• 제목/요약/키워드: principal curvature

검색결과 69건 처리시간 0.02초

BERTRAND CURVES IN NON-FLAT 3-DIMENSIONAL (RIEMANNIAN OR LORENTZIAN) SPACE FORMS

  • Lucas, Pascual;Ortega-Yagues, Jose Antonio
    • 대한수학회보
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    • 제50권4호
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    • pp.1109-1126
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    • 2013
  • Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

비대칭 이중곡률 스테인리스 원형강관 보-기둥의 좌굴내력에 관한 실험적 연구 (An Experimental Study on the Buckling Strength of subject to Asymmetrical Double Curvature Stainless Steel Circular Hollow Section Beam-Columns)

  • 장호주;박재선;양영성
    • 한국강구조학회 논문집
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    • 제21권4호
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    • pp.351-360
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    • 2009
  • 본 연구에서는 스테인리스 강관의 구조재로서 적용성 검토를 위해 편심 축하중을 받는 스테인리스 원형강관 보-기둥에 대한 좌굴강 도와 거동을 파악하고자 한다. 주요변수는 축력과 양단 비대칭 모멘트를 받는 이중곡률 보-기둥에 세장비(細長比)와 편심비(e/k)로 한 스테인리 스 원형강관의 최대내력 및 변형능력 등의 역학적 특성을 규명하며, 이론해석을 통한 실험값과 비교함으로서 스테인리스 강관 구조설계을 위한 기초 자료를 구하는데 그 목적이 있다. 실험결과를 해석결과와 비교해본 결과, 세장비 70의 편심비가 0인 시험체만이 낮고, 그 외 모든 시험체는 해석을 통한 M-P 상관곡선을 상회하는 결과를 보이나, 편심비가 작을수록 해석값에 근접하고 있어, 이론해석에서 적용한 세장비를 고려한 좌굴계수나 강도저감계수가 스테인리스 원형강관에 대해서는 별도의 값이 적용될 가능성이 있는 것으로 판단되며, 더 많은 실험에 의해 확증되어야 할 것이다.

통기성 상자 구조물에 대한 유한요소 해석 (Finite Element Analysis of a Ventilating Box Structure)

  • 박종민;권순구
    • Journal of Biosystems Engineering
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    • 제27권6호
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    • pp.557-564
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    • 2002
  • Corrugated board is an efficient low-cost structure material fur the boxes that are widely used for transporting, storing and distributing goods. Corrugated board is also considered as an orthotropic because the principal material directions are the same as in paperboard. The purpose of this study was to elucidate the principal design parameters of ventilating box through the FEA on the various types of ventilating hole. From the viewpoint of the stress distribution and stress level, the optimum pattern and location of the ventilating hole were vertically oblong, and symmetry position with a short distance to the right and left from the center of front and rear panel. And, the optimum location and pattern of hand hole were a short distance to the top from the center of both side panels, and modified shape to increase the radius of curvature of both side in horizontal oblong. In general, the optimum pattern and location of both the ventilating hole and hand hole based on the FEM analysis were well verified by experimental investigation. It is suggested that decrease in compressive strength of the box could be minimized in the same ventilating hole area under the condition of the length of major axis of ventilating hole is less than 1/4 of box length, the ratio of minor axis/major axis is 113.5∼l/2.5, and number of the ventilating holes is even and symmetrical.

진공 용기 제작시 공정별 변형 예측에 관한 연구 (A Study on the Prediction of Welding Distortion of Vacuum Vessel during Fabrication Process)

  • 이동주;김하근;신상범
    • 대한용접접합학회:학술대회논문집
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    • 대한용접접합학회 2009년 추계학술발표대회
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    • pp.96-96
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    • 2009
  • The purpose of this study is to clarify the transitional behavior and main factor of excessive welding distortion caused by fabrication process of STS 304 vacuum vessel having double curvature for the efficient quality control of vacuum vessel. In order to do it, the predictive equations of the welding distortion in simple weldment of vacuum vessel were established by conventional finite element analysis. And the principal factor controlling the welding distortion was identified by evaluating the welding distortion of vacuum vessel in each fabrication process with FEA and simplified thermo elastic method. Based on the results, the principal factors of distortion of vacuum vessel were clarified as angular distortion and transverse shrinkage which are a source of excessive out-of plane distortion in the double curved vacuum vessel. It was expected that the FE analysis results of this study could contribute to establish the proper control method of welding distortion for double curved vacuum vessel.

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탄성계수 감소곡선에 근거한 철도노반의 회복탄성계수 모델 개발 및 평가 (Development and Assessment for Resilient Modulus Prediction Model of Railway Trackbeds Based on Modulus Reduction Curve)

  • 박철수;황선근;최찬용;목영진
    • 한국철도학회:학술대회논문집
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    • 한국철도학회 2008년도 추계학술대회 논문집
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    • pp.805-814
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    • 2008
  • This study focused on the resilient modulus prediction model, which is the functions of mean effective principal stress and axial strain, for three types of railroad trackbed materials such as crushed stone, weathered soil, and crushed-rock soil mixture. The model is composed with the maximum Young's modulus and nonlinear values for higher strain in parallel with dynamic shear modulus. The maximum values is modeled by model parameters, $A_E$ and the power of mean effective principal stress, $n_E$. The nonlinear portion is represented by modified hyperbolic model, with the model parameters of reference strain, ${\varepsilon}_r$ and curvature coefficient, a. To assess the performance of the prediction models proposed herein, the elastic response of a test trackbed near PyeongTaek, Korea was evaluated using a 3-D nonlinear elastic computer program (GEOTRACK) and compared with measured elastic vertical displacement during the passages of freight and passenger trains. The material types of sub-ballasts are crushed stone and weathered granite soil, respectively. The calculated vertical displacements within the sub-ballasts are within the order of 0.6mm, and agree well with measured values with the reasonable margin. The prediction models are thus concluded to work properly in the preliminary investigation.

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검사용 로봇을 위한 원기둥형 물체의 자세 추정 방법 (Pose Estimation of a Cylindrical Object for an Inspection Robot)

  • 정규원
    • 한국공작기계학회논문집
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    • 제12권1호
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    • pp.8-15
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    • 2003
  • The cylindrical object such as a water pipe or an oil pipeline are widely used in the infrastructure. Those pipes should be inspected periodically by human or a robot. However, since there is no edge or vertex in the pipe, it is very difficult for the robot to navigate along the pipe. In this paper in order to guide the robot along the axis of the pipe, an algorithm which find the axis using the measured range data from the robot to the pipe wall is developed The algorithm is verified using both the simulated range data and the measured one.

SLANT HELICES IN THE THREE-DIMENSIONAL SPHERE

  • Lucas, Pascual;Ortega-Yagues, Jose Antonio
    • 대한수학회지
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    • 제54권4호
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    • pp.1331-1343
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    • 2017
  • A curve ${\gamma}$ immersed in the three-dimensional sphere ${\mathbb{S}}^3$ is said to be a slant helix if there exists a Killing vector field V(s) with constant length along ${\gamma}$ and such that the angle between V and the principal normal is constant along ${\gamma}$. In this paper we characterize slant helices in ${\mathbb{S}}^3$ by means of a differential equation in the curvature ${\kappa}$ and the torsion ${\tau}$ of the curve. We define a helix surface in ${\mathbb{S}}^3$ and give a method to construct any helix surface. This method is based on the Kitagawa representation of flat surfaces in ${\mathbb{S}}^3$. Finally, we obtain a geometric approach to the problem of solving natural equations for slant helices in the three-dimensional sphere. We prove that the slant helices in ${\mathbb{S}}^3$ are exactly the geodesics of helix surfaces.

Underwater explosion and its effects on nonlinear behavior of an arch dam

  • Moradi, Melika;Aghajanzadeh, Seyyed Meisam;Mirzabozorg, Hasan;Alimohammadi, Mahsa
    • Coupled systems mechanics
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    • 제7권3호
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    • pp.333-351
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    • 2018
  • In the present paper, the behavior of the Karaj double curvature arch dam is studied focusing on the effects of structural nonlinearity on the responses of the dam body when an underwater explosion occurred in the reservoir medium. The explosive sources are located at different distances from the dam and the effects of the cavitation and the initial shock wave of the explosion are considered. Different amount of TNT are considered. Two different linear and nonlinear behavior are assumed in the analysis and the dam body is assumed with and without contraction joints. Radial, tangential and vertical displacements of the dam crest are obtained. Moreover, maximum and minimum principal stress distributions are plotted. Based on the results, the dam body responses are sensitive to the insertion of joints and constitutive model considered for the dam body.

LAGUERRE CHARACTERIZATION OF SOME HYPERSURFACES

  • Fang, Jianbo;Li, Fengjiang
    • 대한수학회보
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    • 제53권3호
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    • pp.875-884
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    • 2016
  • Let x : $^{Mn-1}{\rightarrow}{\mathbb{R}}^n$ ($n{\geq}4$) be an umbilical free hyper-surface with non-zero principal curvatures. Then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, and a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. We denote the Laguerre scalar curvature by R and the trace-free Laguerre tensor by ${\tilde{L}}:=L-{\frac{1}{n-1}}tr(L)g$. In this paper, we prove a local classification result under the assumption of parallel Laguerre form and an inequality of the type $${\parallel}{\tilde{L}}{\parallel}{\leq}cR$$ where $c={\frac{1}{(n-3){\sqrt{(n-2)(n-1)}}}$ is appropriate real constant, depending on the dimension.

A CHARACTERIZATION OF CONCENTRIC HYPERSPHERES IN ℝn

  • Kim, Dong-Soo;Kim, Young Ho
    • 대한수학회보
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    • 제51권2호
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    • pp.531-538
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    • 2014
  • Concentric hyperspheres in the n-dimensional Euclidean space $\mathbb{R}^n$ are the level hypersurfaces of a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$. The magnitude $||{\nabla}f||$ of the gradient of such a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ is a function of the function f. We are interested in the converse problem. As a result, we show that if the magnitude of the gradient of a function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with isolated critical points is a function of f itself, then f is either a radial function or a function of a linear function. That is, the level hypersurfaces are either concentric hyperspheres or parallel hyperplanes. As a corollary, we see that if the magnitude of a conservative vector field with isolated singularities on $\mathbb{R}^n$ is a function of its scalar potential, then either it is a central vector field or it has constant direction.