• Title/Summary/Keyword: Equation of plane

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A Study of a Variety of Sands in Stress-dilatancy Relationships (각 종 모래의 Stress-dilatancy 관계에 관한 연구)

  • 박춘식;장정욱
    • Journal of the Korean Geotechnical Society
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    • v.18 no.1
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    • pp.41-48
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    • 2002
  • Anisotropy of stiffness, from extremely small strains to post-failure strains, of isotropically consolidated air-pluviated sands in plane strain compression was studied by using the newly developed instrumentation fur small strain measurements, Seven types of sand of world-wide origins were tested, which have been extensively used for research purposes. Stress-strain relationships for a wide range of strain from about 0.0001% to the peak were obtained by measuring axial and lateral strains locally free from the effects of bedding and membrane penetration errors at the specimen boundaries. The result showed that the relationship between the principal stress ratio and the principal strain increment ratio was constant, being rarely affected by the over-consolidation ratio and the confining pressure. Although in the small strain the anisotropy hardly affected the relationship between the principal stress ratio and the principal strain increment ratio, the K value around the peak varied according to the $\delta$ value. In general, Rowe\`s stress-dilatancy equation works fairly well from the small strain to the peak.

$J_{1C}$ and J-integral Behavior of Low-Carbon Steel using Double Edge Tension Specimen (양쪽 크랙 인장시험편을 이용한 저탄소강의 $J_{1C}$ 및 J적분 거동)

  • 고성위
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.21 no.2
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    • pp.151-156
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    • 1985
  • In this paper, the plane stress fracture toughness of cold rolled 4.5mm thick SS41 steel plate was investigated for various crack ratios respectively in case of base metal, normalized and annealed heat-treated specimens using the method of J-integral. The specimen geometry used was double edge tension (DET) specimen. The experiments were performed on an Instron machine and all the crack lengths were measured by travelling microscope. The plane stress fracture toughness obtained by the method of Rice equation was J sub(1C)=22.8kgf/mm for the base metal, j sub(1C)-24.7kgf/mm for the normalized specimen and J sub(1C)=26.9 kgf/mm for the annealed. The J-integral computed at the limit load was found unsuitable for fracture toughness determination, because of large variation depending on the crack ratio.

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Shielding effectiveness of an Aperture in Infinite Conducting plane Due to HEMP Incidence (무한 도체평판 개구에 입사하는 HEMP 파형에 따른 침투 전자파의 차폐효과)

  • Lim, Byoung-Jin;Seo, Hun-Wook;Lim, Sung-Min;Kim, Ki-Chai
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.15 no.8
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    • pp.1647-1652
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    • 2011
  • This paper presents the shielding effectiveness for the IEC 61000-2-9 standard when HEMP source penetrates through an aperture in a planar conducting plane of infinite extent. An integral equation is derived and solved by applying Galerkin's method of moments for calculating the electric shielding effectiveness. The electric shielding effectiveness is examined based on changing the aperture length and width. It is shown that the electric shielding effectiveness is suddenly decreases as the aperture width of 0.4 ~ 0.45${\lambda}$. It is also found that the penetrated electric field for the IEC 61000-2-9 incident field is different from the Bell Laboratory incident field, but the frequency characteristic of the electric shielding effectiveness becomes the same shape.

Effects of diffraction in regular head waves on added resistance and wake using CFD

  • Lee, Cheol-Min;Park, Sung-Chul;Yu, Jin-Won;Choi, Jung-Eun;Lee, Inwon
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.11 no.2
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    • pp.736-749
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    • 2019
  • This paper employs computational tools to investigate the diffraction effects in regular head waves on the added resistance and wake on the propeller plane. The objective ships are a 66,000 DWT bulk carrier and a 3,600 TEU container ship. Fixed and free to heave and pitch conditions at design speed have been taken into account. Two-phase unsteady Reynolds averaged Navier-Stokes equations have been solved using the finite volume method; and a realizable k-ε model has been applied for the turbulent closure. The free surface is obtained by solving a VOF equation. The computations are carried out at the same scale of the model tests. Grid and numerical wave damping zones are applied to remove unwanted wave reflection at the boundaries. The computational results are analyzed using the Fourier series. The added resistances in waves at the free condition are higher than those at the fixed condition, which are nearly constant for all wavelengths. The wake velocity in waves is higher than that in calm water, and is accelerated where the wave crest locates on the propeller plane. When the vertical motion at the stern goes upward, the wake velocity also accelerated.

On Teaching of Complex Numbers in 10-th Grade Mathematics (제 10-단계 수학에서 복소수 지도에 관한 연구)

  • Kim, Heung-Ki;Lee, Chong-Cheol
    • School Mathematics
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    • v.9 no.2
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    • pp.291-312
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    • 2007
  • As a result of observing the 10-th grade text books on mathematics now in use which show the way of introducing complex numbers for the first time, it is easy to see all the text books on mathematics use a quadratic equation $x^2+1=0$ for a new number i. However, Since using the new number i is artificial, this make students get confused in understanding the way of introducing complex numbers. And students who have problems with the quadratic equation can also have difficulty in understanding complex numbers. On the other hand, by using a coordinate plane with ordered pairs and arrows, students can understand complex numbers better because the number system can be extended systematically through intuitive methods. The problem is that how to bring and use ordered pairs and arrows to introduce complex numbers in highschool mathematics. To solve this problem, in this study, We developed a systematic and visible learning contents which make it possible to study the process of the step-by-step extension of number system that will be applied through elementary and middle school curriculum and all the way up to the introduction of complex numbers. After having applied the developed learning contents to the teaching and learning procedure, we can know that the developed learning contents are more efficient than the contents used in the text books on mathematics now in use.

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A Three-Dimensional Galerkin-FEM Model with Density Variation (밀도 변화를 포함하는 3차원 연직함수 전개모형)

  • 이호진;정경태;소재귀;강관수;정종율
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.2
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    • pp.123-136
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    • 1996
  • A three-dimensional Galerkin-FEM model which can handle the temporal and spatial variation of density is presented. The hydrostatic approximation is used and density effects are included by means of conservation equation of heat and the equation of state. The finite difference grids are used in the horizontal plane and a set of linear-shape functions is used for the vertical expansion. The similarity transform is introduced to solve resultant matrix equations. The proposed model was first applied to the density-driven circulation in an idealized basin in the presence of the heat exchange between the air and the sea. The advection terms in the momentum equation were ignored, while the convection terms were retained in the heat equation. Coefficients of the vertical eddy viscosity and diffusivity were fixed to be constant. Calculation in a non-rotating idealized basin shows that the difference in heat capacity with depth gives rise to the horizontal gradient of temperature. Consequently, there is a steady new in the upper layer in the direction of increasing depth with compensatory counter flow .in the lower layer. With Coriolis force, geostrophic flow was predominant due to the balance between the pressure gradient and the Coriolis force. As a test in region of irregular topography, the model is applied to the Yellow Sea. Although the resultant flow was very complex, the character of the flow Showed to be geostrophic on the whole.

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Method for Measurement of Complex Relative Permittivity of Semi-Solid Materials Using Novel Cavity Resonator Design (캐비티 공진기를 이용한 반고체 상태 물질의 복소 비유전율 측정 방법)

  • Park, Rae-Seoung;Jang, Jihyun;Park, Byungdeok;Kim, Junhwan;Park, Sangbok;Chung, Young-Seek;Cheon, Changyul
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.25 no.8
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    • pp.872-878
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    • 2014
  • This paper proposes a measurement method of the complex relative permittivity of semi-solid materials using a new cavity structure. Semi-solid materials are positioned in the proposed cavity where an aperture exists on each corner of the upper part and a ground plane is separated. In order to show the validation of the proposed method, we measured the complex relative permittivity of distilled water and 0.9 % saline by sensing a shift of resonant frequency and using Critical-Points Method, and compared the results with those derived from the Cole-Cole equation.

Rate Capability of LiFePO4 Cathodes and the Shape Engineering of Their Anisotropic Crystallites

  • Alexander, Bobyl;Sang-Сheol, Nam;Jung-Hoon, Song;Alexander, Ivanishchev;Arseni, Ushakov
    • Journal of Electrochemical Science and Technology
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    • v.13 no.4
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    • pp.438-452
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    • 2022
  • For cuboid and ellipsoid crystallites of LiFePO4 powders, by X-ray diffraction (XRD) and microscopic (TEM) studies, it is possible to determine the anisotropic parameters of the crystallite size distribution functions. These parameters were used to describe the cathode rate capability within the model of averaging the diffusion coefficient D over the length of the crystallite columns along the [010] direction. A LiFePO4 powder was chosen for testing the developed model, consisting of big cuboid and small ellipsoid crystallites (close to them). When analyzing the parts of big and small rate capabilities, the fitting values D = 2.1 and 0.3 nm2/s were obtained for cuboids and ellipsoids, respectively. When analyzing the results of cyclic voltammetry using the Randles-Sevcik equation and the total area of projections of electrode crystallites on their (010) plane, slightly different values were obtained, D = 0.9 ± 0.15 and 0.5 ± 0.15 nm2/s, respectively. We believe that these inconsistencies can be considered quite acceptable, since both methods of determining D have obvious sources of error. However, the developed method has a clearly lower systematic error due to the ability to actually take into account the shape and statistics of crystallites, and it is also useful for improving the accuracy of the Randles-Sevcik equation. It has also been demonstrated that the shape engineering of crystallites, among other tasks, can increase the cathode capacity by 15% by increasing their size correlation coefficients.

An Experimental Study on the Turbulent Flow of a 45$^{\circ}C$ Free Cross Jet (450自由衝突 噴射 의 亂流流動 에 관한 實驗的 硏究)

  • 노병준;김장권
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.8 no.5
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    • pp.442-449
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    • 1984
  • Turbulent jet flow has been studied in many ways; a plane jet, a rectangular jet, an annular jet, a round jet, a wall jet, a parallel jet, a valve jet, a cross jet, a slit jet and etc. In this report, a 45.deg. cross jet flow was tried by using two same dimensioned nozzels(dia..phi.20)which were set up at the exit of the subsonic wind tunnel. Each jet flows to the direction of 22.5.deg. to the axis of downstream of the mixed flow. The centerline of each jet meets at the distance of 217.3mm and their mixing flow could be imagined to develop beyond that distance, so the measurement was effectuated at X/X$_{0}$=1.2-1.5. The section of the mixed flow a elliptic circle which is formed by the 22.5.deg. inclined flows to the X direction. This experimental study aimed at the investigation of the turbulent mixing process of two jets; the mean velocities, the turbulent shear stresses, the correlation coefficients, and the momentum were respectively measured. The mean velocity distribution profiles of the down-stream component measured in the Y direction coincide well with the empirical equation of Gortler and those measured in the Z direction agree with the equation of H. Schlichting. Other mean velocities V over bar and W over bar components were randomly distributed. The higher values with same order of the intensity of turbulence were largely distributed at the central part of the flow. The momentum was decreased up to 70% by the shock losses and the development of intense turbulences, but it kept its value constantly beyond X/d=14. Two-channel hot-wire anemometer systems (model 1050 series), X-type hot-wire made of tungsten (dia. .phi.e.mu.m, long 3mm, model 0252 T5), a computer(model HP 9845B0, and a plotter (model HP 9872C) were used for the experiments and the analyses.s.

A first-principles theoretical investigation of the structural, electronic and magnetic properties of cubic thorium carbonitrides ThCxN(1-x)

  • Siddique, Muhammad;Rahman, Amin Ur;Iqbal, Azmat;Azam, Sikander
    • Nuclear Engineering and Technology
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    • v.51 no.5
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    • pp.1373-1380
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    • 2019
  • Besides promising implications as fertile nuclear materials, thorium carbonitrides are of great interest owing to their peculiar physical and chemical properties, such as high density, high melting point, good thermal conductivity. This paper reports first-principles simulation results on the structural, electronic and magnetic properties of cubic thorium carbonitrides $ThC_xN_{(1-x)}$ (X = 0.03125, 0.0625, 0.09375, 0.125, 0.15625) employing formalism of density-functional-theory. For the simulation of physical properties, we incorporated full-potential linearized augmented plane-wave (FPLAPW) method while the exchange-correlation potential terms in Kohn-Sham Equation (KSE) are treated within Generalized-Gradient-Approximation (GGA) in conjunction with Perdew-Bruke-Ernzerhof (PBE) correction. The structural parameters were calculated by fitting total energy into the Murnaghan's equation of state. The lattice constants, bulk moduli, total energy, electronic band structure and spin magnetic moments of the compounds show dependence on the C/N concentration ratio. The electronic and magnetic properties have revealed non-magnetic but metallic character of the compounds. The main contribution to density of states at the Fermi level stems from the comparable spectral intensity of Th (6d+5f) and (C+N) 2p states. In comparison with spin magnetic moments of ThSb and ThBi calculated earlier with LDA+U approach, we observed an enhancement in the spin magnetic moments after carbon-doping into ThN monopnictide.