• Title/Summary/Keyword: infinite case

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Dislocation in Semi-infinite Half Plane Subject to Adhesive Complete Contact with Square Wedge: Part II - Approximation and Application of Corrective Functions (직각 쐐기와 응착접촉 하는 반무한 평판 내 전위: 제2부 - 보정 함수의 근사 및 응용)

  • Kim, Hyung-Kyu
    • Tribology and Lubricants
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    • v.38 no.3
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    • pp.84-92
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    • 2022
  • In Part I, developed was a method to obtain the stress field due to an edge dislocation that locates in an elastic half plane beneath the contact edge of an elastically similar square wedge. Essential result was the corrective functions which incorporate a traction free condition of the free surfaces. In the sequel to Part I, features of the corrective functions, Fkij,(k = x, y;i,j = x,y) are investigated in this Part II at first. It is found that Fxxx(ŷ) = Fxyx(ŷ) where ŷ = y/η and η being the location of an edge dislocation on the y axis. When compared with the corrective functions derived for the case of an edge dislocation at x = ξ, analogy is found when the indices of y and x are exchanged with each other as can be readily expected. The corrective functions are curve fitted by using the scatter data generated using a numerical technique. The algebraic form for the curve fitting is designed as Fkij(ŷ) = $\frac{1}{\hat{y}^{1-{\lambda}}I+yp}$$\sum_{q=0}^{m}{\left}$$\left[A_q\left(\frac{\hat{y}}{1+\hat{y}} \right)^q \right]$ where λI=0.5445, the eigenvalue of the adhesive complete contact problem introduced in Part I. To investigate the exponent of Fkij, i.e.(1 - λI) and p, Log|Fkij|(ŷ)-Log|(ŷ)| is plotted and investigated. All the coefficients and powers in the algebraic form of the corrective functions are obtained using Mathematica. Method of analyzing a surface perpendicular crack emanated from the complete contact edge is explained as an application of the curve-fitted corrective functions.

Effects of inclined bedrock on dissimilar pile composite foundation under vertical loading

  • Kaiyu, Jiang;Weiming, Gong;Jiang, Xu;Guoliang, Dai;Xia, Guo
    • Geomechanics and Engineering
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    • v.31 no.5
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    • pp.477-488
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    • 2022
  • Pile composite foundation (PCF) has been commonly applied in practice. Existing research has focused primarily on semi-infinite media having equal pile lengths with little attention given to the effects of inclined bedrock and dissimilar pile lengths. This investigation considers the effects of inclined bedrock on vertical loaded PCF with dissimilar pile lengths. The pile-soil system is decomposed into fictitious piles and extended soil. The Fredholm integral equation about the axial force along fictitious piles is then established based on the compatibility of axial strain between fictitious piles and extended soil. Then, an iterative procedure is induced to calculate the PCF characteristics with a rigid cap. The results agree well with two field load tests of a single pile and numerical simulation case. The settlement and load transfer behaviors of dissimilar 3-pile PCFs and the effects of inclined bedrock are analyzed, which shows that the embedded depth of the inclined bedrock significantly affects the pile-soil load sharing ratios, non-dimensional vertical stiffness N0/wdEs, and differential settlement for different length-diameter ratios of the pile l/d and pile-soil stiffness ratio k conditions. The differential settlement and pile-soil load sharing ratios are also influenced by the inclined angle of the bedrock for different k and l/d. The developed model helps better understand the PCF characteristics over inclined bedrock under vertical loading.

PERISTALTIC PUMPING OF AN ELLIS FLUID IN AN INCLINED ASYMMETRIC CHANNEL

  • A. SMALL;P. NAGARANI;M. NARAHARI
    • Journal of applied mathematics & informatics
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    • v.41 no.1
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    • pp.51-70
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    • 2023
  • The flow of an incompressible Ellis fluid in an inclined asymmetric channel, driven by peristaltic waves was studied under low Reynolds number and long wavelength assumptions. The wave on each side of the channel are assumed to be an infinite train of sinusoidal waves, both having the same constant wave speed and wavelength however, they vary in wave amplitude, channel half width and phase angle. We derived expressions for the axial and transverse velocities, volume flow rate, pressure rise per unit wavelength and streamlines. The effects of varying the wave amplitudes, the phase angle, the channel width, the angle of inclination of the channel as well as the fluid parameters on the flow were analyzed. Trapping conditions were determined and the presence of reflux highlighted using the streamlines for the necessary channel and fluid conditions. By varying the fluid parameters, changes in the fluid that deviated from the Newtonian case resulted in a reduction in the axial velocity in the neighborhood of the center of the channel and a simultaneous increase in the velocity at the periphery of the channel. A nonlinear relation was observed with the pressure rise and the volume flow rate. This nonlinear relation is more pronounced with an increase in the absolute value of the volume flow rate. For Newtonian fluids a linear relation exists between these two variables. The fluid parameters had little effects on the streamlines. However, variations of the wave amplitudes, volume flow, channel width and phase angle had greater effects on the streamlines and hence the trapped region.

A Risk Evaluation Method of Slope Failure Due to Rainfall using a Digital Terrain Model (수치지형모델을 이용한 강우시 사면 붕괴 위험도 평가에 관한 제안)

  • Chae, JongGil;Jung, MinSu;Torii, Nobuyuki;Okimura, Takashi
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.6C
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    • pp.219-229
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    • 2010
  • Slope failure in South Korea generally occurs by the localized heavy rain in a rainy season and typhoon, and it annually causes huge losses of both life and property because nearly 70% of territory in South Korea is covered with mountains. It is required to measure the risk of slope failure quantitatively before proper prevention methods are provided. However, there is no way to estimate the risk based on realtime rainfall, geological characteristics, and geotechnical engineering properties. This study presents the development of digital terrion model to predict slope stability using infinite slope stability theory combined with temporal groundwater change. Case studies were performed to investigate factors to affect slope stability in Japan.

Slopes Risk Assessment Techniques through Pattern Classification (패턴분류를 통한 산지사면의 위험도 평가 기법)

  • Kim, Min-Seub;Kim, Jin-Young
    • The Journal of Engineering Geology
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    • v.25 no.2
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    • pp.189-199
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    • 2015
  • Our country's leading granite weathered soil of the ground slope failures that occur in cutting slope most cases, it does not require in-depth to the shear strength most of the surface layer is affected by weathering (1~2 m) at a shallow depth close to the ground, it is important to identify the reliability. Based on the result obtained in actual field investigation, the field slope type was classified by each type of wedge slope, Infinite slope, finite slope -I and finite slope -II, and the slope stability was examined respectively. In addition, using the numerical analysis results, the relationship between the slope inclination angle and safety factor was analyzed and it tried to offer basic data to which the stability in the field slope was able to be estimated by analyzing the safety factor change of the slope according to the slope type. In this study, classified into four types of natural slope, safety factor estimation method by slope types is proposed through the numerical analysis. However, some limit exists in generalizing in this research because it does not test various case studies. Therefore, the case study of a wide range of various sypes to assess the safety of various types slope can be made, accommodate a wide range of field conditions reasonable risk evaluation criteria may be derived.

Analysis on Characteristics of Sediment Produce by Landslide in a Basin 1. Simulation of Sediment Produce and its Verification (유역 내에서의 산사태에 의한 토사발생특성 분석 1. 토사발생모의 및 검증)

  • Yoo, Chul-Sang;Kim, Kee-Wook;Kim, Seong-Joon;Lee, Mi-Seon
    • Journal of the Korean Society of Hazard Mitigation
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    • v.10 no.3
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    • pp.133-145
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    • 2010
  • This study analyzed the characteristics of sediment produce by landslide triggered by rainfall. One-dimensional unsaturated groundwater model and infinite slope stability analysis were used to estimate the behavior of soil moisture and slope stability according to rainfall, respectively. Slope stability analysis was performed considering on soil depth and characteristics of trees. As the results considering on recovery of the failed slopes, much amount of sediment was produced in 1963, 1970, and 2002. As the results of verification of simulation results using Landsat 5 TM images, we can find differences of landslide location between the results from model and satellite images. These differences can be caused by uncertainties of the rough parameters in the model. However, in the case that Obong-dam basin was divided into two subbasin, Wangsan-chun and Doma-chun basin, the results of each subbasin show errors around 20%. And only 4% of error occurred in the case of comparing landslide area on the entire Obong-dam basin. These errors seem insignificant considering on the errors which can be caused from the analyses in this study such as estimation of sediment produce, soil cover classification, and estimation of landslide area.

Finite Element Simulation of Laser-Generated Ultrasound and Interaction with Surface Breaking Cracks (유한요소법을 이용한 레이저 유도 초음파와 표면 균열과의 상호작용 모델링)

  • Jeong, Hyun-Jo;Park, Moon-Cheol
    • Journal of the Korean Society for Nondestructive Testing
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    • v.24 no.3
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    • pp.259-267
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    • 2004
  • A finite element method is used to simulate interaction of laser-based ultrasounds with surface breaking tracks in elastic media. The laser line source focused on the surface of semi-infinite medium is modeled as a shear dipole in 2-D plane strain finite elements. The shear dipole-finite clement model is found to give correct directivity patterns for generated longitudinal and shear waves. The interaction of surface waves with surface breaking cracks (2-D machined slot) is considered in two ways. Both the source and receiver are fixed with respect to the cracks in the first case, while the source is moving in another case. It is shown that the crack depth tested in the range of 0.3-5.0mm $({\lambda}_R/d=0.21{\sim}3.45)$ can be measured using the corner reflected waves produced by the fixed laser source. The moving laser source is found to cause a large amplitude change of reflected waves near crack, and the crack whose depth is one order lower than the wavelength ran be detected from this change.

Structural Analysis of Damping Hinge for Built-in Side-by-Side Refrigerator and Design Improvement of Bracket Pin to Reduce Stress Concentration (빌트인 양문형 냉장고 댐핑힌지의 구조해석 및 브래킷핀의 응력집중 저감을 위한 설계개선)

  • Lee, Boo-Youn
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.1
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    • pp.373-379
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    • 2020
  • This study performed stress and fatigue life analysis of the damping hinge of a built-in side-by-side refrigerator that occurs when the door is opened to the maximum angle. An analysis of the initial design showed that stress concentration occurred at the corner between the cylinder and upper disk of the bracket pin, and the maximum stress exceeded the yield strength. The maximum stress location and the calculated fatigue life were consistent with the door opening-and-closing endurance test results for a prototype. Three cases of design improvement for the bracket pin were derived with the aim of reducing the stress concentration that appeared in the initial design. An analysis of the cases showed that inserting a fillet between the disk and the cylinder of the bracket pin reduced the stress and increased the fatigue life. Moreover, changing the disk into two steps was more favorable. In conclusion, the best design improvement was the case that the disk was changed to two steps and the fillet with a large radius was inserted. In that case, the stress was the smallest and the fatigue life was infinite.

Numerical Analysis of Dynamic Response of Floating Offshore Wind Turbine to the Underwater Explosion using the PML Non-reflecting Technique (PML 무반사 기법을 이용한 부유식 해상풍력발전기의 수중폭발에 따른 동응답 수치해석)

  • Cho, Jin-Rae;Jeon, Soo-Hong;Jeong, Weui-Bong
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.29 no.6
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    • pp.521-527
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    • 2016
  • This paper is concerned with the numerical analysis of dynamic response of floating offshore wind turbine subject to underwater explosion using an effective non-reflecting technique. An infinite sea water domain was truncated into a finite domain, and the non-reflecting technique called the perfectly matched layer(PML) was applied to the boundary of truncated finite domain to absorb the inherent reflection of out-going impact wave at the boundary. The generalized transport equations that govern the inviscid compressible water flow was split into three PML equations by introducing the direction-wise absorption coefficients and state variables. The fluid-structure interaction problem that is composed of the wind turbine and the sea water flow was solved by the iterative coupled Eulerian FVM and Largangian FEM. And, the explosion-induced hydrodynamic pressure was calculated by JWL(Jones-Wilkins-Lee) equation of state. Through the numerical experiment, the hydrodynamic pressure and the structural dynamic response were investigated. It has been confirmed that the case using PML technique provides more reliable numerical results than the case without using PML technique.

Exploring the Implications of Peirce's Abduction in Science Education by Theoretical Investigation (Peirce의 귀추법에 관한 이론적 고찰을 통한 과학교육적 함의 탐색)

  • Joung, Yong-Jae;Song, Jin-Woong
    • Journal of The Korean Association For Science Education
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    • v.26 no.6
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    • pp.703-722
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    • 2006
  • The purpose of this study is to investigate the characteristics of abduction suggested by C. S. Peirce, and to discuss its implications in science education. Peirce's abduction is the logic of generating hypothesis. Abduction is a kind of logical inference, which colligates general rule and the observed result, and then it makes us judge the observed result as a case of the general rule on the basis of their resemblance. The process of abduction is also the logic of inquiry. In a Peirce's view, inquiry is a struggle for escaping from the condition of 'doubt' and to 'belief the nature of which is the establishment of habits. Because what habit an object has is its whole meaning, in his views, the fixation of belief is the way of attaining the truth related to it. The beliefs of individuals, however, are always fallible. So, to attain a truth, we need the terminal opinion of community of inquiry that could conduct infinite inquiry. These characteristics of Peirce's abduction give suggestions in science education as follows; firstly, hypothesis generating which transforms the condition of 'doubt' into the 'belief by considering practical effects should be highlighted, secondly, logical inference which makes us judge the observed result as a case of the general rule on the basis of resemblance should be highlighted, and thirdly, communities of inquiry which stand on the view of modest realism should be intended toward. These results could be expected in playing a role in critical discussion on science education relating to abduction.