• Title/Summary/Keyword: Cubic law

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Nonlinear vibration and primary resonance of multilayer functionally graded shallow shells with porous core

  • Kamran Foroutan;Liming Dai
    • Steel and Composite Structures
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    • v.48 no.3
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    • pp.335-351
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    • 2023
  • This research studies the primary resonance and nonlinear vibratory responses of multilayer functionally graded shallow (MFGS) shells under external excitations. The shells considered with functionally graded porous (FGP) core and resting on two types of nonlinear viscoelastic foundations (NVEF) governed by either a linear model with two parameters of Winkler and Pasternak foundations or a nonlinear model of hardening/softening cubic stiffness augmented by a Kelvin-Voigt viscoelastic model. The shells considered have three layers, sandwiched by functionally graded (FG), FGP, and FG materials. To investigate the influence of various porosity distributions, two types of FGP middle layer cores are considered. With the first-order shear deformation theory (FSDT), Hooke's law, and von-Kármán equation, the stress-strain relations for the MFGS shells with FGP core are developed. The governing equations of the shells are consequently derived. For the sake of higher accuracy and reliability, the P-T method is implemented in numerically analyzing the vibration, and the method of multiple scales (MMS) as one of the perturbation methods is used to investigate the primary resonance. The results of the present research are verified with the results available in the literature. The analytical results are compared with the P-T method. The influences of material, geometry, and nonlinear viscoelastic foundation parameters on the responses of the shells are illustrated.

The Relation of Three Burning Space And Nutrient & Defensive Qi (삼초(三焦)와 영위(營衛)의 상관성(相關性))

  • Mun, Seong-sik;Kang, Jung-Soo
    • Journal of Haehwa Medicine
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    • v.9 no.1
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    • pp.105-112
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    • 2000
  • Three burning space concentrating mainly on the text of ${\ll}NeiChing{\gg}$, we got this conclusion by looking at a longitudial perspective of three burning space function, nutrient & defensive qi creation, movement and numbers. 1. Longitudial movement is the law of the universe, by looking at oriental medicine by the thought of heaven and man unity we can tell that longitudial movement concept is used to analyze the physiology of our body. And we can look at our body in a cubic movement suck as top and bottom, left and right, outside and inside, internal and external, upward and downward movement. 2. In Nei Ching the concept of three burning space is seperated in to four different types of three burning space which are three burning space as a fu, three burning space as a water metabolism and excretion organ, and three burning space by its position. 3. nutrient & defensive qi's movement in the channel is the same as the twelve regular channels movement in our body, nutrient qi circulates the yang part twenty five during the day and circulates the ying part twenty five times during the night. Since channel functions corresponds with the sun, moon, and the stars the ups and downs of nutrient & defensive qi's property varies with the difference of the periods. 4. By comparing nutrient & defensive qi's production and property with three burning space's positional property, we can see that three burning space's positional property comes out from the longitudial movement of nutrient & defensive qi.

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Preparation, Structural and Magnetic Properties of Ordered Perovskite (BaLa)(MgMo)O$_6$

  • Choy Jin-Ho;Hong Seung-Tae
    • Bulletin of the Korean Chemical Society
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    • v.10 no.1
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    • pp.8-12
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    • 1989
  • The polycrystalline powder of (BaLa)(MgMo)$O_6$ has been prepared at $1350^{\circ}C$ in a nitrogen flowing atmosphere. The powder X-ray diffraction pattern indicates that (BaLa)(MgMo)$O_6$ has a cubic perovskite structure ($a_0$ = 8.019(3) $\AA)$ with 1:1 ordering or $Mg^{2+}$ and $Mo^{5+}$ in the oxide lattice. The infrared spectrum shows two strong absorption bands with their maxima at 600(${\nu}3$) and 365(${\nu}4$) cm-1, which are attributed to $2T_{1U}$, modes of molybdenum octahedra MoO6 in the crystal lattice. According to the magnetic susceptibility measurement, the compound shows a paramagnetic behavior which follows the Curie-Weiss law below room temperature with the effective magnetic moment 1.60(1){$\mu}B$, which is consistent with that of spin only value ($1.73{\mu}B$) for $Mo^{5+}$ ($4d^1$ electronic configuration). From the thermogravimetric and X-ray diffraction analyses, it has been found that (BaLa)(MgMo)$O_6$ decomposes gradually into $BaMoO_4$, $MoO_3$ and unidentified phases above $900^{\circ}C$ in an ambient atmosphere, absorbing about 0.25 mole $O_2$ per mole of Mo ion, which also supports that oxidation state of $Mo^{5+}$ in the (BaLa)(MgMo)$O_6$.

Interaction Behavior between Lanthanide Element and Ferritic-Martensitic Steel (란탄족 원소와 Ferritic-Martensitic 강의 반응 거동)

  • Kim, Jun Hwan;Baek, Jong Hyuk;Lee, Byoung Oon;Lee, Chan Bock;Yoon, Young Soo
    • Korean Journal of Metals and Materials
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    • v.48 no.8
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    • pp.691-698
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    • 2010
  • A study has been carried out to evaluate the interaction behavior between a lanthanide element and clad material in order to analyze the effect of the lanthanide element on the fuel cladding chemical interaction (FCCI). A diffusion couple test between Misch metal (70Ce-30La) and ferritic-martensitic steel (Gr.92) was performed at $660^{\circ}C$, followed by a microstructural analysis of the coupled sample. The results showed that Ce in the Misch metal, rather than La, reacted with the ferritic-martensitic steel (FMS) to form an interaction layer that penetrated the clad thickness. Fe diffused outside the clad interface to form an $Fe_2Ce$ compound, leaving a depletion of Fe caused by excess diffusion as well as by the formation of Cr-rich precipitation inside the interaction layer. The rate of growth followed the cubic rate law, which indicated that Fe depletion was caused by the diffusion of Fe and that the associated Cr-rich phase formation controlled the whole diffusion process.

Distribution of Coastal Ground Water Discharge from Surficial Aquifers of Major River Districts (권역별 충적층 지하수의 해안 유출량 분포)

  • Han, Soo Young;Hong, Sung Hun;Park, Namsik
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.26 no.1B
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    • pp.1-6
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    • 2006
  • Amount of coastal ground water discharge(CGD) of surficial aquifer via coastlines of Nakdong River watershed, Seomjin River watershed, Youngsan River watershed and Keum River watershed is estimated. Compared to other major hydrological components, such as evapo-transpiration and river discharge, CGD is not so large in the amount. However, it is important since coastal ground water can be developed relatively free of environmental impact on downstream area and since most of coastal areas currently suffers water shortage. Regional groundwater investigation data and assessment based on Darcy's law are used for estimating coastal groundwater discharge. In this work the amount of CGD across the coastlines of the four rivers is estimated as 1.8 billion cubic meter per year and that is about 2.3 percentage of total amount of annual precipitation. Nakdong River watershed is most appropriate region in view of developing groundwater.

Development of 2.5D Photon Dose Calculation Algorithm (2.5D 광자선 선량계산 알고리즘 개발)

  • 조병철;오도훈;배훈식
    • Progress in Medical Physics
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    • v.10 no.2
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    • pp.103-114
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    • 1999
  • In this study, as a preliminary study for developing a full 3D photon dose calculation algorithm, We developed 2.5D photon dose calculation algorithm by extending 2D calculation algorithm to allow non-coplanar configurations of photon beams. For this purpose, we defined the 3d patient coordinate system and the 3d beam coordinate system, which are appropriate to 3d treatment planning and dose calculation. and then, calculate a transformation matrix between them. For dose calculation, we extended 2d "Clarkson-Cunningham" model to 3d one, which can calculate wedge fields as well as regular and irregular fields on arbitrary plane. The simple Batho's power-law method was implemented as an inhomogeneity correction. We evaluated the accuracy of our dose model following procedures of AAPM TG#23; radiation treatment planning dosimetry verifications for 4MV of Varian Clinac-4. As results, PDDs (percent depth dose) of cubic fields, the accuracy of calculation are within 1% except buildup region, and $\pm$3% for irregular fields and wedge fields. And for 45$^{\circ}$ oblique incident beam, the deviations between measurements and calculations are within $\pm$4%. In the case of inhomogeneity correction, the calculation underestimate 7% at the lung/water boundary and overestimate 3% at the bone/water boundary. At the conclusions, we found out our model can predict dose with 5% accuracy at the general condition. we expect our model can be used as a tool for educational and research purpose.. purpose..

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Development of a Pipe Network Fluid-Flow Modelling Technique for Porous Media based on Statistical Percolation Theory (통계적 확산이론에 기초한 다공질체의 유동관망 유동해석 기법 개발)

  • Shin, Hyu-Soung
    • The Journal of Engineering Geology
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    • v.23 no.4
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    • pp.447-455
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    • 2013
  • A micro-mechanical pipe network model with the shape of a cube was developed to simulate the behavior of fluid flow through a porous medium. The fluid-flow mechanism through the cubic pipe network channels was defined mainly by introducing a well-known percolation theory (Stauffer and Aharony, 1994). A non-uniform flow generally appeared because all of the pipe diameters were allocated individually in a stochastic manner based on a given pore-size distribution curve and porosity. Fluid was supplied to one surface of the pipe network under a certain driving pressure head and allowed to percolate through the pipe networks. A percolation condition defined by capillary pressure with respect to each pipe diameter was applied first to all of the network pipes. That is, depending on pipe diameter, the fluid may or may not penetrate a specific pipe. Once pore pressures had reached equilibrium and steady-state flow had been attained throughout the network system, Darcy's law was used to compute the resultant permeability. This study investigated the sensitivity of network size to permeability calculations in order to find out the optimum network size which would be used for all the network modelling in this study. Mean pore size and pore size distribution curve obtained from field are used to define each of pipe sizes as being representative of actual oil sites. The calculated and measured permeabilities are in good agreement.

The Changes of Aperture Variation and Hydraulic Conductivity for Compression Variability (압력에 따른 균열 간극변화와 수리전도도 변화 관찰)

  • 채병곤;이철우;정교철;김용제
    • Journal of Soil and Groundwater Environment
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    • v.8 no.4
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    • pp.1-11
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    • 2003
  • In order to measure aperture variation dependent on normal stress and to characterize on relationship between aperture variation and hydraulic conductivity this study measured apertures of rock fractures under a high resolution confocal laser scanning microscope (CLSM) with application of five stages of uniaxial normal stresses. From this method the response of aperture can be continuously characterized on one specimen by different loads of normal stress. The results of measurements showed a rough geometry of fracture bearing non-uniform aperture. They also revealed different values of aperture variations according to the load stages on each position along a fracture due to the fracture roughness. Laboratory permeability tests were also conducted to evaluate the changes of permeability coefficients related to the aperture variations by different loads. The results of permeability tests revealed that the hydraulic conductivity was not reduced at a fixed rate with increase of normal load. Moreover, the rates of aperture variations did not match to those of hydraulic conductivity. The hydraulic conductivity calculated in this study did not follow the cubic law, representing that the parallel plate model is not suitable to express the fracture geometry corresponding to the results of aperture measurements under the CLSM.

Program Development to Evaluate Permeability Tensor of Fractured Media Using Borehole Televiewer and BIPS Images and an Assessment of Feasibility of the Program on Field Sites (시추공 텔리뷰어 및 BIPS의 영상자료 해석을 통한 파쇄매질의 투수율텐서 계산 프로그램 개발 및 현장 적용성 평가)

  • 구민호;이동우;원경식
    • The Journal of Engineering Geology
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    • v.9 no.3
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    • pp.187-206
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    • 1999
  • A computer program to numerically predict the permeability tensor of fractured rocks is developed using information on discontinuities which Borehole Televiewer and Borehole Image Processing System (BIPS) provide. It uses orientation and thickness of a large number of discontinuities as input data, and calculates relative values of the 9 elements consisting of the permeability tensor by the formulation based on the EPM model, which regards a fractured rock as a homogeneous, anisotropic porous medium. In order to assess feasibility of the program on field sites, the numerically calculated tensor was obtained using BIPS logs and compared to the results of pumping test conducted in the boreholes of the study area. The degree of horizontal anisotropy and the direction of maximum horizontal permeability are 2.8 and $N77^{\circ}CE$, respectively, determined from the pumping test data, while 3.0 and $N63^{\circ}CE$ from the numerical analysis by the developed program. Disagreement between two analyses, especially for the principal direction of anisotropy, seems to be caused by problems in analyzing the pumping test data, in applicability of the EPM model and the cubic law, and in simplified relationship between the crack size and aperture. Aside from these problems, consideration of hydraulic parameters characterizing roughness of cracks and infilling materials seems to be required to improve feasibility of the proposed program. Three-dimensional assessment of its feasibility on field sites can be accomplished by conducting a series of cross-hole packer tests consisting of an injecting well and a monitoring well at close distance.

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Hydro-Mechanical Modelling of Fault Slip Induced by Water Injection: DECOVALEX-2019 TASK B (Step 1) (유체 주입에 의한 단층의 수리역학적 거동 해석: 국제공동연구 DECOVALEX-2019 Task B 연구 현황(Step 1))

  • Park, Jung-Wook;Park, Eui-Seob;Kim, Taehyun;Lee, Changsoo;Lee, Jaewon
    • Tunnel and Underground Space
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    • v.28 no.5
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    • pp.400-425
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    • 2018
  • This study presents the research results and current status of the DECOVALEX-2019 project Task B. Task B named 'Fault slip modelling' is aiming at developing a numerical method to simulate the coupled hydro-mechanical behavior of fault, including slip or reactivation, induced by water injection. The first research step of Task B is a benchmark simulation which is designed for the modelling teams to familiarize themselves with the problem and to set up their own codes to reproduce the hydro-mechanical coupling between the fault hydraulic transmissivity and the mechanically-induced displacement. We reproduced the coupled hydro-mechanical process of fault slip using TOUGH-FLAC simulator. The fluid flow along a fault was modelled with solid elements and governed by Darcy's law with the cubic law in TOUGH2, whereas the mechanical behavior of a single fault was represented by creating interface elements between two separating rock blocks in FLAC3D. A methodology to formulate the hydro-mechanical coupling relations of two different hydraulic aperture models and link the solid element of TOUGH2 and the interface element of FLAC3D was suggested. In addition, we developed a coupling module to update the changes in geometric features (mesh) and hydrological properties of fault caused by water injection at every calculation step for TOUGH-FLAC simulator. Then, the transient responses of the fault, including elastic deformation, reactivation, progressive evolutions of pathway, pressure distribution and water injection rate, to stepwise pressurization were examined during the simulations. The results of the simulations suggest that the developed model can provide a reasonable prediction of the hydro-mechanical behavior related to fault reactivation. The numerical model will be enhanced by continuing collaboration and interaction with other research teams of DECOLVAEX-2019 Task B and validated using the field data from fault activation experiments in a further study.