• Title/Summary/Keyword: Cauchy method

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Shape Design of Disk Seal in $SF_6$ Gas Safety Valve using Taguchi method (다구찌법을 이용한 $SF_6$가스 안전밸브용 디스크 시일 형상의 설계)

  • Cho Seunghyun;Kim Chungkyun;Kim Younggyu
    • Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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    • 2004.11a
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    • pp.237-240
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    • 2004
  • Sulfur Hexafluoride, SF6 is widely used for leak detection and as a gaseous dielectric in transformers, condensers and circuit breakers. SF6 gas is also effective as a cleanser in the semiconductor industry. This paper presents a numerical study of the sealing force of disk type seal in SF6 gas safety valve. The sealing force on the disk seal is analyzed by the FEM method based on the Taguch's experimental design technique. Disk seals in SF6 gas safety valve are designed with 9 design models based on 3 different contact length, compressive ratio and gas pressure. The calculated results of Cauchy stress and strain showed that the sealing characteristics of Teflon PTFE is more effective compared to that of FKM(Viton), which is related to the stiffness of the materials. And also, the contact length of the disk seal is important design parameter for sealing the SF6 gas leakage in the safety valve.

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Large deflection analysis of edge cracked simple supported beams

  • Akbas, Seref Doguscan
    • Structural Engineering and Mechanics
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    • v.54 no.3
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    • pp.433-451
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    • 2015
  • This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

Nuclide composition non-uniformity in used nuclear fuel for considerations in pyroprocessing safeguards

  • Woo, Seung Min;Chirayath, Sunil S.;Fratoni, Massimiliano
    • Nuclear Engineering and Technology
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    • v.50 no.7
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    • pp.1120-1130
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    • 2018
  • An analysis of a pyroprocessing safeguards methodology employing the Pu-to-$^{244}Cm$ ratio is presented. The analysis includes characterization of representative used nuclear fuel assemblies with respect to computed nuclide composition. The nuclide composition data computationally generated is appropriately reformatted to correspond with the material conditions after each step in the head-end stage of pyroprocessing. Uncertainty in the Pu-to-$^{244}Cm$ ratio is evaluated using the Geary-Hinkley transformation method. This is because the Pu-to-$^{244}Cm$ ratio is a Cauchy distribution since it is the ratio of two normally distributed random variables. The calculated uncertainty of the Pu-to-$^{244}Cm$ ratio is propagated through the mass flow stream in the pyroprocessing steps. Finally, the probability of Type-I error for the plutonium Material Unaccounted For (MUF) is evaluated by the hypothesis testing method as a function of the sizes of powder particles and granules, which are dominant parameters to determine the sample size. The results show the probability of Type-I error is occasionally greater than 5%. However, increasing granule sample sizes could surmount the weakness of material accounting because of the non-uniformity of nuclide composition.

Multiple unequal cracks between an FGM orthotropic layer and an orthotropic substrate under mixed mode concentrated loads

  • M. Hassani;M.M. Monfared;A. Salarvand
    • Structural Engineering and Mechanics
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    • v.86 no.4
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    • pp.535-546
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    • 2023
  • In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

3-Dimensional Finite Element Analysis of Thermoforming Processes (열성형공정의 3차원 유한요소해석)

  • G.J. Nam;D.S. Son;Lee, J.W.
    • The Korean Journal of Rheology
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    • v.11 no.1
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    • pp.18-27
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    • 1999
  • Predicting the deformation behaviors of sheets in thermoforming processes has been a daunting challenge due to the strong nonlinearities arising from very large deformations, mold-polymer contact condition and hyperelasticity constitutive equations. Nonlinear numerical analysis is always required to face this challenge especially for realistic processing conditions. In this study a 3-D algorithm and the membrane approximation are developed for thermoforming processes. The constitutive equation is expressed in terms of the 2nd Piola-Kirchhoff stress tensor and the Cauchy-Green deformation tensor. The 2-term Mooney-Rivlin model is used for the material model equation. The algorithm is established by the finite element formulation employing the total Lagrangian coordinate. The deformation behavior and the stress distribution results of 3-D algorithm with various point boundary conditions are compared to those of the membrane approximation algorithm. Also, the slip boundary condition and the no-slip boundary condition are applied for the systems that have molds. Finally, the effect of sheet temperatures on the final thickness distribution is investigated for the ABS material.

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Experimental and numerical analysis of RC structure with two leaf cavity wall subjected to shake table

  • Onat, Onur;Lourenco, Paulo B.;Kocak, Ali
    • Structural Engineering and Mechanics
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    • v.55 no.5
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    • pp.1037-1053
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    • 2015
  • This paper presents finite element (FE) based pushover analysis of a reinforced concrete structure with a two-leaf cavity wall (TLCW) to estimate the performance level of this structure. In addition to this, an unreinforced masonry (URM) model was selected for comparison. Simulations and analyses of these structures were performed using the DIANA FE program. The mentioned structures were selected as two storeys and two bays. The dimensions of the structures were scaled 1:1.5 according to the Cauchy Froude similitude law. A shake table experiment was implemented on the reinforced concrete structure with the two-leaf cavity wall (TLCW) at the National Civil Engineering Laboratory (LNEC) in Lisbon, Portugal. The model that simulates URM was not experimentally studied. This structure was modelled in the same manner as the TLCW. The purpose of this virtual model is to compare the respective performances. Two nonlinear analyses were performed and compared with the experimental test results. These analyses were carried out in two phases. The research addresses first the analysis of a structure with only reinforced concrete elements, and secondly the analysis of the same structure with reinforced concrete elements and infill walls. Both researches consider static loading and pushover analysis. The experimental pushover curve was plotted by the envelope of the experimental curve obtained on the basis of the shake table records. Crack patterns, failure modes and performance curves were plotted for both models. Finally, results were evaluated on the basis of the current regulation ASCE/SEI 41-06.

A study of fracture of a fibrous composite

  • Mirsalimov, Vagif M.;Hasanov, Shahin H.
    • Structural Engineering and Mechanics
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    • v.73 no.5
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    • pp.585-598
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    • 2020
  • We develop design model within which nucleation and propagation of crack in a fibrous composite is described. It is assumed that under loading, crack initiation and fracture of material happens in the composite. The problem of equilibrium of a composite with embryonic crack is reduced to the solution of the system of nonlinear singular integral equations with the Cauchy type kernel. Normal and tangential forces in the crack nucleation zone are determined from the solution of this system of equations. The crack appearance conditions in the composite are formed with regard to criterion of ultimate stretching of the material's bonds. We study the case when near the fiber, the binder has several arbitrary arranged rectilinear prefracture zones and a crack with interfacial bonds. The proposed computational model allows one to obtain the size and location of the zones of damages (prefracture zones) depending on geometric and mechanical characteristics of the fibrous composite and applied external load. Based on the suggested design model that takes into account the existence of damages (the zones of weakened interparticle bonds of the material) and cracks with end zones in the composite, we worked out a method for calculating the parameters of the composite, at which crack nucleation and crack growth occurs.

The Nonlinear Motions of Cylinders(II) - Translating and Heaving Problem, Body Motion in Waves - (주상체의 비선형 운동(II) -전진동요문제, 파랑중의 운동-)

  • H.Y. Lee;J.H. Hwang
    • Journal of the Society of Naval Architects of Korea
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    • v.30 no.1
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    • pp.45-64
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    • 1993
  • This paper dealt with the application of a numerical method developed by the authors using the matching method proposed in the previous paper on "The Nonlinear motions of cylinders(I)[16]", and Cauchy's theorem to the problems associated with hydrodynamic forces acting on a heaving cylinders translating in a calm water and also motions of cylinders in waves. In spectral method. body boundary condition in submerged case is satisfied exactly but one in floating case is not satisfied exactly. In the numerical code developed here, the boundary condition at the free-surface and body surface is satisfied exactly at its instaneous position. It is of interest to note that the present scheme could be applied to a free-surface-piercing body without experiencing a difficulty in the numerical convergence. The computed results are compared with other results([6], [12]).

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Combined Image Retrieval System using Clustering and Condensation Method (클러스터링과 차원축약 기법을 통합한 영상 검색 시스템)

  • Lee Se-Han;Cho Jungwon;Choi Byung-Uk
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.43 no.1 s.307
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    • pp.53-66
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    • 2006
  • This paper proposes the combined image retrieval system that gives the same relevance as exhaustive search method while its performance can be considerably improved. This system is combined with two different retrieval methods and each gives the same results that full exhaustive search method does. Both of them are two-stage method. One uses condensation of feature vectors, and the other uses binary-tree clustering. These two methods extract the candidate images that always include correct answers at the first stage, and then filter out the incorrect images at the second stage. Inasmuch as these methods use equal algorithm, they can get the same result as full exhaustive search. The first method condenses the dimension of feature vectors, and it uses these condensed feature vectors to compute similarity of query and images in database. It can be found that there is an optimal condensation ratio which minimizes the overall retrieval time. The optimal ratio is applied to first stage of this method. Binary-tree clustering method, searching with recursive 2-means clustering, classifies each cluster dynamically with the same radius. For preserving relevance, its range of query has to be compensated at first stage. After candidate clusters were selected, final results are retrieved by computing similarities again at second stage. The proposed method is combined with above two methods. Because they are not dependent on each other, combined retrieval system can make a remarkable progress in performance.

Initialization by using truncated distributions in artificial neural network (절단된 분포를 이용한 인공신경망에서의 초기값 설정방법)

  • Kim, MinJong;Cho, Sungchul;Jeong, Hyerin;Lee, YungSeop;Lim, Changwon
    • The Korean Journal of Applied Statistics
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    • v.32 no.5
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    • pp.693-702
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    • 2019
  • Deep learning has gained popularity for the classification and prediction task. Neural network layers become deeper as more data becomes available. Saturation is the phenomenon that the gradient of an activation function gets closer to 0 and can happen when the value of weight is too big. Increased importance has been placed on the issue of saturation which limits the ability of weight to learn. To resolve this problem, Glorot and Bengio (Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 249-256, 2010) claimed that efficient neural network training is possible when data flows variously between layers. They argued that variance over the output of each layer and variance over input of each layer are equal. They proposed a method of initialization that the variance of the output of each layer and the variance of the input should be the same. In this paper, we propose a new method of establishing initialization by adopting truncated normal distribution and truncated cauchy distribution. We decide where to truncate the distribution while adapting the initialization method by Glorot and Bengio (2010). Variances are made over output and input equal that are then accomplished by setting variances equal to the variance of truncated distribution. It manipulates the distribution so that the initial values of weights would not grow so large and with values that simultaneously get close to zero. To compare the performance of our proposed method with existing methods, we conducted experiments on MNIST and CIFAR-10 data using DNN and CNN. Our proposed method outperformed existing methods in terms of accuracy.