• Title/Summary/Keyword: Upper-lower solutions

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Effect of the welding speed on the characteristics of Nd:YAG laser welds for automotive application : 600MPa PH high strength steel (600MPa급 자동차용 석출경화형 고장력강판 Nd:YAG 레이저 용접부의 특성에 미치는 용접속도의 영향)

  • Han, Tae-Kyo;Jung, Byung-Hun;Kang, Chung-Yun
    • Laser Solutions
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    • v.10 no.3
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    • pp.25-32
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    • 2007
  • The effect of welding speed on the weldability, microstructures, hardness, tensile property of Nd:YAG laser welding joint in 600MPa grade precipitation hardening high strength steel was investigated. A shielding gas was not used, and bead-on-plate welding was performed using various welding speeds at a power of 3.5kW. Porosity in the joints occurred at 1.8m/min, but were not observed over the welding speed of 2.1m/min. However, spatter occurred over the welding speed of 6.6m/min. The hardness was the highest at heat affected zone(HAZ) near fusion zone(FZ), and was decreased on approaching to the base metal. The maximum hardness increased with increasing welding speed. The microstructure of FZ was composed of coarse grain boundary ferrite and bainite(upper) but the HAZ near the FZ contained bainite(Lower) and fine ferrite at a low welding speed. With increasing welding speed, ferrite at the FZ and the HAZ became finely and upper binite changed to lower bainite. In a perpendicular tensile test to the weld line, all specimens were fractured at the base metal, and the tensile strength and the yield strength of joints was equal to those of raw material. Elongation was found to be lower than that of the raw material.

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Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory

  • Adim, Belkacem;Daouadji, Tahar Hassaine
    • Advances in materials Research
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    • v.5 no.4
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    • pp.223-244
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    • 2016
  • In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

Analytical approaches to the charging process of stratified thermal storage tanks with variable inlet temperature (변온유입 성층축열조의 충전과정에 대한 해석적 접근)

  • Yoo, Hoseon
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.9 no.1
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    • pp.43-54
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    • 1997
  • This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

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Some Aspects of Kaoline-Pyrophyllite Deposits in Southern Korea (한반도(韓半島) 남부지역(南部地域)의 고령토-납석광상(鑛床) 생성기구(生成機構))

  • Sang, Ki Nam
    • Economic and Environmental Geology
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    • v.19 no.spc
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    • pp.43-52
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    • 1986
  • Kaolin-pyrophyllite are locally abundant in the three hydrothermal areas at Yangsan-Tongnae area, Hadong-Sancheong area and Haenam area, deposits are originally composed of acidic volcanic rocks and anorthositic rocks in Hadong-Sancheong area. The clay deposits are formed in the near shallow depths environment through acid hydrothermal alteration. Hadong-Sancheong halloysite deposits are formed by alteration of anorthosite. These differences are mainly on the various country rocks, geological structure and properties of hydrothermal solutions. Country rock is mostly underlain by rhyolitic tuffaceous and anorthositic rocks and a large number of clay deposits were formed during volcanic activity through upper Cretaceous-lower Tertiary. Intrusive rocks is broadly distributed in this area and clay deposits are variable in shapelayer and funnel typed. Zonal pattern of mineral assemblage is as follows, Yangsan-Tongnae deposits-kaolinite, pyrophyllite, dumortierite, andalusite and sericite, Hadong-Sancheong-mostly halloysite, and Haenam-dickite, pyrophyllite, alunite and diaspore. The difference in the zonal pattern of altered rock is considered to depend on differences in the initial acidity of related hydrothermal solution, initial acidity was controlled by the oxygen fugacity.

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Lap joint Laser Welding of Hot Stamped Ultra High Strength Steel for Automotive Application (자동차용 핫스탬핑 고강도강 판재의 겹치기 레이저용접)

  • Kim, Yong;Park, Ki-Young;Lee, Kyoung-Don
    • Laser Solutions
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    • v.15 no.1
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    • pp.1-5
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    • 2012
  • Recently ultra high strength steels(UHSS) has been widely applied to the structural or safety components in the automotive industry. Specially, hot stamping boron steel 22MnB5 has shown the crash-resistant characteristics when applying to bumpers and pillars. Lap joint Laser welding of the hot stamped and die quenched sheets of Boron steel was carried out using 3kW Nd/YAG laser. The appropriate Lap joint laser welding conditions were founded separately for four lap joint combinations. The lower sheest is a hot stamped sheet in common and the upper sheet is selected among the hot stamped steel and high strength steels such as SPCC, 370MPa, and 590MPa grade high strength steels. Cross bead sections and local hardening and softening were observed as well as tensile-shear test results.

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Finite Element Model Updating of Framed Structures Using Constrained Optimization (구속조건을 가진 최적화기법을 이용한 골조구조물의 유한요소모델 개선기법)

  • Yu, Eun-Jong;Kim, Ho-Geun
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2007.11a
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    • pp.446-451
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    • 2007
  • An Improved finite element model updating method to address the numerical difficulty associated with ill-conditioning and rank-deficiency. These difficulties frequently occur in model updating problems, when the identification of a larger number of physical parameters is attempted than that warranted by the information content of the experimental data. Based on the standard Bounded Variables Least-squares (BVLS) method, which incorporates the usual upper/lower-bound constraints, the proposed method is equipped with new constraints based on the correlation coefficients between the sensitivity vectors of updating parameters. The effectiveness of the proposed method is investigated through the numerical simulation of a simple framed structure by comparing the results of the proposed method with those obtained via pure BVLS and the regularization method. The comparison indicated that the proposed method and the regularization method yield approximate solutions with similar accuracy.

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Application of Adaptive Particle Swarm Optimization to Bi-level Job-Shop Scheduling Problem

  • Kasemset, Chompoonoot
    • Industrial Engineering and Management Systems
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    • v.13 no.1
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    • pp.43-51
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    • 2014
  • This study presents an application of adaptive particle swarm optimization (APSO) to solving the bi-level job-shop scheduling problem (JSP). The test problem presented here is $10{\times}10$ JSP (ten jobs and ten machines) with tribottleneck machines formulated as a bi-level formulation. APSO is used to solve the test problem and the result is compared with the result solved by basic PSO. The results of the test problem show that the results from APSO are significantly different when compared with the result from basic PSO in terms of the upper level objective value and the iteration number in which the best solution is first identified, but there is no significant difference in the lower objective value. These results confirmed that the quality of solutions from APSO is better than the basic PSO. Moreover, APSO can be used directly on a new problem instance without the exercise to select parameters.

RATIONAL DIFFERENCE EQUATIONS WITH POSITIVE EQUILIBRIUM POINT

  • Dubickas, Arturas
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.645-651
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    • 2010
  • In this note we study positive solutions of the mth order rational difference equation $x_n=(a_0+\sum{{m\atop{i=1}}a_ix_{n-i}/(b_0+\sum{{m\atop{i=1}}b_ix_{n-i}$, where n = m,m+1,m+2, $\ldots$ and $x_0,\ldots,x_{m-1}$ > 0. We describe a sufficient condition on nonnegative real numbers $a_0,a_1,\ldots,a_m,b_0,b_1,\ldots,b_m$ under which every solution $x_n$ of the above equation tends to the limit $(A-b_0+\sqrt{(A-b_0)^2+4_{a_0}B}$/2B as $n{\rightarrow}{\infty}$, where $A=\sum{{m\atop{i=1}}\;a_i$ and $B=\sum{{m\atop{i=1}}\;b_i$.

An Approximate Analysis of a Stochastic Fluid Flow Model Applied to an ATM Multiplexer (ATM 다중화 장치에 적용된 추계적 유체흐름 모형의 근사분석)

  • 윤영하;홍정식;홍정완;이창훈
    • Journal of the Korean Operations Research and Management Science Society
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    • v.23 no.4
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    • pp.97-109
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    • 1998
  • In this paper, we propose a new approach to solve stochastic fluid flow models applied to the analysis of ceil loss of an ATM multiplexer. Existing stochastic fluid flow models have been analyzed by using linear differential equations. In case of large state space, however. analyzing stochastic fluid flow model without numerical errors is not easy. To avoid this numerical errors and to analyze stochastic fluid flow model with large state space. we develope a new computational algorithm. Instead of solving differential equations directly, this approach uses iterative and numerical method without calculating eigenvalues. eigenvectors and boundary coefficients. As a result, approximate solutions and upper and lower bounds are obtained. This approach can be applied to stochastic fluid flow model having general Markov chain structure as well as to the superposition of heterogeneous ON-OFF sources it can be extended to Markov process having non-exponential sojourn times.

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A SUFFICIENT CONDITION FOR THE UNIQUENESS OF POSITIVE STEADY STATE TO A REACTION DIFFUSION SYSTEM

  • Kang, Joon-Hyuk;Oh, Yun-Myung
    • Journal of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.377-385
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    • 2002
  • In this paper, we concentrate on the uniquencess of the positive solution for the general elliptic system $\Delta$u+u($g_1$(u)-$g_2$(v))=0 $\Delta$u+u($h_1$(u)-$h_2$(v))=0 in$R_{+}$ $\times$ $\Omega$, $u\mid\partial\Omega = u\mid\partial\Omega = 0$. This system is the general model for the steady state of a competitive interacting system. The techniques used in this paper are upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.