• Title/Summary/Keyword: Non-linear response

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Analysis of Removal Characteristics and Optimization of Livestock Wastewater using a Factorial Design in the Coagulation Process (화학적 응집공정에서 요인배치 중심합성설계법을 이용한 축산폐수의 COD 제거특성 평가 및 최적화 연구)

  • Cho, Il-Hyoung;Lee, Nae-Hyun;Chang, Soon-Woong;An, Sang-Woo;Yoon, Young-Han;Zoh, Kyung-Duk
    • Journal of Korean Society on Water Environment
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    • v.23 no.1
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    • pp.111-121
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    • 2007
  • The experimental design and response surface methodologies haven been applied to the investigation of the chemical coagulation of livestock wastewater. The chemical coagulation reactions were mathematically described as a function of parameters raping mixing (rpm) of chemical coagulation ($X_1$), slow mixing (rpm) of chemical coagulation ($X_2$), $FeCl_3 $ concentration (mg/L) ($X_3$) and pH ($X_4$) being modeled by use of the central composite design. Empirical models were developed to describe relationship between the experimental variables and response. Statistical analysis indicates that three factors ($X_1$: raping mixing (rpm), $X_2$: slow mixing (rpm), $X_3$: $FeCl_3 $ concentration (mg/L) on the linear term (main effect), slow mixing (rpm) (${X_2}^2$) on the non-linear term (quadratic), and two factors ($X_1-X_3$, $X_2-X_3$) on the non-linear term (cross-product) had significant effects, respectively. The estimated ridge of maximum responses and optimal conditions for CODcr using canonical analysis was 87.44% ($X_1$: 229 rpm, $X_2$: 51 rpm, $X_3$: 877 mg/L, $X_4$: 4.3). To confirm this optimum condition, three additional experiments were performed and the mean CODcr removal (%) and concentration (mg/L) with a standard deviation of $87{\pm}1.2%$ ($576{\pm}34ppm$) were obtained.

Optimal design of car suspension springs by using a response surface method (반응 표면 분석법을 활용한 자동차용 현가스프링 최적화 설계)

  • Yoo, Dong-Woo;Kim, Do-Yeop;Shin, Dong-Gyu
    • Proceeding of EDISON Challenge
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    • 2016.03a
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    • pp.246-255
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    • 2016
  • When spring of the suspension is exerted by an external load, a car should be designed to prevent predictable damages and designed for a ride comfort. We used experiments design to design VON-MISES STRESS and K, a constant, of spring of suspension which is installed in a car as a goal level. We analyzed the result from Edison's Elastic - Plastic Analysis SW(CSD_EPLAST) by setting D, d, n as external diameter of coil, internal diameter of coil, the number of total coil respectively. The experiment design let the outcome be as Full-second order by using Box-Behnken which is one of response surface methods. Experimented and analyzed results based on the established experiments design, We found out design parameter which has desired VON-MISES STRESS and the constant K. Additionally, we predicted life time of when the external load was exerted by repeated load by using fatigue equation, and verification of plastic deformation has also been made. Additionally we interpreted a model, which is formed by optimized design parameter, with linear analysis and non-linear analysis, at the same time we also analyzed plastic deformation with the values from the both models. Finally, we predicted fatigue life of optimized model by using fatigue estimation theory and also evaluated a ride comfort with oscillation analysis.

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A Study on the Dynamic Strength Analysis of the Hull Girder Among Waves Considering Non-Linear Hydrodynamic forces (선박의 비선형 유체력을 고려한 파랑중 동적 강도 해석법에 관한 연구)

  • Ku-Kyun Shin;Sa-Soo Kim;Sung-Wan Son
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.4
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    • pp.152-172
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    • 1992
  • The ship sailing among waves are suffered the various wave loads that comes from its motion throughout its life. Because there are dynamic, the analysis of ship structure must be considered as the dynamic problem precisely. In the rationally-based design, the dynamic structural analysis is carried out using dynamic wave loads provided from the results of the ship mouton calculation as the rigid body. This method is based on the linear theory assumed low wave height and small amplitude of motion. But at the rough sea condition, high wave height, relatively ship's depth, is induced the large ship motion, so the ship section configulation below water line is rapidly changed at each time. This results in non-linear problem. Considering above situation in this paper, the strength analysis method is introduced for the hull glider among waves considering non-linear hydrodynamic forces. This paper considers that the overall or primary level of the ship structural dynamic loading and dynamic response provided from the non-linear wave forces, and bottom and bow flare impact forces estimated by momentum slamming theory, in which the ship is idealized as a hollow thin-walled box beam using thin-walled beam theory and the finite element method. This method is applied to 40,000 Ton Double-Skin Tanker and attention is paid to the influence of the response of ship speed, wave length and wave height compared with linear strip theory.

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Calibration of the Broadband Sensor(STS-2) using the Step Method (스텝방법을 이용한 광대역지진계 센서(STS-2)의 검증)

  • 류용규;이덕기;이전희;오석훈
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • 2001.09a
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    • pp.11-18
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    • 2001
  • A close examination of the step calibrations for STS-2 seismometers installed by KMA has been done to deduce the response parameters of those instrument including angular corner frequency, damping factor and coil constant factor. A non-linear least square inversion method has been apple iud to estimate these parameters. The estimated parameters coincide with the manufactory specification with less than 1% error. This method will be extended near- future to deduce the response parameters for SS-1 short period seismometer.

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Non-linear analysis of side-plated RC beams considering longitudinal and transversal interlayer slips

  • Kolsek, Jerneja;Hozjan, Tomaz;Kroflic, Ales;Saje, Miran;Planinc, Igor
    • Steel and Composite Structures
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    • v.16 no.6
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    • pp.559-576
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    • 2014
  • A new mathematical model and its finite element formulation for the non-linear stress-strain analysis of a planar beam strengthened with plates bolted or adhesively bonded to its lateral sides is presented. The connection between the layers is considered to be flexible in both the longitudinal and the transversal direction. The following assumptions are also adopted in the model: for each layer (i.e., the beam and the side plates) the geometrically linear and materially non-linear Bernoulli's beam theory is assumed, all of the layers are made of different homogeneous non-linear materials, the debonding of the beam from the side-plates due to, for example, a local buckling of the side plate, is prevented. The suitability of the theory is verified by the comparison of the present numerical results with experimental and numerical results from literature. The mechanical response arising from the theoretical model and its numerical formulation has been found realistic and the numerical model has been proven to be reliable and computationally effective. Finally, the present formulation is employed in the analysis of the effects of two different realizations of strengthening of a characteristic simply supported flexural beam (plates on the sides of the beam versus the tension-face plates). The analysis reveals that side plates efficiently enhance the bearing capacity of the flexural beam and can, in some cases, outperform the tensile-face plates in a lower loss of ductility, especially, if the connection between the beam and the side plates is sufficiently stiff.

Interaction analysis of three storeyed building frame supported on pile foundation

  • Rasal, S.A.;Chore, H.S.;Sawant, V.A.
    • Coupled systems mechanics
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    • v.7 no.4
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    • pp.455-483
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    • 2018
  • The study deals with physical modeling of a typical three storeyed building frame supported by a pile group of four piles ($2{\times}2$) embedded in cohesive soil mass using three dimensional finite element analysis. For the purpose of modeling, the elements such as beams, slabs and columns, of the superstructure frame; and that of the pile foundation such as pile and pile cap are descretized using twenty noded isoparametric continuum elements. The interface between the pile and the soil is idealized using sixteen node isoparametric surface element. The soil elements are modeled using eight nodes, nine nodes and twelve node continuum elements. The present study considers the linear elastic behaviour of the elements of superstructure and substructure (i.e., foundation). The soil is assumed to behave non-linear. The parametric study is carried out for studying the effect of soil- structure interaction on response of the frame on the premise of sub-structure approach. The frame is analyzed initially without considering the effect of the foundation (non-interaction analysis) and then, the pile foundation is evaluated independently to obtain the equivalent stiffness; and these values are used in the interaction analysis. The spacing between the piles in a group is varied to evaluate its effect on the interactive behaviour of frame in the context of two embedment depth ratios. The response of the frame included the horizontal displacement at the level of each storey, shear force in beams, axial force in columns along with the bending moments in beams and columns. The effect of the soil- structure interaction is observed to be significant for the configuration of the pile groups and in the context of non-linear behaviour of soil.

Comparative Study on Wave Induced Fatigue Analysis Methods for Steel Catenary Riser (파랑하중에 의한 Steel Catenary Riser 피로손상 평가 방법의 비교검토)

  • Lee, Jeong-Dae;Lee, Sung-Je;Jang, Chang-Hwan;Jun, Seock-Hee;Oh, Yeong-Tae
    • Journal of the Society of Naval Architects of Korea
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    • v.52 no.3
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    • pp.222-235
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    • 2015
  • The purpose of this study is to suggest guidelines for riser fatigue analysis in terms of selection of reasonable analysis method. Three analysis methods (spectral, regular wave, rain-flow counting) are introduced and compared. As the riser systems give non-linear response, the time-domain analysis method is more preferred than frequency-domain analysis method. The spectral fatigue analysis method, however, is still useful for identifying fatigue prone areas. Once stress RAO is established, fatigue damage can be calculated very quickly. The regular wave method and the rain-flow counting method are more time consuming but give more exact results compare to spectral method. In case of regular wave method, a set of regular waves which represent random sea states is considered for dynamic analysis. The rain-flow counting method is the most intuitive and exact method because it refers time history stresses containing most of non-linear effects of the riser system. However, it is not common for early design stage to use rain-flow counting method because of its high cost. In this study, it was confirmed that the regular wave method is the most cost effective way in specific cases. However, if the system is highly non-linear, it seems that the regular wave method gives less accurate results than rain-flow counting method. Therefore, it is imperative that the engineers select appropriate analysis method based on design stage and given engineering period. This paper also discusses the theoretical background of each calculation method and hydrodynamic aspects of marine riser systems. A steel catenary riser (SCR) line on FPSO was considered and marine dynamic program (OrcaFlex) was used for static and dynamic analysis.

A finite element analysis for unbonded flexible risers under bending loads

  • Xiqia, Chen;Shixiao, Fu;Yun, Gao;Xiaying, Du
    • Ocean Systems Engineering
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    • v.5 no.2
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    • pp.77-89
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    • 2015
  • As the exploitation of oil and gas resources advances into deeper waters and harsher environments, the design and analysis of the flexible risers has become the research focus in the offshore engineering filed. Due to the complexity of the components and the sliding between the adjacent layers, the bending response of the flexible risers is highly non-linear. This paper presents the finite element analysis of the flexible risers under bending loads. The detailed finite element model of the flexible riser is established in ABAQUS software. This finite element model incorporates all the fine details of the riser to accurately predict its nonlinear structural behavior. Based on the finite element model, the bending moment-curvature relationships of a flexible riser under various axisymmetric loads have been investigated. The results have been compared with the analytical ones obtained from the literature and good agreements have been found. Moreover, the stress of the tendon armors has been studied. The non-linear relationship between the armor tendons' stress and the bending loads has been obtained.