• Title/Summary/Keyword: hyperbolic function

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Estimation of Non-linear Strength and Stiffness for Silty Sands (실트질 모래지반의 비선형 강도 및 강성도 추정법)

  • Lee Kyung-Sook;Kim Hyun-Ju;Lee Jun-Hwan
    • Journal of the Korean Geotechnical Society
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    • v.22 no.1
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    • pp.35-44
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    • 2006
  • In general typically granular soils contain a certain amount of fines. It is also widely recognized that foundation soils under working loads show highly non-linear behavior from very early stages of loading. In the present study, a series of laboratory tests with sands of different silt contents are conducted and methods to assess strength and stiffiness characteristics are proposed. Modified hyperbolic stress-strain model is used to analyze non-linearity of silty sands in terms of non-linear Degradation parameters f and g as a function of silt contents and Relative density Dr. Stress-strain curves were obtained from a series of triaxial tests on sands containing different amounts of silt. Initial shear modulus, which is used to normalize Degradation modulus of silty sands, was determined from resonant column test results. From the laboratory test results, it was observed that, as the Relative density increases, values of f decrease and those of g increase. In addition, it was found that values of f and g increase and decrease respectively as a Skeleton void ratio $(e_{sk})$ increases.

Prediction of Ultimate Load of Drilled Shafts Embedded in Weathered Rock by Extrapolation Method (외삽법을 이용한 풍화암에 근입된 현장타설말뚝의 극한하중 예측)

  • Jung, Sung Jun;Lee, Sang In;Jeon, Jong Woo;Kim, Myoung Mo
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.4C
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    • pp.145-151
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    • 2009
  • In general, a drilled shaft embedded in weathered rock has a large load bearing capacity. Therefore, most of the load tests are performed only up to the load level that confirms the pile design load capacity, and stopped much before the ultimate load of the pile is attained. If a reliable ultimate load value can be extracted from the premature load test data, it will be possible to greatly improve economic efficiency as well as pile design quality. The main purpose of this study is to propose a method for judging the reliability of the ultimate load of piles that is obtained from extrapolated load test data. To this aim, ten static load test data of load-displacement curves were obtained from testing of piles to their failures from 3 different field sites. For each load-displacement curve, loading was assumed as 25%, 50%, 60%, 70%, 80%, and 90% of the actual pile bearing capacity. The limited known data were then extrapolated using the hyperbolic function, and the ultimate capacity was re-determined for each extrapolated data by the Davisson method (1972). Statistical analysis was performed on the reliability of the re-evaluated ultimate loads. The results showed that if the ratio of the maximum-available displacement to the predicted displacement exceeds 0.6, the extrapolated ultimate load may be regarded as reliable, having less than a conservative 20% error on average. The applicability of the proposed method of judgment was also verified with static load test data of driven piles.

Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates

  • Younsi, Abderahman;Tounsi, Abdelouahed;Zaoui, Fatima Zohra;Bousahla, Abdelmoumen Anis;Mahmoud, S.R.
    • Geomechanics and Engineering
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    • v.14 no.6
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    • pp.519-532
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    • 2018
  • In this work, two dimensional (2D) and quasi three-dimensional (quasi-3D) HSDTs are proposed for bending and free vibration investigation of functionally graded (FG) plates using hyperbolic shape function. Unlike the existing HSDT, the proposed theories have a novel displacement field which include undetermined integral terms and contains fewer unknowns. The material properties of the plate is inhomogeneous and are considered to vary continuously in the thickness direction by three different distributions; power-law, exponential and Mori-Tanaka model, in terms of the volume fractions of the constituents. The governing equations which consider the effects of both transverse shear and thickness stretching are determined through the Hamilton's principle. The closed form solutions are deduced by employing Navier method and then fundamental frequencies are obtained by solving the results of eigenvalue problems. In-plane stress components have been determined by the constitutive equations of composite plates. The transverse stress components have been determined by integrating the 3D stress equilibrium equations in the thickness direction of the FG plate. The accuracy of the present formulation is demonstrated by comparisons with the different 2D, 3D and quasi-3D solutions available in the literature.

A generalized 4-unknown refined theory for bending and free vibration analysis of laminated composite and sandwich plates and shells

  • Allam, Othmane;Draiche, Kada;Bousahla, Abdelmoumen Anis;Bourada, Fouad;Tounsi, Abdeldjebbar;Benrahou, Kouider Halim;Mahmoud, S.R.;Adda Bedia, E.A.;Tounsi, Abdelouahed
    • Computers and Concrete
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    • v.26 no.2
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    • pp.185-201
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    • 2020
  • This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

Contact interface fiber section element: shallow foundation modeling

  • Limkatanyu, Suchart;Kwon, Minho;Prachasaree, Woraphot;Chaiviriyawong, Passagorn
    • Geomechanics and Engineering
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    • v.4 no.3
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    • pp.173-190
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    • 2012
  • With recent growing interests in the Performance-Based Seismic Design and Assessment Methodology, more realistic modeling of a structural system is deemed essential in analyzing, designing, and evaluating both newly constructed and existing buildings under seismic events. Consequently, a shallow foundation element becomes an essential constituent in the implementation of this seismic design and assessment methodology. In this paper, a contact interface fiber section element is presented for use in modeling soil-shallow foundation systems. The assumption of a rigid footing on a Winkler-based soil rests simply on the Euler-Bernoulli's hypothesis on sectional kinematics. Fiber section discretization is employed to represent the contact interface sectional response. The hyperbolic function provides an adequate means of representing the stress-deformation behavior of each soil fiber. The element is simple but efficient in representing salient features of the soil-shallow foundation system (sliding, settling, and rocking). Two experimental results from centrifuge-scale and full-scale cyclic loading tests on shallow foundations are used to illustrate the model characteristics and verify the accuracy of the model. Based on this comprehensive model validation, it is observed that the model performs quite satisfactorily. It resembles reasonably well the experimental results in terms of moment, shear, settlement, and rotation demands. The hysteretic behavior of moment-rotation responses and the rotation-settlement feature are also captured well by the model.

Magnetorheological elastomer base isolator for earthquake response mitigation on building structures: modeling and second-order sliding mode control

  • Yu, Yang;Royel, Sayed;Li, Jianchun;Li, Yancheng;Ha, Quang
    • Earthquakes and Structures
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    • v.11 no.6
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    • pp.943-966
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    • 2016
  • Recently, magnetorheological elastomer (MRE) material and its devices have been developed and attracted a good deal of attention for their potentials in vibration control. Among them, a highly adaptive base isolator based on MRE was designed, fabricated and tested for real-time adaptive control of base isolated structures against a suite of earthquakes. To perfectly take advantage of this new device, an accurate and robust model should be built to characterize its nonlinearity and hysteresis for its application in structural control. This paper first proposes a novel hysteresis model, in which a nonlinear hyperbolic sine function spring is used to portray the strain stiffening phenomenon and a Voigt component is incorporated in parallel to describe the solid-material behaviours. Then the fruit fly optimization algorithm (FFOA) is employed for model parameter identification using testing data of shear force, displacement and velocity obtained from different loading conditions. The relationships between model parameters and applied current are also explored to obtain a current-dependent generalized model for the control application. Based on the proposed model of MRE base isolator, a second-order sliding mode controller is designed and applied to the device to provide a real-time feedback control of smart structures. The performance of the proposed technique is evaluated in simulation through utilizing a three-storey benchmark building model under four benchmark earthquake excitations. The results verify the effectiveness of the proposed current-dependent model and corresponding controller for semi-active control of MRE base isolator incorporated smart structures.

Taylor Series-Based Long-Term Creep-Life Prediction of Alloy 617 (Taylor 급수를 이용한 617 합금의 장시간 크리프 수명 예측)

  • Yin, Song-Nan;Kim, Woo-Gon;Park, Jae-Young;Kim, Soen-Jin;Kim, Yong-Wan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.4
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    • pp.457-465
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    • 2010
  • In this study, a Taylor series (T-S) model based on the Arrhenius, McVetty, and Monkman-Grant equations was developed using a mathematical analysis. In order to reduce fitting errors, the McVetty equation was transformed by considering the first three terms of the Taylor series equation. The model parameters were accurately determined by a statistical technique of maximum likelihood estimation, and this model was applied to the creep data of alloy 617. The T-S model results showed better agreement with the experimental data than other models such as the Eno, exponential, and L-M models. In particular, the T-S model was converted into an isothermal Taylor series (IT-S) model that can predict the creep strength at a given temperature. It was identified that the estimations obtained using the converted ITS model was better than that obtained using the T-S model for predicting the long-term creep life of alloy 617.

Analysis of wave propagation and free vibration of functionally graded porous material beam with a novel four variable refined theory

  • Ayache, Belqassim;Bennai, Riadh;Fahsi, Bouazza;Fourn, Hocine;Atmane, Hassen Ait;Tounsi, Abdelouahed
    • Earthquakes and Structures
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    • v.15 no.4
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    • pp.369-382
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    • 2018
  • A free vibration analysis and wave propagation of functionally graded porous beams has been presented in this work using a high order hyperbolic shear deformation theory. Unlike other conventional shear deformation theories, a new displacement field that introduces indeterminate integral variables has been used to minimize the number of unknowns. The constituent materials of the beam are assumed gradually variable along the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The variation of the pores in the direction of the thickness influences the mechanical properties. It is therefore necessary to predict the effect of porosity on vibratory behavior and wave velocity of FG beams in this study. A new function of the porosity factor has been developed. Hamilton's principle is used for the development of wave propagation equations in the functionally graded beam. The analytical dispersion relationship of the FG beam is obtained by solving an eigenvalue problem. Illustrative numerical examples are given to show the effects of volume fraction distributions, beam height, wave number, and porosity on free vibration and wave propagation in a functionally graded beam.

Analysis on an Inducing Current Change between Railway Power Feeding Plants (전기철도 전자기 유도 전류의 급전구간 상대적 위치 관계에 따른 변화 분석)

  • Lee, Sangmu;Choi, Mun Hwan;Cho, Pyung-dong
    • Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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    • 2012.10a
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    • pp.567-569
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    • 2012
  • An inducing current of power feeding line of high-speed railway system is varied by a relative position of telecommunication cable to the feeding line between plants. An analytical calculation formula of this inducing current is described in ITU-T Directives using multiconductor line method or two line method. In this paper, using the two line method, a variation characteristic of inducing current is simulated. The inducing current has a characteristic of hyperbolic function which is a symmetric shape of curve in the range between power feeding plants. This basic variation property can be considered when a power induction protection measure is planned.

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Reliability Evaluation of Extrapolated Failure Load of Drilled Shafts Embedded in Weathered Rock (풍화암에 근입된 현장타설말뚝의 외삽 파괴하중 신뢰성 분석)

  • Jung, Sung-Jun;Lee, Sang-Inn;Jeon, Jong-Woo;Kim, Myoung-Mo
    • Proceedings of the Korean Geotechical Society Conference
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    • 2009.09a
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    • pp.993-1000
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    • 2009
  • In general, a drilled shaft embedded in weathered rock has a large load bearing capacity. Therefore, most of the load tests are performed only up to the load level that confirms the pile design load capacity, and stopped much before the failure load of the pile is attained. If a reliable failure load value can be extracted from the premature load test data, it will be possible to greatly improve economic efficiency as well as pile design quality. The main purpose of this study is to propose a standard for judging the reliability of the failure load of piles that is obtained from extrapolated load test data. To this aim, eleven static load test data of load-displacement curves were obtained from testing of piles to their failures from 3 different field sites. For each load-displacement curve, loading was assumed as 25%, 50%, 60%, 70%, 80%, and 90% of the actual pile bearing capacity. The limited known data were then extrapolated using the hyperbolic function, and the failure load was re-determined for each extrapolated data by the ASCE 20-96 method (1997). Statistical analysis was performed on the reliability of the re-evaluated failure loads. The results showed that if the ratio of the maximum-available displacement to the failure-load displacement exceeds 0.6, the extrapolated failure load may be regarded as reliable, having less than a conservative 20% error on average. The applicability of the proposed standard of judgment was also verified with static load test data of driven piles.

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