• Title/Summary/Keyword: parabolic distribution

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Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle

  • Tayeb, Tayeb Si;Zidour, Mohamed;Bensattalah, Tayeb;Heireche, Houari;Benahmed, Abdelillah;Bedia, E.A. Adda
    • Advances in nano research
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    • 제8권2호
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    • pp.135-148
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    • 2020
  • The incorporation of carbon nanotubes in a polymer matrix makes it possible to obtain nanocomposite materials with exceptional properties. It's in this scientific background that this work was based. There are several theories that deal with the behavior of plates, in this research based on the Mindlin-Reissner theory that takes into account the transversal shear effect, for analysis of the critical buckling load of a reinforced polymer plate with parabolic distribution of carbon nanotubes. The equations of the model are derived and the critical loads of linear and parabolic distribution of carbon nanotubes are obtained. With different disposition of nanotubes of carbon in the polymer matrix, the effects of different parameters such as the volume fractions, the plate geometric ratios and the number of modes on the critical load buckling are analysed and discussed. The results show that the critical buckling load of parabolic distribution is larger than the linear distribution. This variation is attributed to the concentration of reinforcement (CNTs) at the top and bottom faces for the X-CNT type which make the plate more rigid against buckling.

HEAT EQUATION WITH A GEOMETRIC ROUGH PATH POTENTIAL IN ONE SPACE DIMENSION: EXISTENCE AND REGULARITY OF SOLUTION

  • Kim, Hyun-Jung;Lototsky, Sergey V.
    • 대한수학회논문집
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    • 제34권3호
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    • pp.757-769
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    • 2019
  • A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a $H{\ddot{o}}lder$ continuous function, regularity of the resulting solution is in line with the standard parabolic theory.

자연하천의 연직방향 유속분포 추정을 위한 포물선식 (Quadratic Parabolic Equation to Estimate the Vertical Velocity Distribution in the Natural Streamflow)

  • 박승기;김태철
    • 한국수자원학회논문집
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    • 제33권2호
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    • pp.169-179
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    • 2000
  • 이 연구에서는 1995년부터 1997년까지 금강수계 강경지점에서 유속계로 측정한 유속자료를 분석하여 자연하천의 연직방향 유속분포특성을 규명하였다. 또한, 현장유속 측정조건이 불량하여 다점법으로 유속분포를 측정하기 곤란한 경우, 간단하게 표면유속만을 측정하여 상대깊이별 유속을 추정할 수 있는 연직 유속분포식을 유도하였다. 2차 포물선의 유속분포식은 통계적으로 매우 안정적이고, 표면유속과 바닥유속 등과 고도의 유의성을 보였다. 2차 포물선식의 상수 및 계수와 표면유속과의 상관관계를 구하였으며, 실측 검정자료에 적용한 결과, 유속분포특성을 잘 반영하는 것을 확인할 수 있었다. 연직 유속분포식으로 추정된 유속은 실제수심을 적용하여 평균유속과 유량을 결정할 수 있으며, 이는 또한 하천의 오염물질이동 등 수질해석에 적용할 수 있을 것이다.

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태양열집속집열기의 설계 방법에 관한 연구 (A New Approach to Design Method of the Solar Compound Parabolic Concentrator with Tubular Absorber)

  • 김석종;임상훈
    • KIEAE Journal
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    • 제2권3호
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    • pp.33-38
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    • 2002
  • The intermediate range of temperatures($100{\sim}300^{\circ}C$) which can be achieved with CPCs(Compound Parabolic Concentrators) without tracking device provides both economic and thermal advantages for solar collector design. The present paper summarizes critical design considerations for CPC with cylindrical absorber and its optical performance using ray tracing program. Concentration ratios vary as acceptance half angle, ratio of reflector height to aperture width and ratio of reflector area to aperture area. This effects showed that the concentration ratio was increased as acceptance angle but optimum ratio of reflector height to aperture width existed at critical value. As a result of ray tracing, solar ray losses was maximized at acceptance half angle and this problem was solved by increasing absorber tube diameter. The concentrating flux distribution on the absorber surface was uniform but peak flux existed.

Heat Losses from the Receivers of a Multifaceted Parabolic Solar Energy Collecting System

  • Seo, Taebeom;Ryu, Siyoul;Kang, Yongheock
    • Journal of Mechanical Science and Technology
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    • 제17권8호
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    • pp.1185-1195
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    • 2003
  • Heat losses from the receivers of a dish-type solar energy collecting system at the Korea Institute of Energy Research (KIER) are numerically investigated. It is assumed that a number of flat square mirrors are arranged on the parabolic dish structure to serve as a reflector. Two different types of receivers, which have conical and dome shapes, are considered for the system, and several modes of heat losses from the receivers are thoroughly studied. Using the Stine and McDonald model convective heat loss from a receiver is estimated. The Net Radiation Method is used to calculate the radiation heat transfer rate by emission from the inside surface of the cavity receiver to the environment. The Monte-Carlo Method is used to predict the radiation heat transfer rate from the reflector to the receiver. Tracing the photons generated, the reflection loss from the receivers can be estimated. The radiative heat flux distribution produced by a multifaceted parabolic concentrator on the focal plane is estimated using the cone optics method. Also, the solar radiation spillage around the aperture is calculated. Based on the results of the analysis, the performances of two different receivers with multifaceted parabolic solar energy collectors are evaluated.

Instability and vibration analyses of FG cylindrical panels under parabolic axial compressions

  • Kumar, Rajesh;Dey, Tanish;Panda, Sarat K.
    • Steel and Composite Structures
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    • 제31권2호
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    • pp.187-199
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    • 2019
  • This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

Wind-induced response of open type hyperbolic-parabolic membrane structures

  • Xu, Junhao;Zhang, Yingying;Zhang, Lanlan;Wu, Meng;Zhou, Yi;Lei, Ke;Zhang, Qilin
    • Structural Engineering and Mechanics
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    • 제76권2호
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    • pp.269-278
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    • 2020
  • In this paper, the mechanical characteristics of the open type hyperbolic-parabolic membrane structure under wind load were investigated. First, the numerical simulation of a typical plane membrane structure was performed based on the Large-Eddy Simulation method. The accuracy of the simulation method was validated by the corresponding wind tunnel test results. Then, the wind load shape coefficients of open type hyperbolic-parabolic membrane structures are obtained from the series of numerical calculations and compared with the recommended values in the "Technical Specification for Membrane Structures (CECS 158: 2015). Finally, the influences of the wind directions and wind speeds on the mean wind pressure distribution of open type hyperbolic-parabolic membrane structures were investigated. This study aims to gain a better understanding of the wind-induced response for this type of structure and be useful to engineers and researchers.

포물형 근사식 수치모형의 투과 경계조건 (Open Boundary Conditions in Parabolic Approximation Model)

  • 서승남;이동영
    • 한국해안해양공학회지
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    • 제19권2호
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    • pp.170-178
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    • 2007
  • 대부분의 포물형 수치모형은 경계 외측의 수심이 해안방향으로 변하지 않는 Snell 법칙을 적용할 수 있는 조건으로 국한한다. 여기에는 기존의 Kirby 방법이 있으며 본 논문에서는 이를 수정한 방법 그리고 Dirichlet 경계조건에 대해 자세히 기술하고 이에 대한 수치실험 결과를 제시하였다. 일정 수심 위에 존재하는 원형 천퇴에 대한 수치실험 결과 계산영역 좌우에 가상 수치 조정구역을 두고 본 Dirichlet 경계조건을 적용한 경우가 파고비의 분포가 가장 작게 왜곡되는 것으로 나타났다.

성능 중심 설계기준을 위한 콘크리트 압축응력 분포 (Compressive Stress Distribution of Concrete for Performance-Based Design Code)

  • 이재훈;임강섭;황도규
    • 콘크리트학회논문집
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    • 제23권3호
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    • pp.365-376
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    • 2011
  • 현행 콘크리트구조설계기준(2007)은 콘크리트 구조물의 설계에 적용하는 콘크리트의 압축응력 분포로 ACI 318의 등가 직사각형 응력 분포를 규정하고 있다. 단면의 휨강도 해석에는 등가 직사각형 응력 분포가 충분하겠지만, 성능 중심 설계의 한계 상태 검증에는 실제와 가까운 압축응력-변형률 관계가 필요하다. 또 등가 직사각형 응력 분포는 고강도 콘크리트 기둥의 휨강도 해석에 비안전측의 결과를 준다는 것이 알려져 있으므로, 이를 대신하는 새로운 응력 분포 모델이 필요하다. 이 연구에서는 Eurocode와 일본 토목학회의 설계기준에서 채택하고 있는 포물선-직선 형상의 새로운 모델을 제안하였다. 이 응력 분포 모델은 이 연구에서 수행된 압축응력 분포 실험과 타 연구자들의 실험 결과를 분석하여 도출된 것으로서, 보통 강도뿐만 아니라 고강도 콘크리트를 포함한 것이다. 제안 모델의 특성은 미국 ACI 318, 캐나다 CSA, 유럽의 Eurocode, 일본 토목학회 설계기준의 응력 분포 모델과 함께 실험 결과와 비교하여 정리하였다.

COB Line형 LED를 사용한 PAR 조명의 제작 (Manufacturing of PAR Illumination Using COB Line Type LEDs)

  • 윤갑석;유경선;이창수;현동훈
    • 한국생산제조학회지
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    • 제24권4호
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    • pp.448-454
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    • 2015
  • In this paper, the band structural design that is typically in a line was arranged in a ring shape, so as to configure the high power LED lighting in such a way as to form a concentrated light distribution angle of less than 15 degrees. The parabolic aluminized reflector PAR38 that facilitates design using area and the area of the optical system to the same extent, applied a multiple light-source condenser lens optical system for the control of integration. The LED used here implemented a single linear light source using ans LED module with ans LED, flip-chip chip-scale package. The optical system was designed based on the energy star standard.