• Title/Summary/Keyword: hyperbolic function

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A Comparative Study of Material Flow Stress Modeling by Artificial Neural Networks and Statistical Methods (신경망을 이용한 HSLA 강의 고온 유동응력 예측 및 통계방법과의 비교)

  • Chun, Myung-Sik;Yi, Joon-Jeong;Jalal, B.;Lenard, J.G.
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.21 no.5
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    • pp.828-834
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    • 1997
  • The knowledge of material stress-strain behavior is an essential requirement for design and analysis of deformation processes. Empirical stress-strain relationship and constitutive equations describing material behavior during deformation are being widely used, despite suffering some drawbacks in terms of ease of development, accuracy and speed. In the present study, back-propagation neural networks are used to model and predict the flow stresses of a HSLA steel under conditions of constant strain, strain rate and temperature. The performance of the network model is comparedto those of statistical models on rate equations. Well-trained network model provides fast and accurate results, making it superior to statistical models.

Hybrid finite element model for wave transformation analysis (파랑 변형 해석을 위한 복합 유한요소 모형)

  • Jung Tae Hwa;Park Woo Sun;Suh Kyung Duck
    • Proceedings of the KSME Conference
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    • 2002.08a
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    • pp.209-212
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    • 2002
  • Since Berkhoff proposed the mild-slope equation in 1972, it has widely been used for calculation of shallow water wave transformation. Recently, it was extended to give an extended mild-slope equation, which includes the bottom slope squared term and bottom curvature term so as to be capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. In the present study, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize . The computational domain was discretized with proper finite elements, while the radiation condition at infinity was treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model was verified through example analyses of two-dimensional wave reflection and transmission. .

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Constitutive Equation for Clay in Overconsolidation State and Under Cyclic Loading (과압밀상태 및 반복하중을 받는 점토지반에 대한 구성모델)

  • 이승래;김주용
    • Geotechnical Engineering
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    • v.10 no.1
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    • pp.7-18
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    • 1994
  • A new model for describing the behavior of clay under monotonic and cyclic loading is proposed. This model uses the hyperbolic representation for the stress -strain relationship in overconsolidated state and it describes undrained effective stress path on the basis of the critical state theory. The developed constitutive model by using an energy dissipation equation can describe the behavior of clay in heavily overconsolidated state as u.ell as lightly overconsolidated state under monotonic loading. In order to extend the model for the behavior of clay under cyclic loading, a shift function of undrained stress spacing ratio is introduced in the constitutive model developed for monotonlc loading. A single additional parameter is required to represent the cyclic effect and it can be reasonably deter mined from the test results. The measured behavior in undrained cyclic triaxial tests has been easily and precisely predicted by the newly developed constitutive model.

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Evaluation of Creep Behaviors of Alloy 690 Steam Generator Tubing Material (Alloy 690 증기발생기 전열관 재료의 크리프 거동 평가)

  • Kim, Jong Min;Kim, Woo Gon;Kim, Min Chul
    • Transactions of the Korean Society of Pressure Vessels and Piping
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    • v.15 no.2
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    • pp.64-70
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    • 2019
  • In recent years, attention has been paid to the integrity of steam generator (SG) tubes due to severe accident and beyond design basis accident conditions. In these transient conditions, steam generator tubes may be damaged by high temperature and pressure, which might result in a risk of fission products being released to the environment due to the failure. Alloy 690 which has increased the Cr content has been replaced for the SG tube due to its high corrosion resistance against stress corrosion cracking (SCC). However, there is lack of research on the high temperature creep rupture and life prediction model of Alloy 690. In this study, creep test was performed to estimate the high temperature creep rupture life of Alloy 690 using tube specimens. Based on manufacturer's creep data and creep test results performed in this study, creep life prediction was carried out using the Larson-Miller (LM) Parameter, Orr-Sherby-Dorn (OSD) parameter, Manson-Haford (MH) parameter, and Wilshire's approach. And a hyperbolic sine (sinh) function to determine master curves in LM, OSD and MH parameter methods was used for improving the creep life estimation of Alloy 690 material.

A Study on Residual Stress Characteristics for Joint of Rock in Ring Shear Tests (링 전단시험기를 이용한 암석절리의 잔류강도 특성에 관한 연구)

  • 권준욱;김선명;윤지선
    • Journal of the Korean Geotechnical Society
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    • v.16 no.6
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    • pp.35-41
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    • 2000
  • Residual stress is defined as a minimum stress with a large displacement of specimens and the residual stress after peak shear stress appears with displacement volume but there is no provision to select the residual stress. In the previous study, residual stress was recorded when the change of shear load is small in the condition of the strain more than 15%. But, in this study, hyperbolic function((No Abstract.see full/text), b=experimental constant) of soil test is adapted to joint of rock and the propriety is investigated. In a landslide and landsliding of artificial slope, wedge failure of tunnel with a large displacement, tests are simulated from peak stress to residual stress for safety analysis. But now. direct shear stress and triaxial compressive tests are usually performed to find out characteristics of shear stress about joint. Although these tests get a small displacement, that data of peak stress and residual stress are used for safety analysis. In this study, we tried to determine failure criteria for joints of rock using ring shear test machine. The residual stress following shear behavior was determined by the result of ring shear test and direct shear test. In conclusion, after comparing the results of the two test, we found that cohesion(c) and internal friction angle(ø) of ring shear test are 30% and 22% respectively of those of the direct shear test.

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Evaluation methods for Void Closing Behavior in Large Ingot (기공닫힘부 폐쇄정도 결정을 위한 평가방법 연구)

  • Choi, I.J.;Choi, H.J.;Yoon, D.J.;Lee, G.A.;Lim, S.J.
    • Transactions of Materials Processing
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    • v.20 no.5
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    • pp.339-343
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    • 2011
  • This paper presents methods for analyzing the extent of cylindrical-shaped void closure. In addition, a quantitative relationship between change in void fraction and height reduction ratio of a compressed specimen is proposed. The height reduction ratio, number of deformation steps and billet rotation were chosen as key process parameters influencing the void closing behavior, namely, the changes in void shape and size during hot open die forging of a large ingot. The extent of void closure was analyzed from microscopic observations and estimated from tensile test results. The tensile strengths of specimens with closed voids and those without were compared for various reduction ratios in height. The results confirmed that void closure occurs at reduction ratios greater than 30 %. The void closing behavior could be expressed as a hyperbolic tangent function of reduction ratio in height, number of paths, and billet rotation. The knowledge presented in this paper could be helpful for optimizing deformation paths in open die forging processes.

Stress Distributions in a Plate due to Shear Loading Uniformly Distributed on the End Portions of its Side Boundary. (부분적(部分的)인 균일전단하중(均一傳達荷重)을 받는 평판(平板)에서의 응력분포(應力分布))

  • Hyo-Chul,Kim
    • Bulletin of the Society of Naval Architects of Korea
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    • v.7 no.1
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    • pp.37-44
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    • 1970
  • The plate under shear loading umformly distributed on the end portions of its side boundary was considered. Infinite hyperbolic serieses and Fourier serieses were combined as a stress function and from which exact solutions for the 15 cases for the parameters of b/L=0.25, 0.5, 1.0 and l/L=0.2, 0.4, 0.6, 0.8, 1.0 are obtained. In each cases the first 5 terms of the infinite series at the 36 points as shown in Fig. 3. The results are presented in Fig. 4-1, 4-2, and 4-3. The conclusions are as follows: 1) The stresses ${\sigma}_x$ increase very slightly as $\chi$ increases in the range of 0<x<L-l 2) When the parameters satisfy the conditions b/L<0.25 and l/L<0.2, the stresses in the region of 0<x<L-l can be obtained by replacing the uniform shear loading by the equivalent uniform shear loading by the equivalent uniform tensile force and pure bending moment at x=l. 3) The stress ${\sigma}_y$ is negligible throughout the region. 4) When the parameter b/L varies, the stresses ${\sigma}_x$ and u vary as L/b, while strain $\upsilon$ varies as $(L/b)^2$.

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A predictive model for compressive strength of waste LCD glass concrete by nonlinear-multivariate regression

  • Wang, C.C.;Chen, T.T.;Wang, H.Y.;Huang, Chi
    • Computers and Concrete
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    • v.13 no.4
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    • pp.531-545
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    • 2014
  • The purpose of this paper is to develop a prediction model for the compressive strength of waste LCD glass applied in concrete by analyzing a series of laboratory test results, which were obtained in our previous study. The hyperbolic function was used to perform the nonlinear-multivariate regression analysis of the compressive strength prediction model with the following parameters: water-binder ratio w/b, curing age t, and waste glass content G. According to the relative regression analysis, the compressive strength prediction model is developed. The calculated results are in accord with the laboratory measured data, which are the concrete compressive strengths of different mix proportions. In addition, a coefficient of determination $R^2$ value between 0.93 and 0.96 and a mean absolute percentage error MAPE between 5.4% and 8.4% were obtained by regression analysis using the predicted compressive analysis value, and the test results are also excellent. Therefore, the predicted results for compressive strength are highly accurate for waste LCD glass applied in concrete. Additionally, this predicted model exhibits a good predictive capacity when employed to calculate the compressive strength of washed glass sand concrete.

Strength Characteristics and their Behaviours of Marine Silty Sands (실트질 해사의 역학적 특성 및 거동에 관한 연구)

  • 장병욱;송창섭;우철웅
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.36 no.3
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    • pp.74-83
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    • 1994
  • A series of isotropic consolidation tests, undrained and drained triaxial compression tests was carried out to investigate the physical characteristics and behaviours of marine silty sands collected from the western coast of Korea. This study also included a theoretical development of the constitutive equation to evaluate stress-strain relationship and volume change of silty sands. The results and main conclusions of the study are summarized as follows; 1. Isotropic compression and swelling index are linearly decreased with an increase in relative density. 2. Both undrained shear strengh and elastic modulus are increased with an increase in relative density and confining pressure. 3. Internal friction angles obtained from drained and undrained compression tests of the soils are proportional to relative density. 4. The phenomenon of dilatancy of each sample is less profound when confining stress is increased but more profound when relative density is increased. 5. The slope of critical state lines is 1.78 for Saemangum, 1.70 for Siewha and 1.26 for Sukmoon sands. 6. In this study, Drucker-Praper type criterion is used and hardening function of Cap model is modified by hyperbolic fuction. This will improve a lack of physical meaning of hardening parameters in conventional Cap model. 7. A newly developed constitutive equation to the forementioned silty sands and checked its applicability. This is in good agreement with the measured data.

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Study on the Undrained Shear Strength Characteristics (반월지역 해성점토의 비배수 전단강도 특성에 관한 연구)

  • 장병욱;박영곤
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.36 no.3
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    • pp.90-99
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    • 1994
  • To investigate the undrained shear strength characteristics of marine soils with high water content, high compressibility and weak bearing capacity, a series of undrained triaxial tests with pore pressure measurements on undisturbed and disturbed Banwol marine clay in normally consolidated and overconsolidated states is carried out. The results and main conclusions of this study are summarized as follows : 1 . When the consolidation pressure is increased, the maximum deviator stress of disturbed and undistubed clay in normally consolidated state is increased. Pore pressure parameters and internal friction angle of undisturbed clay are greater than those of disturbed clay. 2. The relationship between pore pressure and axial strain of undisturbed clay in normally consolidated state can be expressed as a hyperbolic function like stress-strain relation proposed by Kondner. 3. In the pore pressure-axial strain relation of disturbed clay in normally consolidated state, failure ratio R'f is greatly deviated in the range of 0.7~0.9 proposed by Christian and Desai. 4. For overconsolided clay, when overconsolidation ratio (OCR) is increased, normalized maximum deviator stress is increased and maximum pore pressure is decreased gradually. 5. Cohesion of overconsolidated clay is greater than that of nomally consolidated clay and internal friction angle slightly is decreased. 6. Pore pressure parameter at failure (Af) of overconsolidated clay is varied with OCR, Af becomes negative values with increment in OCR

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