• Title/Summary/Keyword: Nonlinear modelling

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Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory

  • Nebab, Mokhtar;Atmane, Hassen Ait;Bennai, Riadh;Tahar, Benabdallah
    • Earthquakes and Structures
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    • v.17 no.5
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    • pp.447-462
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    • 2019
  • This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

Modelling and packed bed column studies on adsorptive removal of phosphate from aqueous solutions by a mixture of ground burnt patties and red soil

  • Rout, Prangya R.;Dash, Rajesh R.;Bhunia, Puspendu
    • Advances in environmental research
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    • v.3 no.3
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    • pp.231-251
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    • 2014
  • The present study examines the phosphate adsorption potential and behavior of mixture of Ground Burnt Patties (GBP), a solid waste generated from cooking fuel used in earthen stoves and Red Soil (RS), a natural substance in fixed bed column mode operation. The characterization of adsorbent was done by Proton Induced X-ray Emission (PIXE), and Proton Induced ${\gamma}$-ray Emission (PIGE) methods. The FTIR spectroscopy of spent adsorbent reveals the presence of absorbance peak at $1127cm^{-1}$ which appears due to P = O stretching, thus confirming phosphate adsorption. The effects of bed height (10, 15 and 20 cm), flow rate (2.5, 5 and 7.5 mL/min) and initial phosphate concentration (5 and 15 mg/L) on breakthrough curves were explored. Both the breakthrough and exhaustion time increased with increase in bed depth, decrease in flow rate and influent concentration. Thomas model, Yoon-Nelson model and Modified Dose Response model were used to fit the column adsorption data using nonlinear regression analysis while Bed Depth Service Time model followed linear regression analysis under different experimental condition to evaluate model parameters that are useful in scale up of the process. The values of correlation coefficient ($R^2$) and the Sum of Square Error (SSE) revealed the Modified Dose Response model as the best fitted model to the experimental data. The adsorbent mixture responded effectively to the desorption and reusability experiment. The results of this finding advocated that mixture of GBP and RS can be used as a low cost, highly efficient adsorbent for phosphate removal from aqueous solution.

Experimental and numerical investigations on axial strength of back-to-back built-up cold-formed steel angle columns

  • Ananthi, G. Beulah Gnana;Roy, Krishanu;Lim, James B.P.
    • Steel and Composite Structures
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    • v.31 no.6
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    • pp.601-615
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    • 2019
  • In cold-formed steel (CFS) structures, such as trusses, wall frames and columns, the use of back-to-back built-up CFS angle sections are becoming increasingly popular. In such an arrangement, intermediate fasteners are required at discrete points along the length, preventing the angle-sections from buckling independently. Limited research is available in the literature on the axial strength of back-to-back built-up CFS angle sections. The issue is addressed herein. This paper presents the results of 16 experimental tests, conducted on back-to-back built-up CFS screw fastened angle sections under axial compression. A nonlinear finite element model is then described, which includes material non-linearity, geometric imperfections and explicit modelling of the intermediate fasteners. The finite element model was validated against the experimental test results. The validated finite element model was then used for the purpose of a parametric study comprising 66 models. The effect of fastener spacing on axial strength was investigated. Four different cross-sections and two different thicknesses were analyzed in the parametric study, varying the slenderness ratio of the built-up columns from 20 to 120. Axial strengths obtained from the experimental tests and finite element analysis were used to assess the performance of the current design guidelines as per the Direct Strength Method (DSM); obtained comparison showed that the DSM is over-conservative by 13% on average. This paper has therefore proposed improved design rules for the DSM and verified their accuracy against the finite element and test results of back-to-back built-up CFS angle sections under axial compression.

Analytical Solutions for the Inelastic Lateral-Torsional Buckling of I-Beams Under Pure Bending via Plate-Beam Theory

  • Zhang, Wenfu;Gardner, Leroy;Wadee, M. Ahmer;Zhang, Minghao
    • International journal of steel structures
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    • v.18 no.4
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    • pp.1440-1463
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    • 2018
  • The Wagner coefficient is a key parameter used to describe the inelastic lateral-torsional buckling (LTB) behaviour of the I-beam, since even for a doubly-symmetric I-section with residual stress, it becomes a monosymmetric I-section due to the characteristics of the non-symmetrical distribution of plastic regions. However, so far no theoretical derivation on the energy equation and Wagner's coefficient have been presented due to the limitation of Vlasov's buckling theory. In order to simplify the nonlinear analysis and calculation, this paper presents a simplified mechanical model and an analytical solution for doubly-symmetric I-beams under pure bending, in which residual stresses and yielding are taken into account. According to the plate-beam theory proposed by the lead author, the energy equation for the inelastic LTB of an I-beam is derived in detail, using only the Euler-Bernoulli beam model and the Kirchhoff-plate model. In this derivation, the concept of the instantaneous shear centre is used and its position can be determined naturally by the condition that the coefficient of the cross-term in the strain energy should be zero; formulae for both the critical moment and the corresponding critical beam length are proposed based upon the analytical buckling equation. An analytical formula of the Wagner coefficient is obtained and the validity of Wagner hypothesis is reconfirmed. Finally, the accuracy of the analytical solution is verified by a FEM solution based upon a bi-modulus model of I-beams. It is found that the critical moments given by the analytical solution almost is identical to those given by Trahair's formulae, and hence the analytical solution can be used as a benchmark to verify the results obtained by other numerical algorithms for inelastic LTB behaviour.

Forecasting the Sea Surface Temperature in the Tropical Pacific by Neural Network Model (신경망 모델을 이용한 적도 태평양 표층 수온 예측)

  • Chang You-Soon;Lee Da-Un;Seo Jang-Won;Youn Yong-Hoon
    • Journal of the Korean earth science society
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    • v.26 no.3
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    • pp.268-275
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    • 2005
  • One of the nonlinear statistical modelling, neural network method was applied to predict the Sea Surface Temperature Anomalies (SSTA) in the Nino regions, which represent El Nino indices. The data used as inputs in the training step of neural network model were the first seven empirical orthogonal functions in the tropical Pacific $(120^{\circ}\;E,\;20^{\circ}\;S-20^{\circ}\;N)$ obtained from the NCEP/NCAR reanalysis data. The period of 1951 to 1993 was adopted for the training of neural network model, and the period 1994 to 2003 for the forecasting validation. Forecasting results suggested that neural network models were resonable for SSTA forecasting until 9-month lead time. They also predicted greatly the development and decay of strong E1 Nino occurred in 1997-1998 years. Especially, Nino3 region appeared to be the best forecast region, while the forecast skills rapidly decreased since 9-month lead time. However, in the Nino1+2 region where they are relatively low by the influence of local effects, they did not decrease even after 9-month lead time.

Investigating Remotely Sensed Precipitation from Different Sources and Their Nonlinear Responses in a Physically Based Hydrologic Model (다른 원격탐사 센서로 추출한 강우자료의 이질성과 이에 의한 비선형유출반응에 미치는 영향)

  • Oh, Nam-Sun;Lee, Khil-Ha;Kim, Sang-Jun
    • Journal of Korea Water Resources Association
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    • v.39 no.10 s.171
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    • pp.823-832
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    • 2006
  • Precipitation is the most important component to the study of water and energy cycle in hydrology. In this study we investigate rainfall retrieval uncertainty from different sources of remotely sensed precipitation field and then probable error propagation in the simulation of hydrologic variables especially, runoff on different vegetation cover. Two remotely sensed rainfall retrievals (space-borne IR-only and ground radar rainfall) are explored and compared visually and statistically. Then, an offline Community Land Model (CLM) is forced with in situ meteorological data to simulate the amount of runoff and determine their impact on model predictions. A fundamental assumption made in this study is that CLM can adequately represent the physical land surface processes. Results show there are big differences between different sources of precipitation fields in terms of the magnitude and temporal variability. The study provides some intuitions on the uncertainty of hydrologic prediction via the interaction between the land surface and near atmosphere fluxes in the modelling approach. Eventually it will contribute to the understanding of water resources redistribution to the climate change in Korean Peninsula.

Spatial Downscaling of Grid Precipitation Using Support Vector Machine Regression (SVM 회귀 모형을 활용한 격자 강우량 상세화 기법)

  • Moon, Heewon;Baik, Jongjin;Hwang, Sukhwan;Choi, Minha
    • Journal of Korea Water Resources Association
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    • v.47 no.11
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    • pp.1095-1105
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    • 2014
  • A spatial downscaling method using the Support Vector Machine (SVM) Regression for 25 km Tropical Rainfall Measuring Mission (TRMM) Monthly precipitation is proposed. The nonlinear relationship among hydrometeorological variables and precipitation was effectively depicted by the SVM for predicting downscaled grid precipitation. The accuracy of spatially downscaled precipitation was estimated by comparing with rain gauge data from sixty-four stations and found to be improved than the original TRMM data in overall. Especially the positive bias of the original TRMM data was effectively removed after the downscaling procedure. The spatial distributions of 25 km and 1 km grid precipitation were generally similar, while the local spatial trend was better detected by 1 km grid precipitation. The downscaled grid data derived from the proposed method can be applied in hydrological modelling for higher accuracy and further be studied for developing optimized downscaling method incorporation other regression methods.

Development of the Large-Capacity Mooring Fittings according to MEG4(Mooring Equipment Guideline 4) (MEG4(Mooring Equipment Guideline 4) 적용에 따른 대용량 무어링 피팅 개발)

  • Myung-Su Yi;Kwang-Cheol Seo;Joo-Shin Park
    • Journal of the Korean Society of Marine Environment & Safety
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    • v.29 no.7
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    • pp.950-957
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    • 2023
  • For safe mooring and towing between the ship and port, the equipment must be designed in accordance with the relevant international regulations. However, some small shipyards and engineering companies often do not fully comprehend the core contents. Therefore, the international regulations regarding towing and mooring equipment are reviewed and the bollard and chock are newly developed based on the Mooring Equipment Guideline 4 (MEG4) standards. A bollard is a mooring equipment used to fix a mooring rope to the hull. It has two columns and is mostly used in a figure eight pattern knots under the mooring condition. The chock, which is used to change the mooring rope direction coming into the ship from outside, is manufactured using a casting with curvature. The two mooring equipment are widely used in the stern, bow, and mid-side. Owing to the increase in the size of container vessels and LNG ships, the mooring rope load has increased and the safe working load of the mooring equipment must be revised. This study summarizes and examines the results of the allowable stress method obtained using finite element analysis modelling. To consider the mesh size effect, a reasonable criteria was suggested by referring the existing class guidance. Additionally, the safe working load was verified through nonlinear collapse analysis, and the elastic region against load increments was confirmed. Furthermore, the proposed evaluation method can be used to develop similar equipment in the near future.

An analysis of horizontal deformation of a pile in soil using a beam-on-spring model for the prediction of the eigenfrequency of the offshore wind turbine (해상풍력터빈의 고유진동수 예측을 위한 지반에 인입된 파일의 탄성지지보 모델 기반 수평 거동 해석)

  • Ryue, Jungsoo;Baik, Kyungmin;Kim, Tae-Ryong
    • The Journal of the Acoustical Society of Korea
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    • v.35 no.4
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    • pp.261-271
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    • 2016
  • In the prediction of response of a pile in soil, numerical approaches such as a finite element method are generally applied due to complicate nonlinear behaviors of soils. However, the numerical methods based on the finite elements require heavy efforts in pile and soil modelling and also take long computing time. So their usage is limited especially in the early design stage in which principal dimensions and properties are not specified and tend to vary. On the contrary, theoretical approaches adopting linear approximations for soils are relatively simple and easy to model and take short computing time. Therefore, if they are validated to be reliable, they would be applicable in predicting responses of a pile in soil, particularly in early design stage. In case of wind turbines regarded in this study, it is required to assess their natural frequencies in early stages, and in this simulation the supporting pile inserted in soil could be replaced with a simplified elastic boundary condition at the bottom end of the wind turbine tower. To do this, analysis for a pile in soil is performed in this study to extract the spring constants at the top end of the pile. The pile in soil can be modelled as a beam on elastic spring by assuming that the soils deform within an elastic range. In this study, it is attempted to predict pile deformations and influence factors for lateral loads by means of the beam-on-spring model. As two example supporting structures for wind turbines, mono pile and suction pile models with different diameters are examined by evaluating their influence factors and validated by comparing them with those reported in literature. In addition, the deflection profiles along the depth and spring constants at the top end of the piles are compared to assess their supporting features.

Dynamic Behavior of Reactor Internals under Safe Shutdown Earthquake (안전정기지진하의 원자로내부구조물 거동분석)

  • 김일곤
    • Computational Structural Engineering
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    • v.7 no.3
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    • pp.95-103
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    • 1994
  • The safety related components in the nuclear power plant should be designed to withstand the seismic load. Among these components the integrity of reactor internals under earthquake load is important in stand points of safety and economics, because these are classified to Seismic Class I components. So far the modelling methods of reactor internals have been investigated by many authors. In this paper, the dynamic behaviour of reactor internals of Yong Gwang 1&2 nuclear power plants under SSE(Safe Shutdown Earthquake) load is analyzed by using of the simpled Global Beam Model. For this, as a first step, the characteristic analysis of reactor internal components are performed by using of the finite element code ANSYS. And the Global Beam Model for reactor internals which includes beam elements, nonlinear impact springs which have gaps in upper and lower positions, and hydrodynamical couplings which simulate the fluid-filled cylinders of reactor vessel and core barrel structures is established. And for the exciting external force the response spectrum which is applied to reactor support is converted to the time history input. With this excitation and the model the dynamic behaviour of reactor internals is obtained. As the results, the structural integrity of reactor internal components under seismic excitation is verified and the input for the detailed duel assembly series model could be obtained. And the simplicity and effectiveness of Global Beam Model and the economics of the explicit Runge-Kutta-Gills algorithm in impact problem of high frequency interface components are confirmed.

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