• Title/Summary/Keyword: method of differential equation

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Development of Technique for Predicting Horizontal Displacement of Retaining Wall Induced by Earthquake (지진시 옹벽의 수평변위 예측기법의 개발)

  • Lee, Seung-Hyun;Kim, Byoung-Il
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.22 no.5
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    • pp.143-150
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    • 2021
  • To develop the technique for predicting the horizontal displacement of a retaining wall induced by an earthquake, an equation of motion that depicts the retaining wall-soil vibrating system was derived. The resulting differential equation was solved using the Runge-Kutta-Nystr?m method. Considering the pre-mentioned derivation process, the analysis procedures for obtaining horizontal displacement induced by an earthquake were programmed. The core algorithm of the displacement-force relationship, which is the main engine of the developed program, was suggested. Considering the results obtained by adopting the developed program to the assumed retaining wall under an earthquake, the relationships between the time-displacement, time-force, and displacement-force were reasonable. According to the results computed by the program, the displacements to the front direction of the wall occurred, and the displacement per cycle converged after some cycles elapsed. Displacements with a natural period were calculated, which showed that the maximum displacement was observed when the natural frequency was slightly different from the excitation frequency rather than the same values of the two frequencies. This happens because the vibrating system was modeled by two springs with different stiffness.

Exact Solutions for Vibration and Buckling of Rectangular Plates Loaded at Two Simply-Supported Opposite Edges by In-Plane Moments, Free along the Other Two Edges (면내(面內) 모멘트를 받는 단순지지된 두 모서리와 자유경계인 나머지 두 모서리를 갖는 직사각형 판의 진동과 좌굴의 엄밀해)

  • Shim, Hyun-Ju;Woo, Ha-Young;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.6 no.4 s.22
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    • pp.81-92
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    • 2006
  • This paper presents exact solutions for the free vibrations and buckling of rectangular plates having two opposite, simply supported edges subjected to linearly varying normal stresses causing pure in-plane moments, the other two edges being free. Assuming displacement functions which are sinusoidal in the direction of loading (x), the simply supported edge conditions are satisfied exactly. With this the differential equation of motion for the plate is reduced to an ordinary one having variable coefficients (in y). This equation is solved exactly by assuming power series in y and obtaining its proper coefficients (the method of Frobenius). Applying the free edge boundary conditions at y=0, b yields a fourth order characteristic determinant for the critical buckling moments and vibration frequencies. Convergence of the series is studied carefully. Numerical results are obtained for the critical buckling moments and some of their associated mode shapes. Comparisons are made with known results from less accurate one-dimensional beam theory. Free vibration frequency and mode shape results are also presented. Because the buckling and frequency parameters depend upon Poisson's ratio ( V ), results are shown for $0{\leq}v{\leq}0.5$, valid for isotropic materials.

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Development of Numerical Method for Large Deformation of Soil Using Particle Method (입자법을 이용한 토사의 대변형 해석법 개발)

  • Park, Sung-Sik;Lee, Do-Hyun;Kwon, Min-Ho
    • Journal of the Korean Geotechnical Society
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    • v.29 no.12
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    • pp.35-44
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    • 2013
  • In this study, a particle method without using grid was applied for analysing large deformation problems in soil flows instead of using ordinary finite element or finite difference methods. In the particle method, a continuum equation was discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. Soil behavior changes from solid to liquid state with increasing water content or external load. The Mohr-Coulomb failure criterion was incorporated into the particle method to analyze such three-dimensional soil behavior. The yielding and hardening behavior of soil before failure was analyzed by treating soil as a viscous liquid. First of all, a sand column test without confining pressure and strength was carried out and then a self-standing clay column test with cohesion was carried out. Large deformation from such column tests due to soil yielding or failure was used for verifying the developed particle method. The developed particle method was able to simulate the three-dimensional plastic deformation of soils due to yielding before failure and calculate the variation of normal and shear stresses both in sand and clay columns.

Stress Constraint Topology Optimization using Backpropagation Method in Design Sensitivity Analysis (설계민감도 해석에서 역전파 방법을 사용한 응력제한조건 위상최적설계)

  • Min-Geun, Kim;Seok-Chan, Kim;Jaeseung, Kim;Jai-Kyung, Lee;Geun-Ho, Lee
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.35 no.6
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    • pp.367-374
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    • 2022
  • This papter presents the use of the automatic differential method based on the backpropagation method to obtain the design sensitivity and its application to topology optimization considering the stress constraints. Solving topology optimization problems with stress constraints is difficult owing to singularities, the local nature of stress constraints, and nonlinearity with respect to design variables. To solve the singularity problem, the stress relaxation technique is used, and p-norm for stress constraints is applied instead of local stresses for global stress measures. To overcome the nonlinearity of the design variables in stress constraint problems, it is important to analytically obtain the exact design sensitivity. In conventional topology optimization, design sensitivity is obtained efficiently and accurately using the adjoint variable method; however, obtaining the design sensitivity analytically and additionally solving the adjoint equation is difficult. To address this problem, the design sensitivity is obtained using a backpropagation technique that is used to determine optimal weights and biases in the artificial neural network, and it is applied to the topology optimization with the stress constraints. The backpropagation technique is used in automatic differentiation and can simplify the calculation of the design sensitivity for the objectives or constraint functions without complicated analytical derivations. In addition, the backpropagation process is more computationally efficient than solving adjoint equations in sensitivity calculations.

Application model research on visualizing anti-inflammation effects by using the virtual cell (가상세포를 활용한 항염증 효능 응용모델 연구)

  • Kim, Chul;Yea, Sang-Jun;Kim, Jin-Hyun;Kim, Sang-Kyun;Jang, Hyun-Chul;Kim, An-Na;Nam, Ky-Youb;Song, Mi-Young
    • Herbal Formula Science
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    • v.18 no.2
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    • pp.227-239
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    • 2010
  • Objective : The purpose of this study was to develop the simulator which can analyze the anti-inflammatory effects of herbs based on e-cell, or the virtual cell. Method : We have ensured the medical herbs and its active compounds by investigating the oriental medicine records and NBCI(Biomedicine database). Also we have developed the web-based search system for confirming database related to anti-inflammation. We have researched the cell signal pathway related with inflammatory response control and established the mathematical model of herb interaction on selected signal pathway in e-cell. Finally we have developed the prototype which can confirm the result of this model visibly. Results : We constructed the database of 62 cases of anti-inflammatory active compounds in 61 cases of medical herbs which have been known anti-inflammation effects in the paper, 16 cases of inflammatory factors, 10 cases of signal pathways related with inflammatory response and 6,834 cases of URL(Uniform Resource Locator) of referenced papers. And we embodied the web-based research system, which can research this database. User can search basic and detailed information of medical plants related with anti-inflammatory by using information system. And user can acquire information on an active compounds, a signal pathway and a link URL of related paper. Among investigated ten pathways, we selected NF-${\kappa}B$, which plays important role in activation of immune system, and we searched the mechanisms of actions of proteins which could be components of this pathway. We reduced total network into IKK-$I{\kappa}B$ - NF-${\kappa}B$, and completed mathematic modeling by using ordinary differential equations and response variables of $I{\kappa}B-NF-{\kappa}B$ signaling model network which is suggested by Baltimore Group. We designed OED(Ordinary Differential Equation) for response of IKK, $I{\kappa}B$, $NF-{\kappa}B$ in e-cell's cytoplasm and nucleus, and measured whether an active compound of medicinal plants which is inputted by an user would have a anti-inflammation effects in obedience to change in concentration over time. The proposed model was verified by using experimental results of the papers which are listed on NCBI.

The Effect of Herding Behavior and Perceived Usefulness on Intention to Purchase e-Learning Content: Comparison Analysis by Purchase Experience (무리행동과 지각된 유용성이 이러닝 컨텐츠 구매의도에 미치는 영향: 구매경험에 의한 비교분석)

  • Yoo, Chul-Woo;Kim, Yang-Jin;Moon, Jung-Hoon;Choe, Young-Chan
    • Asia pacific journal of information systems
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    • v.18 no.4
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    • pp.105-130
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    • 2008
  • Consumers of e-learning market differ from those of other markets in that they are replaced in a specific time scale. For example, e-learning contents aimed at highschool senior students cannot be consumed by a specific consumer over the designated period of time. Hence e-learning service providers need to attract new groups of students every year. Due to lack of information on products designed for continuously emerging consumers, the consumers face difficulties in making rational decisions in a short time period. Increased uncertainty of product purchase leads customers to herding behaviors to obtain information of the product from others and imitate them. Taking into consideration of these features of e-learning market, this study will focus on the online herding behavior in purchasing e-learning contents. There is no definite concept for e-learning. However, it is being discussed in a wide range of perspectives from educational engineering to management to e-business etc. Based upon the existing studies, we identify two main view-points regarding e-learning. The first defines e-learning as a concept that includes existing terminologies, such as CBT (Computer Based Training), WBT (Web Based Training), and IBT (Internet Based Training). In this view, e-learning utilizes IT in order to support professors and a part of or entire education systems. In the second perspective, e-learning is defined as the usage of Internet technology to deliver diverse intelligence and achievement enhancing solutions. In other words, only the educations that are done through the Internet and network can be classified as e-learning. We take the second definition of e-learning for our working definition. The main goal of this study is to investigate what factors affect consumer intention to purchase e-learning contents and to identify the differential impact of the factors between consumers with purchase experience and those without the experience. To accomplish the goal of this study, it focuses on herding behavior and perceived usefulness as antecedents to behavioral intention. The proposed research model in the study extends the Technology Acceptance Model by adding herding behavior and usability to take into account the unique characteristics of e-learning content market and e-learning systems use, respectively. The current study also includes consumer experience with e-learning content purchase because the previous experience is believed to affect purchasing intention when consumers buy experience goods or services. Previous studies on e-learning did not consider the characteristics of e-learning contents market and the differential impact of consumer experience on the relationship between the antecedents and behavioral intention, which is the target of this study. This study employs a survey method to empirically test the proposed research model. A survey questionnaire was developed and distributed to 629 informants. 528 responses were collected, which consist of potential customer group (n = 133) and experienced customer group (n = 395). The data were analyzed using PLS method, a structural equation modeling method. Overall, both herding behavior and perceived usefulness influence consumer intention to purchase e-learning contents. In detail, in the case of potential customer group, herding behavior has stronger effect on purchase intention than does perceived usefulness. However, in the case of shopping-experienced customer group, perceived usefulness has stronger effect than does herding behavior. In sum, the results of the analysis show that with regard to purchasing experience, perceived usefulness and herding behavior had differential effects upon the purchase of e-learning contents. As a follow-up analysis, the interaction effects of the number of purchase transaction and herding behavior/perceived usefulness on purchase intention were investigated. The results show that there are no interaction effects. This study contributes to the literature in a couple of ways. From a theoretical perspective, this study examined and showed evidence that the characteristics of e-learning market such as continuous renewal of consumers and thus high uncertainty and individual experiences are important factors to be considered when the purchase intention of e-learning content is studied. This study can be used as a basis for future studies on e-learning success. From a practical perspective, this study provides several important implications on what types of marketing strategies e-learning companies need to build. The bottom lines of these strategies include target group attraction, word-of-mouth management, enhancement of web site usability quality, etc. The limitations of this study are also discussed for future studies.

Theoretical modelling of post - buckling contact interaction of a drill string with inclined bore-hole surface

  • Gulyayev, V.I.;Andrusenko, E.N.;Shlyun, N.V.
    • Structural Engineering and Mechanics
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    • v.49 no.4
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    • pp.427-448
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    • 2014
  • At present, the time of easy oil and gas is over. Now, the largest part of fossil fuels is concentrated in the deepest levels of tectonic structures and in the sea shelves. One of the most cumbersome operations of their extraction is the bore-hole drilling. In connection with austere tectonic and climate conditions, their drivage every so often is associated with great and diversified technological difficulties causing emergencies on frequent occasions. As a rule, they are linked with drill string accidents. A key role in prediction of these situations should play methods of theoretical modelling. For this reason, there is a growing need for development and implementation of new numerical methods for computer simulation of critical and post-critical behavior of drill strings (DSs). In this paper, the processes of non-linear deforming of a DS in cylindrical cavity of a deep bore-hole are considered. On the basis of the theory of curvilinear flexible rods, non-linear constitutive differential equations are deduced. The effects of the longitudinal non-uniform preloading, action of torque and interaction between the DS and the bore-hole surface are taken into account. Owing to the use of curvilinear coordinates in the constraining cylindrical surface and a specially chosen concomitant reference frame, it became possible to separate the desired variables and to reduce the total order of the equation system. To solve it, the method of continuation the solution by parameter and the transfer matrix technique are applied. As a result of the completed numerical analysis, the critical states of the DS loading in the cylindrical channels of inclined bore-holes are found. It is shown that the modes of the post-critical deforming of the DS are associated with its irregular spiral curving prevailing in the zone of bottom-hole-assembly. The possibility of invariant state generation during post-critical deforming is established, condition of its bifurcation is formulated. It is shown that infinite variety of loads can correspond to one geometrical configuration of the DS. They differ each from other by contact force functions.

Modeling of the friction in the tool-workpiece system in diamond burnishing process

  • Maximov, J.T.;Anchev, A.P.;Duncheva, G.V.
    • Coupled systems mechanics
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    • v.4 no.4
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    • pp.279-295
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    • 2015
  • The article presents a theoretical-experimental approach developed for modeling the coefficient of sliding friction in the dynamic system tool-workpiece in slide diamond burnishing of low-alloy unhardened steels. The experimental setup, implemented on conventional lathe, includes a specially designed device, with a straight cantilever beam as body. The beam is simultaneously loaded by bending (from transverse slide friction force) and compression (from longitudinal burnishing force), which is a reason for geometrical nonlinearity. A method, based on the idea of separation of the variables (time and metric) before establishing the differential equation of motion, has been applied for dynamic modeling of the beam elastic curve. Between the longitudinal (burnishing force) and transverse (slide friction force) forces exists a correlation defined by Coulomb's law of sliding friction. On this basis, an analytical relationship between the beam deflection and the sought friction coefficient has been obtained. In order to measure the deflection of the beam, strain gauges connected in a "full bridge" type of circuit are used. A flexible adhesive is selected, which provides an opportunity for dynamic measurements through the constructed measuring system. The signal is proportional to the beam deflection and is fed to the analog input of USB DAQ board, from where the signal enters in a purposely created virtual instrument which is developed by means of Labview. The basic characteristic of the virtual instrument is the ability to record and visualize in a real time the measured deflection. The signal sampling frequency is chosen in accordance with Nyquist-Shannon sampling theorem. In order to obtain a regression model of the friction coefficient with the participation of the diamond burnishing process parameters, an experimental design with 55 experimental points is synthesized. A regression analysis and analysis of variance have been carried out. The influence of the factors on the friction coefficient is established using sections of the hyper-surface of the friction coefficient model with the hyper-planes.

Development of Hydrologic Simulation Model to Predict Flood Runoff in a Small Mountaineous Watershed (산지 소유역의 홍수유출 예측을 위한 모의발생 수문모형의 개발)

  • 권순국;고덕구
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.30 no.3
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    • pp.58-68
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    • 1988
  • Most of the Korean watersheds are mountaineous and consist of various soil types and land uses And seldom watersheds are found to have long term hydrologic records. The SNUA, a hydrologic watershed model was developed to meet the unique characteristics of Korean watershed and simulate the storm hydrographs from a small mountaineous watershed. Also the applicability of the model was tested by comparing the simulated storm hydrographs and the observed from Dochuk watershed, Gwangjugun, Kyunggido The conclusions obtained in this study could be summarized as follows ; 1. The model includes the simulation of interception, evaporation and infiltration for land surface hydrologic cycle on the single storm basis and the flow routing features for both overland and channel systems. 2. Net rainfall is estimated from the continuous computation of water balance at the surface of interception storage accounting for the rainfall intensities and the evaporation losses at each time step. 3. Excess rainfall is calculated by the abstraction of infiltration loss estimated by the Green and Ainpt Model from the net rainfall. 4. A momentum equation in the form of kinematic wave representation is solved by the finite differential method to obtain the runoff rate at the exit of the watershed. 5. The developed SNUA Model is a type of distributed and event model that considers the spatial distribution of the watershed parameters and simulates the hydrograph on a single storm basis. 6. The results of verification test show that the simulated peak flows agree with the observed in the occurence time but have relative enors in the range of 5.4-40.6% in various flow rates and also show that the simulated total runoff have 6.9-32% of relative errors against the observed. 7. To improve the applicability of the model, it was thought that more studies like the application test to the other watersheds of various types or the addition of the other hydrologk components describing subsurface storages are needed.

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Thermal, electrical and mechanical buckling loads of sandwich nano-beams made of FG-CNTRC resting on Pasternak's foundation based on higher order shear deformation theory

  • Arani, Ali Ghorbanpour;Pourjamshidian, Mahmoud;Arefi, Mohammad;Arani, M.R. Ghorbanpour
    • Structural Engineering and Mechanics
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    • v.69 no.4
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    • pp.439-455
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    • 2019
  • This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.