• 제목/요약/키워드: Exact solution

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일정변단면(一定變斷面) 장주(長柱)의 임계좌굴하중(臨界挫屈荷重)의 결정(決定) (The Determination of Critical Buckling Load Applied to Tapered Columns)

  • 유철수;손성원
    • 대한토목학회논문집
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    • 제4권1호
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    • pp.93-101
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    • 1984
  • 본(本) 논문(論文)에서는 일정변단면장주(一定變斷面長柱)의 탄성임좌굴하중(彈性臨挫屈荷重)을 구하는 각산식(咯算式)을 제시(提示)하였다. 특히, 고가도로설계시(高架道路設計時) 자주 나타나는 일단고정(一端固定) 타단자유(他端自由)인 중실원형(中實圓形) 및 구형단면(矩形斷面)에 한(限)하였다. 처짐곡선 미분방정식(微分方程式)의 정밀해(精密解)는 Bessel 함수(凾數)로 나타나는데, Bisection method를 이용하여 Computer로 수치해석(數値解析)하였다. 또 자중(自重)고려시 F.E.M에 의한 해석(解析)은 고유치(固有値) 문제(問題)가 되므로 Jacobi method를 이용하여 수치해석(數値解析)하였고, 균일단면장주(均一斷面長柱)의 정밀해(精密解)와 비교(比較)하여 F.E.M에 의한 근사해(近似解)의 신뢰도(信賴度)를 높였다. 그 결과(結果) 일정변단면장주(一定變斷面長柱)의 임계좌굴하중(臨界挫屈荷重)은 형상계수(形狀係數)와 단면변화율(斷面變化率)에 대해 균일단면장주(均一斷面長柱)의 비례식(比例式)으로 나타낼 수 있었다.

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분포하중(分布荷重)을 받는 주변고정(周邊固定) 구형판(矩形板)의 탄성해석(彈性解析) (Analysis of Rectangular Plates under Distributed Loads of Various Intensity with All Edges Built In)

  • 장석윤
    • 대한조선학회지
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    • 제13권4호
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    • pp.19-24
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    • 1976
  • Some method of analysis of rectangular plates under distributed load of various intensity with all edges built in are presented in. Analysis of many structures such as bottom, side shell, and deck plate of ship hull, and flat slab, deck systems of bridges is a problem of plate with continuous supports or clamped edges. When the four edges of rectangular plate is simply supported, the double fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and boundary condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a plate under distributed loads of various intensity with all edges built in is carried out by applying Navier solution and Levy's method as well as "Principle of Superposition" In discussing this problem we start with the solution of the problem for a simply supported rectangular plate and superpose on the deflection of such a plate the deflections of the plate by slopes distributed along the all edges. These slopes we adjust in such a manner as to satisfy the condition of no rotation at the boundary of the clamped plate. This method can be applied for the cases of plates under irregularly distributed loads of various intensity with two opposite edges simply supported and the other two edges clamped and all edges simply supported and this method can also be used to solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

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농축물의 Benzo($a$)pyrene 함량 측정을 위한 전처리 방법의 개선 (Improving Method of Pre-treatment for Detection Benzo($a$)pyrene Contents in Concentrates)

  • 구본순
    • 한국식품영양학회지
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    • 제24권4호
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    • pp.797-802
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    • 2011
  • I assessed the B($a$)P content from the Ginseng extract, Red ginseng extract, and Ssangwha extract which have high viscosities. It wasn't easy to extract oil from these samples, consequently measuring of B($a$)P was difficult. In order to know the exact detecting contents, I injected standard material of B($a$)P to the above extractions and pre-treated for measurement but it was also difficult to measure of contents exactly. To improve of detecting method, I removed mucinous materials using a 85% phosphoric acid solution or 10% citric acid solution and then processed continuously with $60^{\circ}C$ hot water. The analysis revealed that extracting the samples contained B($a$)P determined the rate of each 70%, 55%, 67% could increase. As a result the detecting method of B($a$)P contents could be improved.

A FINITE ELEMENT SOLUTION FOR THE CONSERVATION FORM OF BBM-BURGERS' EQUATION

  • Ning, Yang;Sun, Mingzhe;Piao, Guangri
    • East Asian mathematical journal
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    • 제33권5호
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    • pp.495-509
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    • 2017
  • With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

KINK WAVE SOLUTIONS TO KDV-BURGERS EQUATION WITH FORCING TERM

  • Chukkol, Yusuf Buba;Muminov, Mukhiddin
    • 대한수학회논문집
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    • 제35권2호
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    • pp.685-695
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    • 2020
  • In this paper, we used modified tanh-coth method, combined with Riccati equation and secant hyperbolic ansatz to construct abundantly many real and complex exact travelling wave solutions to KdV-Burgers (KdVB) equation with forcing term. The real part is the sum of the shock wave solution of a Burgers equation and the solitary wave solution of a KdV equation with forcing term, while the imaginary part is the product of a shock wave solution of Burgers with a solitary wave travelling solution of KdV equation. The method gives more solutions than the previous methods.

원료불출기의 역기구학 : 여유자유도와 구속조건을 이용한 닫힌 형태의 해 (Inverse Kinematics of a Serial Manipulator : Redundancy and a Closed-rom Solution by Exploting Geomertiric Constraints)

  • 홍금식;김영민;최진태;신기태;염영일
    • 한국정밀공학회:학술대회논문집
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    • 한국정밀공학회 1996년도 춘계학술대회 논문집
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    • pp.661-665
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    • 1996
  • An inverse kinemetics problem of a reclaimer which digs and transports ironstones or coals in the raw yard is investigated. Because of the special features of the reclaimer of which scooping buckets are attached around the rotating drum at the end of boom, kinematic redundancy occurs in determining the joint varialbes For a given reclaiming point in space the forward kinematics yields 3 equations, however the number of involved variables in the equations are four. A plane equation approximating the surface near a reclaiming point is obtained by considering 8 adjacent points surrounding the reclaiming point. One extra equation to overcome redunduncyis further obtained from the condition that the normal vector at a reclaiming point is perpendicular to the plane. An approximate solution for a simplified problem is first discussed, Numerical solution for the oritinal nonlinear porblem with a constraint equation is also investigated. Finally a closed form solution which is not exact but sufficiently close enough is proposed by exploiting geometric constraint.

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속도차를 갖는 두 회전판에 의해 유도되는 원통 내부 유동 (Flows in a confined cylindrical container with differential rotating top and bottom disks)

  • 박준상
    • 한국전산유체공학회:학술대회논문집
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    • 한국전산유체공학회 2008년도 춘계학술대회논문집
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    • pp.487-490
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    • 2008
  • A theoretical study is made of the flow in a confined cylindrical container with differential rotating top and bottom disks. Two kinds of theoretical solution for the azimuthal velocity were obtained: one is an exact solution of Bessel function type and the other is an approximate solution of exponential function type which comes from WKB approximation. Both theoretical solutions are shown to be self consistent with each other as well as a good agreement with previous studies. Moreover, in a range of relatively low Reynolds number, the obtained solution of Bessel function type shows better result than previous solutions.

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