• Title/Summary/Keyword: curvature equation

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FE Based Numerical Model to Consider Bond-slip Effect in Composite Beams (합성보의 부착슬립 효과를 고려한 유한요소 기반의 수치해석모델)

  • Kwak, Hyo-Gyoung;Hwang, Jin-Wook
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.23 no.1
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    • pp.95-110
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    • 2010
  • A numerical model to simulate bond-slip behavior of composite beam bridges is introduced in this paper. Assuming a linear bond stress-slip relation along the interface between the slab and girder, the slip behavior is implemented into a finite element formulation. Adopting the introduced model, the slip behavior can be taken account even in a beam element which is composed of both end nodes only. Governing equation of the slip behavior, based on the linear partial interaction theory, can be determined from the force equilibrium and a constant curvature distribution across the section of a composite beam. Since the governing equation for the slip behavior requires the moment values at both end nodes, the piecewise linear distribution of the constant bending moment in an element is assumed. Analysis results by the model are compared with numerical results and experimental values, and load-displacement relations of composite beams were then evaluated to verify the validity of the proposed model.

Standard Penetration Test Performance in Sandy Deposits (모래지반에서 표준관입시험에 따른 관입거동)

  • Dung, N.T.;Chung, Sung-Gyo
    • Journal of the Korean Geotechnical Society
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    • v.29 no.10
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    • pp.39-48
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    • 2013
  • This paper presents an equation to depict the penetration behavior during the standard penetration test (SPT) in sandy deposits. An energy balance approach is considered and the driving mechanism of the SPT sampler is conceptually modeled as that of a miniature open-ended steel pipe pile into sands. The equation consists of three sets of input parameters including hyperbolic parameters (m and ${\lambda}$) which are difficult to determine. An iterative technique is thus applied to determine the optimized values of m and ${\lambda}$ using three measured values from a routine SPT data. It is verified from a well-documented record that the simulated penetration curves are in good agreement with the measured ones. At a given depth, the increase in m results in the decrease in ${\lambda}$ and the increase in the curvature of the penetration curve as well as the simulated N-value. Generally, the predicted penetration curve becomes nearly straight for the portion of exceeding the seating drive zone, which is more pronounced as soil density increases. Thus, the simulation method can be applied to extrapolating a prematurely completed test data, i.e., to determining the N value equivalent to a 30 cm penetration. A simple linear equation is considered for obtaining similar results.

Effects of Organic Additives on Residual Stress and Surface Roughness of Electroplated Copper for Flexible PCB

  • Kim, Jongsoo;Kim, Heesan
    • Corrosion Science and Technology
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    • v.6 no.4
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    • pp.154-158
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    • 2007
  • For the application of flexible printed circuit board (FPCB), electroplated copper is required to have low surface roughness and residual stress. In the paper, the effects of surface roughness and residual stress of electroplated copper as thick as $8{\mu}m$ were studied on organic additives such as inhibitor, leveler and accelerator. Polyimide film coated with sputtered copper was used as a substrate. Surface roughness and surface morphology were measured by 3D-laser surface analysis and FESEM, respectively. Residual stress was calculated by Stoney's equation after measuring radius curvature of specimen. The addition of additives except high concentration of accelerator in the electrolyte decreased surface roughness of electroplated copper film. Such a tendency was explained by the function of additives among which the inhibitor and the leveler inhibit electroplating on a whole surface and prolusions, respectively. The accelerator plays a role in accelerating the electroplating in valley parts. The inhibitors and the leveler increased residual stress, whereas the accelerator decreased it. It was thought to be related with entrapped additives on electroplated copper film rather than the preferred orientation of electroplated copper film. The reason why additives lead to residual stress remains for the future work.

Flow Measurements and Performance Analysis using a 5-Hole Pitot Tube and a Rotating Hot-Wire Probe in an Axial Flow Fan (5공 피토관 및 회전 열선 유속계에 의한 축류 홴 내부 유동장 계측 및 평가)

  • Jang, Choon-Man;Kim, Kwang-Yong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.12
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    • pp.1750-1757
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    • 2003
  • This paper describes the flow measurements inside the blade passage of an axial flow fan by using a rotating hot-wire probe sensor from a relative flame of reference fixed to the rotor blades. The validity of fan rotor designed by a streamline curvature equation was performed by the measurement of the three-dimensional flow upstream and downstream of the fan rotor using a 5-hole pitot tube. The vortical flow structure near the rotor tip can be clearly observed by the measurements of a relative velocity and its fluctuation on quasi-orthogonal planes to a tip leakage vortex. Larger vortical flow, which results in higher blockage in the main flow, is formed according to decrease a flow rate. The vortical flow spreads out to the 30 percent span from the rotor tip at near stall condition. In the design operating condition, the tip leakage vortex is moved downstream while the center of the vortex keeps constant in the spanwise direction. Detailed characteristics of a velocity fluctuation with relation to the vortex were also analyzed.

Numerical study on the characteristics of the flow through injector orifice by multi-block computations (다중블럭계산에 의한 분사기 오리피스 유동특성 해석)

  • Kim, Yeong-Mok
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.3
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    • pp.414-426
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    • 1997
  • Numerical computations were conducted to characterize the three-dimensional laminar flow through an injector orifice having an inclined angle of 30 .deg.. For this study, the incompressible Navier-Stokes equations in generalized curvilinear coordinates, using a pseudocompressibility approach for continuity equation, were solved. The computations were performed using the finite difference implicit, approximately factored scheme of Beam and Warming and multi-block grids of complete continuity at block interfaces. The multi-block computations were validated for the steady state using direct comparison of multi-block solutions with equivalent single-block ones, including 2-D 180.deg. TAD and 3-D 90.deg. pipe bend. The comparisons between the numerical solutions and the flow field measurements for a tube with sudden contraction were presented in this work for solution validation. Computational results showed the nature of complex flow fields within the inclined injector orifice, including strong pressure-driven secondary flows in the cross stream induced by the effect of streamline curvature. In addition, asymmetric secondary flows were induced in the Reynolds number range above assumed laminar flow regime considered. However, turbulence calculations and grid dependency studies are needed for more accurate computations.

Topological View of Viscous Flow behind Transom Stern (트랜섬 선미 후방의 점성 유동장 Topology 관찰)

  • Kim, Wu-Joan;Park, Il-Ryong
    • Journal of the Society of Naval Architects of Korea
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    • v.42 no.4 s.142
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    • pp.322-329
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    • 2005
  • Viscous flows behind transom stern are analyzed based on CFD simulation results. Stern wave pattern is often complicated due to the abrupt change of stern surface curvature and flow separation at transom. When a ship advances at high speed, whole transom stern is exposed out of water, resulting in the so-called 'dry transom'. However, in the moderate speed regime, stern wave development in conjunction of flow separation makes unstable wavy surface partially covering transom surface, i.e., the so-called 'wetted transom'. Transom wave formation is usually affecting the resistance characteristics of a ship, since the pressure contribution on transom surface as well as the wave-making resistance is changed. Flow modeling for 'wetted transom' is difficult, while the 'dry transom modeling' is often applied for the high-speed vessels. In the present study CFD results from the RANS equation solver using a finite volume method with level-set treatment are utilized to assess the topology of transom flow pattern for a destroyer model (DTMB5415) and a container ship (KCS). It is found that transom flow patterns are quite different for the two ships, in conformity to the shape of submerged transom. Furthermore, the existence of free surface seems to after the flow topology in case of KCS.

Investigation on the Developing Turbulent Flow In a Curved Duct of Square Cross-Section Using a Low Reynolds Number Second Moment Turbulence Closure (2차모멘트 난류모형을 이용한 정사각 단면 곡덕트 내 발달하는 난류유동 변화에 대한 고찰)

  • Chun, Kun-Ho;Choi, Young-Don;Shin, Jong-Keun
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.23 no.8
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    • pp.1063-1071
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    • 1999
  • Fine grid calculations are reported for the developing turbulent flow in a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=Rc/D_H=3.357 $ and a bend angle of 720 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number algebraic second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

Theoretical Studies on Mechanism and Kinetics of the Hydrogen-Abstraction Reaction of CF3CH2CHO with OH Radicals

  • Ci, Cheng-Gang;Yu, Hong-Bo;Wan, Su-Qin;Liu, Jing-Yao;Sun, Chia-Chung
    • Bulletin of the Korean Chemical Society
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    • v.32 no.4
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    • pp.1187-1194
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    • 2011
  • The hydrogen abstraction reaction of $CF_3CH_2CHO$ + OH has been studied theoretically by dual-level direct dynamics method. Two stable conformers, trans- and cis-$CF_3CH_2CHO$, have been located, and there are four distinct OH hydrogen-abstraction channels from t-$CF_3CH_2CHO$ and two channels from c-$CF_3CH_2CHO$. The required potential energy surface information for the kinetic calculation was obtained at the MCG3-MPWB//M06-2X/aug-cc-pVDZ level. The rate constants, which were calculated using improved canonical transitionstate theory with small-curvature tunneling correction (ICVT/SCT) were fitted by a four-parameter Arrhenius equation. It is shown that the reaction proceeds predominantly via the H-abstraction from the -CHO group over the temperature range 200-2000 K. The calculated rate constants were in good agreement with the experimental data between 263 and 358 K.

Nonlinear finite element solutions of thermoelastic flexural strength and stress values of temperature dependent graded CNT-reinforced sandwich shallow shell structure

  • Mehar, Kulmani;Panda, Subrata K.
    • Structural Engineering and Mechanics
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    • v.67 no.6
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    • pp.565-578
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    • 2018
  • This research article reported the nonlinear finite solutions of the nonlinear flexural strength and stress behaviour of nano sandwich graded structural shell panel under the combined thermomechanical loading. The nanotube sandwich structural model is derived mathematically using the higher-order displacement polynomial including the full geometrical nonlinear strain-displacement equations via Green-Lagrange relations. The face sheets of the sandwich panel are assumed to be carbon nanotube-reinforced polymer composite with temperature dependent material properties. Additionally, the numerical model included different types of nanotube distribution patterns for the sandwich face sheets for the sake of variable strength. The required equilibrium equation of the graded carbon nanotube sandwich structural panel is derived by minimizing the total potential energy expression. The energy expression is further solved to obtain the deflection values (linear and nonlinear) via the direct iterative method in conjunction with finite element steps. A computer code is prepared (MATLAB environment) based on the current higher-order nonlinear model for the numerical analysis purpose. The stability of the numerical solution and the validity are verified by comparing the published deflection and stress values. Finally, the nonlinear model is utilized to explore the deflection and the stresses of the nanotube-reinforced (volume fraction and distribution patterns of carbon nanotube) sandwich structure (different core to face thickness ratios) for the variable type of structural parameter (thickness ratio, aspect ratio, geometrical configurations, constraints at the edges and curvature ratio) and unlike temperature loading.

SOME RESULTS ON CONCIRCULAR VECTOR FIELDS AND THEIR APPLICATIONS TO RICCI SOLITONS

  • CHEN, BANG-YEN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1535-1547
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    • 2015
  • A vector field on a Riemannian manifold (M, g) is called concircular if it satisfies ${\nabla}X^v={\mu}X$ for any vector X tangent to M, where ${\nabla}$ is the Levi-Civita connection and ${\mu}$ is a non-trivial function on M. A smooth vector field ${\xi}$ on a Riemannian manifold (M, g) is said to define a Ricci soliton if it satisfies the following Ricci soliton equation: $$\frac{1}{2}L_{\xi}g+Ric={\lambda}g$$, where $L_{\xi}g$ is the Lie-derivative of the metric tensor g with respect to ${\xi}$, Ric is the Ricci tensor of (M, g) and ${\lambda}$ is a constant. A Ricci soliton (M, g, ${\xi}$, ${\lambda}$) on a Riemannian manifold (M, g) is said to have concircular potential field if its potential field is a concircular vector field. In the first part of this paper we determine Riemannian manifolds which admit a concircular vector field. In the second part we classify Ricci solitons with concircular potential field. In the last part we prove some important properties of Ricci solitons on submanifolds of a Riemannian manifold equipped with a concircular vector field.