• Title/Summary/Keyword: Gauss 곡률

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동근공에 가까운 볼록폐곡면

  • 임지선;고성은
    • Communications of the Korean Mathematical Society
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    • v.15 no.2
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    • pp.325-330
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    • 2000
  • 3차원 Euclid 공간의 볼록폐곡면의 평균곡률과 Gauss 곡률의 비가 상수함수와 충분히 가까우면 그 곡면은 중심이 같고 반지름이 거의 같은 두 개의 둥근공 사이에 놓이게 됨을 보였다.

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$H^3$의 둥근공의 구별짓기

  • 이승원;고성은
    • Communications of the Korean Mathematical Society
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    • v.13 no.3
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    • pp.589-594
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    • 1998
  • 쌍곡공간$^3$에 들어있는 닫힌 곡면의 주곡률함수가 특별한 함수 관계를 만족시킨다면 그 곡면은 둥근공임을 보였다. 이 결과를 이용하여 Gauss-Kronecker 곡률이 상수인 닫힌 곡면은 둥근공 뿐이 없음도 보였다.

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Curvature Radius of Equivalent Lens Obtained by Recursive Numerical Solving of Gaussian Equations (재귀적 수치 계산법을 이용한 등가 렌즈의 곡률 계산)

  • Lee, Kyu Haeng
    • Korean Journal of Optics and Photonics
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    • v.33 no.6
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    • pp.275-286
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    • 2022
  • As a first step in the optical design process, we derive a recursive numerical calculation method that can give a solution to the Gaussian equation that the paraxial rays satisfy. Given the refractive power, the angle of incidence to the first principal plane of the lens, the angle of exit to the second principal plane of the lens, and the distance between the principal planes, the radii of curvature of the front and back surfaces of a lens can be obtained by applying the recursive numerical calculation method proposed in this paper according to the thickness of the lens. If a module consists of two or more lenses, the thickness and radius of curvature of each lens can be similarly determined after selecting the distance between the principal planes of the lens under the condition of the design specification while increasing the number of lenses one by one.

A Determination of Approximated Cylindrical Surfaces of Doubly Curved Surfaces for the Least Line Heating (최소 2차 가공을 위한 이중 곡면의 롤러 굽힘 형상 결정)

  • Dae-Kyu Yun;Jong-Gye Shin;Cheol-Ho Ryu
    • Journal of the Society of Naval Architects of Korea
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    • v.36 no.3
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    • pp.134-143
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    • 1999
  • The ship's bows and sterns are assembled with the curved blocks. In shipyards, the roller bending and the line heating or others are being used to fabricate such doubly curved shell. Firstly, the cylinder- or cone-type is formed through the roller bending, and then, the line heating is implemented to form the rest. This paper presents an algorithm to determine the direction for the roller bending and the shape to be formed as fabrication information. The direction for the roller bending is determined with Gauss mapping of the desired surface and the shape to form is calculated by comparing the bent shape with the desired shape.

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Dipole Distributions on a Hyperboloidal Panel (쌍곡면 패널에의 다이폴 분포)

  • Chang-Sup Lee;Jung-Chun Suh
    • Journal of the Society of Naval Architects of Korea
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    • v.32 no.2
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    • pp.32-42
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    • 1995
  • When the thickness becomes so small as in the case of the trailing edge of the propeller blade or when the curvature of the surface varies rapidly as in ship stem, the existing panel method employing a flat-surface panel, obtained by collapsing the original non-planar surface into its mean location, suffers the leakage problem and also gives inaccurate induction upon the field point very close to the panel. The hyperboloidal panel deals with the induction from the dipole distributed on the non-planar surface without approximation, overcoming the defects of the flat-surface panel. This paper introduces two distinct derivations of the formulae to compute the integral for the potential induced by a dipole of uniform density distributed on a non-planar hyperboloidal surface element. One method is based on the Gauss-Bonnet theorem and the other is based on the transformation of the surface integral into a line integral.

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An Analysis of Continuous Beam by Material Non-linear Transfer Matrix Method (재료비선형 전달행렬법에 의한 연속보의 해석)

  • Seo, Hyun Su;Kim, Jin Sup;Kwon, Min Ho
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.15 no.1
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    • pp.77-84
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    • 2011
  • This study is to develop nonlinear analysis algorithm for transfer matrix method, which can be applied to continuous beam analysis. Gauss-Lobatto integral rule is adopted and the transfer matrix is derived from stiffness matrix. In the transfer matrix method, the system equation has a constant number of unknowns regardless of number of D.O.F. Therefore, the transfer matrix method has computational efficiencies not only in linear elastic analysis but also in nonlinear analysis. To verify the developed method, the analysis results of several examples are compared with commercial code in moment-curvature, moment-displacement and load-displacement relation.

Curvature Region Analysis for Application of Plates Forming (곡판 가공방법 적용을 위한 곡률면적 분석)

  • Kim, Chan Suk;Son, Seung Hyeok;Shin, Jong Gye
    • Journal of the Society of Naval Architects of Korea
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    • v.52 no.1
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    • pp.70-76
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    • 2015
  • The ship hull is accomplished by assembling various curved surfaces. There are numerous existing methods for ship hull processing, which need certain appropriate processing methods to enable it to be more efficient. The curved hull plates can be divided into convex region and saddle region. It is common to use line heating method to form a saddle region, when it comes to a convex region, it will be triangle heating method to be utilized. A precise analysis for curvature domain is required for the application of proper processing method. There exist various problems on existing calculation methods of curvature domain. Therefore, a more powerful method is demanded to it more accurately. In this study, a method called Dual Contouring is applied to extract curved surfaces, which is able to improve accuracy of extracted area. Based on all above, a best-suited heat processing method should be selected.