• 제목/요약/키워드: fourth-order equations

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Variational Formulation for Shape Optimization of Spatial Beam Structures (정식화를 이용한 3차원 구조물의 형상 최적설계)

  • 최주호;김종수
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.04a
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    • pp.123-130
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    • 2002
  • A general formulation for shape design sensitivity analysis over three dimensional beam structure is developed based on a variational formulation of the beam in linear elasticity. Sensitivity formula is derived based on variational equations in cartesian coordinates using the material derivative concept and adjoint variable method for the displacement and Von-Mises stress functionals. Shape variation is considered for the beam shape in general 3-dimensional direction as well as for the orientation angle of the beam cross section. In the sensitivity expression, the end points evaluation at each beam segment is added to the integral formula, which are summed over the entire structure. The sensitivity formula can be evaluated with generality and ease even by employing piecewise linear design velocity field despite the bending model is fourth order differential equation. For the numerical implementation, commercial software ANSYS is used as analysis tool for the primal and adjoint analysis. Once the design variable set is defined using ANSYS language, shape and orientation variation vector at each node is generated by making finite difference to the shape with respect to each design parameter, and is used for the computation of sensitivity formula. Several numerical examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. The results are found excellent even by employing a simple linear function for the design velocity evaluation. Shape optimization is carried out for the geometric design of an archgrid and tilted bridge, which is to minimize maximum stress over the structure while maintaining constant weight. In conclusion, the proposed formulation is a useful and easy tool in finding optimum shape in a variety of the spatial frame structures.

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Three-dimensional dynamics of vortex-induced vibration of a pipe with internal flow in the subcritical and supercritical regimes

  • Duan, Jinlong;Chen, Ke;You, Yunxiang;Wang, Renfeng;Li, Jinlong
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.10 no.6
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    • pp.692-710
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    • 2018
  • The Three-dimensional (3-D) dynamical behaviors of a fluid-conveying pipe subjected to vortex-induced vibration are investigated with different internal flow velocity ${\nu}$. The values of the internal flow velocity are considered in both subcritical and supercritical regimes. During the study, the 3-D nonlinear equations are discretized by the Galerkin method and solved by a fourth-order Runge-Kutta method. The results indicate that for a constant internal flow velocity ${\nu}$ in the subcritical regime, the peak Cross-flow (CF) amplitude increases firstly and then decrease accompanied by amplitude jumps with the increase of the external reduced velocity. While two response bands are observed in the In-line (IL) direction. For the dynamics in the lock-in condition, 3-D periodic, quasi-periodic and chaotic vibrations are observed. A variety of CF and IL responses can be detected for different modes with the increase of ${\nu}$. For the cases studied in the supercritical regime, the dynamics shows a great diversity with that in the subcritical regime. Various dynamical responses, which include 3-D periodic, quasi-periodic as well as chaotic motions, are found while both CF and IL responses are coupled while ${\nu}$ is beyond the critical value. Besides, the responses corresponding to different couples of ${\mu}_1$ and ${\mu}_2$ are obviously distinct from each other.

Nonlinear Dynamic Analysis of Steel Lazy Wave Riser using Lumped Mass Line Model (집중질량 라인모델을 이용한 Steel Lazy Wave Riser의 비선형 동적 해석)

  • Oh, Seunghoon;Jung, Jae-Hwan;Park, Byeongwon;Kwon, Yong-Ju;Jung, Dongho
    • Journal of Ocean Engineering and Technology
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    • v.33 no.5
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    • pp.400-410
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    • 2019
  • In this study, the numerical code for the 3D nonlinear dynamic analysis of an SLWR (Steel Lazy Wave Riser) was developed using the lumped mass line model in a FORTRAN environment. Because the lumped mass line model is an explicit method, there is no matrix operation. Thus, the numerical algorithm is simple and fast. In the lumped mass line model, the equations of motion for the riser were derived by applying the various forces acting on each node of the line. The applied forces at the node of the riser consisted of the tension, shear force due to the bending moment, gravitational force, buoyancy force, riser/ground contact force, and hydrodynamic force based on the Morison equation. Time integration was carried out using a Runge-Kutta fourth-order method, which is known to be stable and accurate. To validate the accuracy of the developed numerical code, simulations using the commercial software OrcaFlex were carried out simultaneously and compared with the results of the developed numerical code. To understand the nonlinear dynamic characteristics of an SLWR, dynamic simulations of SLWRs excited at the hang-off point and of SLWRs in regular waves were carried out. From the results of these dynamic simulations, the displacements at the maximum bending moments at important points of the design, like the hang-off point, sagging point, hogging points, and touch-down point, were observed and analyzed.

Development of a Daily Solar Major Flare Occurrence Probability Model Based on Vector Parameters from SDO/HMI

  • Lim, Daye;Moon, Yong-Jae;Park, Jongyeob;Lee, Kangjin;Lee, Jin-Yi
    • The Bulletin of The Korean Astronomical Society
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    • v.42 no.2
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    • pp.59.5-60
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    • 2017
  • We present the relationship between vector magnetic field parameters and solar major flare occurrence rate. Based on this, we are developing a forecast model of major flare (M and X-class) occurrence rate within a day using hourly vector magnetic field data of Space-weather HMI Active Region Patch (SHARP) from May 2010 to April 2017. In order to reduce the projection effect, we use SHARP data whose longitudes are within ${\pm}60$ degrees. We consider six SHARP magnetic parameters (the total unsigned current helicity, the total photospheric magnetic free energy density, the total unsigned vertical current, the absolute value of the net current helicity, the sum of the net current emanating from each polarity, and the total unsigned magnetic flux) with high F-scores as useful predictors of flaring activity from Bobra and Couvidat (2015). We have considered two cases. In case 1, we have divided the data into two sets separated in chronological order. 75% of the data before a given day are used for setting up a flare model and 25% of the data after that day are used for test. In case 2, the data are divided into two sets every year in order to reduce the solar cycle (SC) phase effect. All magnetic parameters are divided into 100 groups to estimate the corresponding flare occurrence rates. The flare identification is determined by using LMSAL flare locations, giving more numbers of flares than the NGDC flare list. Major results are as follows. First, major flare occurrence rates are well correlated with six magnetic parameters. Second, the occurrence rate ranges from 0.001 to 1 for M and X-class flares. Third, the logarithmic values of flaring rates are well approximated by two linear equations with different slopes: steeper one at lower values and lower one at higher values. Fourth, the sum of the net current emanating from each polarity gives the minimum RMS error between observed flare rates and predicted ones. Fifth, the RMS error for case 2, which is taken to reduce SC phase effect, are smaller than those for case 1.

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Experimental Evaluation of Levitation and Imbalance Compensation for the Magnetic Bearing System Using Discrete Time Q-Parameterization Control (이산시간 Q 매개변수화 제어를 이용한 자기축수 시스템에 대한 부상과 불평형보정의 실험적 평가)

  • ;Fumio Matsumura
    • Journal of KSNVE
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    • v.8 no.5
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    • pp.964-973
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    • 1998
  • In this paper we propose a levitation and imbalance compensation controller design methodology of magnetic bearing system. In order to achieve levitation and elimination of unbalance vibartion in some operation speed we use the discrete-time Q-parameterization control. When rotor speed p = 0 there are no rotor unbalance, with frequency equals to the rotational speed. So in order to make levitatiom we choose the Q-parameterization controller free parameter Q such that the controller has poles on the unit circle at z = 1. However, when rotor speed p $\neq$ 0 there exist sinusoidal disturbance forces, with frequency equals to the rotational speed. So in order to achieve asymptotic rejection of these disturbance forces, the Q-parameterization controller free parameter Q is chosen such that the controller has poles on the unit circle at z = $exp^{ipTs}$ for a certain speed of rotation p ( $T_s$ is the sampling period). First, we introduce the experimental setup employed in this research. Second, we give a mathematical model for the magnetic bearing in difference equation form. Third, we explain the proposed discrete-time Q-parameterization controller design methodology. The controller free parameter Q is assumed to be a proper stable transfer function. Fourth, we show that the controller free parameter which satisfies the design objectives can be obtained by simply solving a set of linear equations rather than solving a complicated optimization problem. Finally, several simulation and experimental results are obtained to evaluate the proposed controller. The results obtained show the effectiveness of the proposed controller in eliminating the unbalance vibrations at the design speed of rotation.

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Optimized Allocation of Water for the Multi-Purpose Use in Agricultural Reservoirs (농업용 저수지의 다목적 이용을 위한 용수의 적정배분)

  • 신일선;권순국
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.29 no.3
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    • pp.125-137
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    • 1987
  • The purpose of this paper is to examine some difficulties in water management of agricultural reservoirs in Korea, for there are approximately more than 15,000 reservoirs which are now being utilized for the purpose of irrigation, along with the much amount of expenses and labors to be invested against droughts and floods periodically occurred. Recently, the effective use of water resources in the agricultural reservoirs with a single purpose, is becomming multiple according to the alterable environment of water use. Therefore, the task to allocate agricultural water rationally and economically must be solved for the multiple use of agricultural reservoirs. On the basis of the above statement, this study aims at suggesting the rational method of water management by introducing an optimal technique to allocate the water in an existing agricultural reservoir rationally, for the sake of maximizing the economic effect. To achieve this objective, a reservoir, called "0-Bongje" as a sample of the case study, is selected for an agricultural water development proiect of medium scale. As a model for the optimum allocation of water in the multi-purpose use of reservoirs a linear programming model is developed and analyzed. As a result, findings of the study are as follows : First, a linear programing model is developed for the optimum allocation of water in the multi-purpose use of agricultural reservoirs. By adopting the model in the case of reservoir called "O-Bongje," the optimum solution for such various objects as irrigation area, the amount of domestic water supply, the size of power generation, and the size of reservoir storage, etc., can be obtained. Second, by comparing the net benefits in each object under the changing condition of inflow into the reservoir, the factors which can most affect the yearly total net benefit can be drawn, and they are in the order of the amount of domestic water supply, irrigation area, and power generation. Third, the sensitivity analysis for the decision variable of irrigation which may have a first priority among the objects indicate that the effective method of water management can be rapidly suggested in accordance with a condition under the decreasing area of irrigation. Fourth, in the case of decision making on the water allocation policy in an existing multi-purpose reservoir, the rapid comparison of numerous alternatives can be possible by adopting the linear programming model. Besides, as the resources can be analyed in connection with various activities, it can be concluded that the linear programing model developed in this study is more quantitative than the traditional methods of analysis. Fifth, all the possible constraint equations, in using a linear programming model for adopting a water allocation problem in the agricultural reservoirs, are presented, and the method of analysis is also suggested in this study. Finally, as the linear programming model in this study is found comprehensive, the model can be adopted in any different kind of conditions of agricultural reservoirs for the purpose of analyzing optimum water allocation, if the economic and technical coefficients are known, and the decision variable is changed in accordance with the changing condition of irrigation area.

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Is Backwards Causation Possible? (후향적인 인과성은 가능한가?)

  • Ahn, Gan-Hun
    • Journal of Korean Philosophical Society
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    • v.105
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    • pp.269-290
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    • 2008
  • The purpose of this paper is to explore the possibility of backwards causation. For study, this paper was divided into four views as follows: The first view was sometimes suggested by the people such as M. Dummett who distinguished observers from behaviors. According to observers' view, backwards causation is impossible, whereas behaviors' view possible. However, in a real or genuine sense, it is incorrect for us to argue for impossibility of backwards causation from the observer aspect. The second view was supported by J. H. Schmidt. He analyzed the possibility of backwards causation in terms of macro and micro level analysis about the causal events. According to micro level analysis, backwards causation is possible, but macro level analysis impossible. Usually the latter makes the former something miraculous. Under the macro level analysis, backwards causation, at first, seems to be miraculous phenomena which belongs to the micro level analysis. The third view had to do with physical equation, and the fourth view physical phenomena, respectively. John Earman argued for the backwards causation by the transformation from Lorentz­-Dirac equation to a second-order integro-differential one in the field of electrodynamic acceleration. His argument was criticized because of his misunderstanding about the relationship between two equations. On the other hand, Phil Dowe defended a version of Reichenbach's own theory about the direction of causation founded on the fork asymmetrical causal relation. However his view was different from Reichenbach's because the former defended the backwards causation model of Bell phenomena in quantum mechanics. On the contrary, Reichenbach put stressed on the priority of cause in the causal process. Subjectivism has recently been defended by H. Price, under the label of perspectivism. According to him, in a certain sense causal asymmetry is not in the world, but is rather a product of our own asymmetric perspective on the world. He also suggested causal net, the symmetry of microphysics, and so on. As mentioned above, there are many kind of suggestions of backwards causation. However none of them replaced objectively the main streams of the direction of causal process. The main stream has been usually defended by pragmatical ground. That is, effects do not precede their causes although causes cannot be without their effects.

Structure of Export Competition between Asian NIEs and Japan in the U.S. Import Market and Exchange Rate Effects (한국(韓國)의 아시아신흥공업국(新興工業國) 및 일본(日本)과의 대미수출경쟁(對美輸出競爭) : 환율효과(換率效果)를 중심(中心)으로)

  • Jwa, Sung-hee
    • KDI Journal of Economic Policy
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    • v.12 no.2
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    • pp.3-49
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    • 1990
  • This paper analyzes U.S. demand for imports from Asian NIEs and Japan, utilizing the Almost Ideal Demand System (AIDS) developed by Deaton and Muellbauer, with an emphasis on the effect of changes in the exchange rate. The empirical model assumes a two-stage budgeting process in which the first stage represents the allocation of total U.S. demand among three groups: the Asian NIEs and Japan, six Western developed countries, and the U.S. domestic non-tradables and import competing sector. The second stage represents the allocation of total U.S. imports from the Asian NIEs and Japan among them, by country. According to the AIDS model, the share equation for the Asia NIEs and Japan in U.S. nominal GNP is estimated as a single equation for the first stage. The share equations for those five countries in total U.S. imports are estimated as a system with the general demand restrictions of homogeneity, symmetry and adding-up, together with polynomially distributed lag restrictions. The negativity condition is also satisfied for all cases. The overall results of these complicated estimations, using quarterly data from the first quarter of 1972 to the fourth quarter of 1989, are quite promising in terms of the significance of individual estimators and other statistics. The conclusions drawn from the estimation results and the derived demand elasticities can be summarized as follows: First, the exports of each Asian NIE to the U.S. are competitive with (substitutes for) Japan's exports, while complementary to the exports of fellow NIEs, with the exception of the competitive relation between Hong Kong and Singapore. Second, the exports of each Asian NIE and of Japan to the U.S. are competitive with those of Western developed countries' to the U.S, while they are complementary to the U.S.' non-tradables and import-competing sector. Third, as far as both the first and second stages of budgeting are coneidered, the imports from each Asian NIE and Japan are luxuries in total U.S. consumption. However, when only the second budgeting stage is considered, the imports from Japan and Singapore are luxuries in U.S. imports from the NIEs and Japan, while those of Korea, Taiwan and Hong Kong are necessities. Fourth, the above results may be evidenced more concretely in their implied exchange rate effects. It appears that, in general, a change in the yen-dollar exchange rate will have at least as great an impact, on an NIE's share and volume of exports to the U.S. though in the opposite direction, as a change in the exchange rate of the NIE's own currency $vis-{\grave{a}}-vis$ the dollar. Asian NIEs, therefore, should counteract yen-dollar movements in order to stabilize their exports to the U.S.. More specifically, Korea should depreciate the value of the won relative to the dollar by approximately the same proportion as the depreciation rate of the yen $vis-{\grave{a}}-vis$ the dollar, in order to maintain the volume of Korean exports to the U.S.. In the worst case scenario, Korea should devalue the won by three times the maguitude of the yen's depreciation rate, in order to keep market share in the aforementioned five countries' total exports to the U.S.. Finally, this study provides additional information which may support empirical findings on the competitive relations among the Asian NIEs and Japan. The correlation matrices among the strutures of those five countries' exports to the U.S.. during the 1970s and 1980s were estimated, with the export structure constructed as the shares of each of the 29 industrial sectors' exports as defined by the 3 digit KSIC in total exports to the U.S. from each individual country. In general, the correlation between each of the four Asian NIEs and Japan, and that between Hong Kong and Singapore, are all far below .5, while the ones among the Asian NIEs themselves (except for the one between Hong Kong and Singapore) all greatly exceed .5. If there exists a tendency on the part of the U.S. to import goods in each specific sector from different countries in a relatively constant proportion, the export structures of those countries will probably exhibit a high correlation. To take this hypothesis to the extreme, if the U.S. maintained an absolutely fixed ratio between its imports from any two countries for each of the 29 sectors, the correlation between the export structures of these two countries would be perfect. Therefore, since any two goods purchased in a fixed proportion could be classified as close complements, a high correlation between export structures will imply a complementary relationship between them. Conversely, low correlation would imply a competitive relationship. According to this interpretation, the pattern formed by the correlation coefficients among the five countries' export structures to the U.S. are consistent with the empirical findings of the regression analysis.

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A Study of the Representation in the Elementary Mathematical Problem-Solving Process (초등 수학 문제해결 과정에 사용되는 표현 방법에 대한 연구)

  • Kim, Yu-Jung;Paik, Seok-Yoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.9 no.2
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    • pp.85-110
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    • 2005
  • The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.

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