• Title/Summary/Keyword: Nonlinear equations

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Development of Sag and Tension Sensitivity Estimation Method for Configuration Control under PPWS Erection in a Suspension Bridge (현수교 PPWS 가설중 형상관리를 위한 PPWS 새그 및 장력민감도 산정법 개발)

  • Jeong, Woon;Seo, Ju Won;Lee, Won Pyo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.5A
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    • pp.255-266
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    • 2012
  • Main cable of a suspension bridge is the important member which shows the overall structure integrity at bridge completion. Configuration of main cable is a free hanging state at cable erection completion and is different from that at bridge completion supporting the dead loads such as hanger, girder, and so on. Accordingly, the configuration control under cable erection is considerably significant because the configuration at cable erection completion has direct influence on that at bridge completion. That is performed by sag adjustments at center, side span and tension adjustments at anchor span. The former needs the sag sensitivity which represents the control quantity of strand length corresponding to that of sag. The latter requires the tension sensitivity which shows the change of strand tension according to that of strand temperature. In this study, the fundamental equations of cable were derived with the assumption of either catenary or parabola shape, the differential-related equations using chain rule on horizontal tension were drawn from those and finally the estimation methods of the sag / tension sensitivity were proposed from both those. The nonlinear numerical analysis flow charts of sag sensitivity based on the catenary equations were proposed and the sag sensitivities grounded on the differential-related equations were compared with the results using them for various parameters of sag change. Also, considering the combinations of sag change parameters, the calculation method of the final variation for the cable sag was suggested. For the real suspension bridge under construction with PPWS method, the sag/tension sensitivity were estimated considering the construction conditions like the change of PPWS length, PPWS temperature, bridge span, etc.. We hope that this study will be a systematic guideline for the configuration control under main cable erection and improved highly by field verification in the real bridge site.

Analytical Formula for the Equivalent Mohr-Coulomb Strength Parameters Best-fitting the Generalized Hoek-Brown Criterion in an Arbitrary Range of Minor Principal Stress (임의 최소주응력 구간에서 일반화된 Hoek-Brown 파괴기준식을 최적 근사하는 등가 Mohr-Coulomb 강도정수 계산식)

  • Lee, Youn-Kyou
    • Tunnel and Underground Space
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    • v.29 no.3
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    • pp.172-183
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    • 2019
  • The generalized Hoek-Brown (GHB) failure criterion developed by Hoek et al. (2002) is a nonlinear function which defines a stress condition at failure of rock mass. The relevant strength parameter values are systematically determined using the GSI value. Since GSI index is a value quantifying the condition of in-situ rock mass, the GHB criterion is a practical failure condition which can take into the consideration of in-situ rock mass quality. Considering that most rock mechanics engineers are familiar with the linear Mohr-Coulomb criterion and that many rock engineering softwares incorporate Mohr-Coulomb criterion, the equations for the equivalent friction angle and cohesion were also proposed along with the release of the GHB criterion. The proposed equations, however, fix the lower limit of the minor principal stress range, where the linear best-fitting is performed, with the tensile strength of the rock mass. Therefore, if the tensile stress is not expected in the domain of analysis, the calculated equivalent friction angle and cohesion based on the equations in Hoek et al. (2002) could be less accurate. In order to overcome this disadvantage of the existing equations for equivalent friction angle and cohesion, this study proposes the analytical formula which can calculate optimal equivalent friction angle and cohesion in any minor principal stress interval, and verified the accuracy of the derived formula.

Growth curve estimates for wither height, hip height, and body length of Hanwoo steers (Bos taurus coreanae)

  • Park, Hu-Rak;Eum, Seung-Hoon;Roh, Seung-Hee;Sun, Du-Won;Seo, Jakyeom;Cho, Seong-Keun;Lee, Jung-Gyu;Kim, Byeong-Woo
    • Korean Journal of Agricultural Science
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    • v.44 no.3
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    • pp.384-391
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    • 2017
  • Growth curves in Hanwoo steers were estimated by Gompertz, Von Bertalanffy, Logistic, and Brody nonlinear models using growth data collected by the Hanwoo Improvement Center from a total of 6,973 Hanwoo (Bos taurus coreanae) steers 6 to 24 months old that were born between 1996 and 2015. The data included three parameters: A, mature size of body measurement; b, growth ratio; and, k, intrinsic growth rate. Nonlinear regression equations for wither height according to Gompertz, Von Bertalanffy, Logistic, and Brody models were $Y_t=144.7e^{-0.5869e^{-0.00301t}}$, $Y_t=145.3(1-0.1816e^{-0.00284t})^3$, $Y_t=143.1(1+0.7356e^{-0.00352t})^{-1}$, and $Y_t=146.8(1+0.4700e^{-0.00249t})^1$, respectively, while those for hip height were $Y_t=144.5e^{-0.5549e^{-0.00312t}}$, $Y_t=145.0(1-0.1724e^{-0.00295t})^3$, $Y_t=143.1(1+0.6863e^{-0.00360t})^{-1}$, and $Y_t=146.2(1+0.4501e^{-0.00263t})^1$, respectively. Equations for body length $Y_t=174.1e^{-0.8342e^{-0.00289t}}$, $Y_t=175.8(1-0.2500e^{-0.00265t})^3$, $Y_t=170.0(1+1.1548e^{-0.00363t})^{-1}$, and $Y_t=180.3(1+0.6077e^{-0.00215t})^1$, respectively, for the same models. Among the four models, the Brody model resulted in the lowest mean square error, with mean square errors of 31.79, 30.57, and 42.13, respectively, for wither height, hip height, and body length. Also, an estimated birth wither height, birth hip height, and birth body length (77.98, 80.57, and 70.97 cm, respectively) were lower in the Brody model than in other models. An inflection point was not observed during the growth phase of Hanwoo steer according to the growth curves calculated using Gompertz, Von Bertalanffy, and Logistic models. Based on the results, we concluded that the regression equation using the Brody model was the most appropriate among the four growth models. To obtain more accurate parameters, however, using data from a wider production period (from birth to shipping) would be required, and the development of a suitable model for body conformation traits would be needed.

Development of Permanent Displacement Model for Seismic Mountain Slope (지진 시 산사면의 영구변위 추정식 개발)

  • Lee, Jong-Hoo;Park, Duhee;Ahn, Jae-Kwang;Park, Inn-Joon
    • Journal of the Korean Geotechnical Society
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    • v.31 no.4
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    • pp.57-66
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    • 2015
  • Empirical seismic displacement equations based on the Newmark sliding block method are widely used to develop seismic landslide hazard map. Most proposed equations have been developed for embankments and landfills, and do not consider the dynamic response of sliding block. Therefore, they cannot be applied to Korean mountain slopes composed of thin, uniform soil-layer underlain by an inclined bedrock parallel to the slope. In this paper, a series of two-dimensional dynamic nonlinear finite difference analyses were performed to estimate the permanent seismic slope displacement. The seismic displacement of mountain slopes was calculated using the Newmark method and the equivalent acceleration time history. The calculated seismic displacements of the mountain slopes were compared to a widely used empirical displacement model. We show that the displacement prediction is significantly enhanced if the slope is modeled as a flexible sliding mass and the amplification characteristics are accounted for. Regression equation, which uses PGA, PGV, Arias intensity of the ground motion and the fundamental period of soil layer, is shown to provide a reliable estimate of the sliding displacement. Furthermore, the empirical equation is shown to reliably predict the hazard category.

Fracture and Hygrothermal Effects in Composite Materials (복합재의 파괴와 hygrothermal 효과에 관한 연구)

  • Kook-Chan Ahn;Nam-Kyung Kim
    • Journal of the Korean Society of Safety
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    • v.11 no.4
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    • pp.143-150
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    • 1996
  • This is an explicit-Implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE ) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for and existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The Ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory Darcy's law Is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full newton-Raphson method is used for solving the nonlinear governing equations.

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Estimation of Permanent Displacement of Gravity Quay Wall Considering Failure Surface under Seismic Loading (지진 시 파괴면을 고려한 중력식 안벽의 영구변위 평가)

  • Han, Insuk;Ahn, Jae-Kwang;Park, Duhee;Kwon, Osoon
    • Journal of the Korean Geotechnical Society
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    • v.35 no.4
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    • pp.15-26
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    • 2019
  • The stability of the gravity quay wall against earthquakes is evaluated on the basis of the allowable displacement of the wall. To estimate the displacement caused by external forces, empirical equations based on the Newmark sliding block method or numerical analysis are widely used. In numerical analysis, it is possible to analyze precisely a complicated site and structure, but difficult to set the appropriate parameters and environments; there are limitations in obtaining reliable results, depending on one's level of expertise. The Newmark method, with only seismic motions, is widely used because it is simpler than numerical simulations when estimating permanent displacement. However, the empirical equations do not have any parameters for the response characteristics and sliding block of the structure, and sliding blocks being assumed as rigid bodies does not consider the nonlinear behavior of the soil and interaction with the structure. Therefore, in order to evaluate the seismic stability of the gravity quay wall, a newly-developed empirical equation is needed to overcome the above-mentioned limitations. In this study, numerical simulations are performed to analyze the response characteristics of the backfill of the structure, and to propose an optimal method of calculating the active area. For this purpose, finite element analyses were performed to analyze the response characteristics, and stress-strain relationships for various seismic motions. As a result, the response characteristics, sliding block, and failure surface of the backfill vary depending on the input seismic motions.

Diffraction Effects of Parabolic Mild-Slope Equations in the Shadow Zone behind a Detached Breakwater (이안제 배후 차폐역에서 포물선형 완경사방정식의 회절효과)

  • 김인철
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.8 no.4
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    • pp.297-304
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    • 1996
  • The purpose of this study is to observe the applicability of parabolic mild-slope equations allowing relatively large angles of wave propagation based on the use of a Pade approximant or minimax approximation and also the applicability of the models with nonlinearity of diffracted waves in the shadow zone behind coastal structures. To accomplish these objectives, numerical solutions are obtained from the above parabolic models and are compared with the results from Watanabe and Maruyama's(1984) hydraulic model test on the wave field with an impermeable detached breakwater. From this study, it is found that computed wave heights increase for the nonlinear results in comparison to the linear results due to the increased diffraction effect across the geometric shadow boundary. The model with a larger aperture with respect to the principal direction was found to spread laterally to a much greater degree where spreading angle (diffraction effect) is relatively large. which causes a distortion in the overall results due to the error accumulated by the approximation of wave length.

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Development of Empirical Formula for Transverse Dispersion Coefficient Based on Theoretical Equation in River Bends (만곡부에서 이론식에 기반한 횡분산계수 경험공식 개발)

  • Baek, Kyong Oh
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.32 no.6B
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    • pp.373-378
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    • 2012
  • In this study, a new empirical equation for the transverse dispersion coefficient has been developed based on the theoretical background in river bends. The nonlinear least-square method was applied to determine regression coefficients of the equation. The estimated dispersion coefficients derived by the new equation were compared with observed transverse dispersion coefficients acquired from natural rivers and coefficients calculated by the other existing empirical equations. From a comparison of the existing transverse dispersion equations and the new proposed equation, it appears that the behavior of the existing formula in a relative sense is very much dependent on the friction factor and the river geometry. However, the new proposed equation does not vary widely according to variation of friction factor. Also, it was revealed that the equation proposed in this study becomes an asymptotic curve as the curvature effect increases.

Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories

  • Attia, Amina;Tounsi, Abdelouahed;Bedia, E.A. Adda;Mahmoud, S.R.
    • Steel and Composite Structures
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    • v.18 no.1
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    • pp.187-212
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    • 2015
  • In this paper, various four variable refined plate theories are presented to analyze vibration of temperature-dependent functionally graded (FG) plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present model is reduced, significantly facilitating engineering analysis. These theories account for parabolic, sinusoidal, hyperbolic, and exponential distributions of the transverse shear strains and satisfy the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Power law material properties and linear steady-state thermal loads are assumed to be graded along the thickness. Uniform, linear, nonlinear and sinusoidal thermal conditions are imposed at the upper and lower surface for simply supported FG plates. Equations of motion are derived from Hamilton's principle. Analytical solutions for the free vibration analysis are obtained based on Fourier series that satisfy the boundary conditions (Navier's method). Non-dimensional results are compared for temperature-dependent and temperature-independent FG plates and validated with known results in the literature. Numerical investigation is conducted to show the effect of material composition, plate geometry, and temperature fields on the vibration characteristics. It can be concluded that the present theories are not only accurate but also simple in predicting the free vibration responses of temperature-dependent FG plates.

Calibration Method of Plenoptic Camera using CCD Camera Model (CCD 카메라 모델을 이용한 플렌옵틱 카메라의 캘리브레이션 방법)

  • Kim, Song-Ran;Jeong, Min-Chang;Kang, Hyun-Soo
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.22 no.2
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    • pp.261-269
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    • 2018
  • This paper presents a convenient method to estimate the internal parameters of plenoptic camera using CCD(charge-coupled device) camera model. The images used for plenoptic camera calibration generally use the checkerboard pattern used in CCD camera calibration. Based on the CCD camera model, the determinant of the plenoptic camera model can be derived through the relationship with the plenoptic camera model. We formulate four equations that express the focal length, the principal point, the baseline, and distance between the virtual camera and the object. By performing a nonlinear optimization technique, we solve the equations to estimate the parameters. We compare the estimation results with the actual parameters and evaluate the reprojection error. Experimental results show that the MSE(mean square error) is 0.309 and estimation values are very close to actual values.