concrete beam bonded with an adhesive

  • Tayeb, Bensatallah;Daouadji, Tahar Hassaine
    • Advances in materials Research
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    • 제9권2호
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    • pp.133-153
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    • 2020
  • In this paper, an improved theoretical interfacial stress and slip analysis is presented for simply supported composite steel-concrete beam bonded with an adhesive. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of elements has been noted in the results. It is observed that large shear is concentrated and slip at the edges of the composite steel-concrete. Comparing with some experimental results from references, analytical advantage of this improvement is possible to determine the normal and shear stress to estimate exact prediction of normal and shear stress interfacial along span between concrete and steel beam. The exact prediction of these stresses will be very important to make an accurate analysis of the mode of fracture. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite steel-concrete beam. This research is helpful for the understanding on mechanical behavior of the connection and design of such structures.

An exact solution for mechanical behavior of BFRP Nano-thin films embedded in NEMS

  • Altabey, Wael A.
    • Advances in nano research
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    • 제5권4호
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    • pp.337-357
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    • 2017
  • Knowledge of thin films mechanical properties is strongly associated to the reliability and the performances of Nano Electro Mechanical Systems (NEMS). In the literature, there are several methods for micro materials characterization. Bulge test is an established nondestructive technique for studying the mechanical properties of thin films. This study improve the performances of NEMS by investigating the mechanical behavior of Nano rectangular thin film (NRTF) made of new material embedded in Nano Electro Mechanical Systems (NEMS) by developing the bulge test technique. The NRTF built from adhesively-bonded layers of basalt fiber reinforced polymer (BFRP) laminate composite materials in Nano size at room temperature and were used for plane-strain bulging. The NRTF is first pre-stressed to ensure that is no initial deflection before applied the loads on NRTF and then clamped between two plates. A differential pressure is applying to a deformation of the laminated composite NRTF. This makes the plane-strain bulge test idea for studying the mechanical behavior of laminated composite NRTF in both the elastic and plastic regimes. An exact solution of governing equations for symmetric cross-ply BFRP laminated composite NRTF was established with taking in-to account the effect of the residual strength from pre-stressed loading. The stress-strain relationship of the BFRP laminated composite NRTF was determined by hydraulic bulging test. The NRTF thickness gradation in different points of hemisphere formed in bulge test was analysed.