• Education of Primary School Mathematics
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• v.8 no.1
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• pp.1-11
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• 2004

Whole number concept is an important part of mathematics learning. Elementary school students should understand and master whole number concept. Models can help students learn whole number concepts. Realistic Mathematics Education in Netherlands had investigated and developed three different structural models: line model, group model, combination model. These models are related whole number concepts and structures closely and compatible. The purpose of this study is to investigate models related with whole numbers in 7th elementary textbooks. As a result of analyses, we found out some pattern and several problems. On the foundation of the analyses, we discussed the better ways of using models in teaching whole number and the research issues concerning these.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2002.05a
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• pp.239-244
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• 2002

Even though, tanks are used at the many industry plants, it is very difficult to control the tank level without any overflow and shortage; moreover, cause of its complication of dynamics and nonlinearity, it's impossible to realize the accurate control using the mathematical model which can be applied to the various operation modes. However, the sliding mode controller(SMC) is known as having the robust variable structures for the nonlinear control systems with the parametric perturbations and with the sudden disturbances, but the auto-tuning of parameters was a problem. Therefore, in this paper, a Genetic Algorithm based Sliding Mode Controller (GA-SMC) for the precise control of the coupled tank level was tried. GA optimized the SMCs switching parameters easily and rapidly. The simulation results are shown that the tank level could be satisfactorily controlled with less overshoot and steady-stale error by the proposed GA-SMC.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.8 s.197
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• pp.108-115
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• 2007

3D nano-scale manufacturing is an important aspect of advanced manufacturing technology. A key element in ability to view, fabricate, and in some cases operate micro-devices is the availability of tightly focused particle beams, particularly of photons, electrons, and ions. The use of ions is the only way to fabricate directly micro-/ nano-scale structures. It has been utilized as a direct-write method for lithography, implantation, and milling of functional devices. The simulation of ion beam induced physical and chemical phenomena based on sound mathematical models associated with simulation methods is presented for 3D micro-/nanofabrication. The results obtained from experimental investigation and characteristics of ion beam induced direct fabrication will be discussed.

• Smart Structures and Systems
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• v.18 no.4
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• pp.707-731
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• 2016

A unified mathematical model of the equations of generalized magneto-thermoelasticty based on fractional derivative heat transfer for isotropic perfect conducting media is given. Some essential theorems on the linear coupled and generalized theories of thermoelasticity e.g., the Lord- Shulman (LS) theory, Green-Lindsay (GL) theory and the coupled theory (CTE) as well as dual-phase-lag (DPL) heat conduction law are established. Laplace transform techniques are used. The method of the matrix exponential which constitutes the basis of the state-space approach of modern theory is applied to the non-dimensional equations. The resulting formulation is applied to a variety of one-dimensional problems. The solutions to a thermal shock problem and to a problem of a layer media are obtained in the present of a transverse uniform magnetic field. According to the numerical results and its graphs, conclusion about the new model has been constructed. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

• Steel and Composite Structures
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• v.21 no.4
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

• Smart Structures and Systems
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• v.14 no.4
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• pp.643-658
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• 2014

This paper presents the design, modelling and, simulation and experimental results of a shape memory alloy (SMA) actuator based critical motion control application. Dynamic performance of SMA and its ability in replacing servo motor is studied for which the famous open loop unstable balancing ball and beam system direct driven by antagonistic SMA is designed and developed. Simulation uses the mathematical model of ball and beam structure derived from the first principles and model estimated for the SMA actuator by system identification. A PID based cascade control system consisting of two loops is designed and control of ball trajectory for various target positions with settling time as control parameter is verified experimentally. The results demonstrate the performance of SMA for a complicated i.e., under actuated, highly nonlinear unstable system, and thereby it's dynamic behaviour. Control strategies bring out the effectiveness of the actuator and its possible application to much more complex applications such as in aerospace control and robotics.

• Steel and Composite Structures
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• v.25 no.4
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• pp.497-503
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• 2017

In this paper, nonlinear vibration of multi-degree of freedom systems are studied. It has been tried to develop the mathematical model of systems by second-order nonlinear partial differential equations. The masses are connected with linear and nonlinear springs in series. A great effort has been done to solve the nonlinear governing equations analytically. A new analytical method called Variational Iteration Method (VIM) is proposed and successfully applied to the problem. The linear and nonlinear frequencies are obtained and the results are compared with numerical solutions. The first order of Variational Iteration Method (VIM) leads us to high accurate solution.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.841-846
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• 2006

This paper addresses the method for the shape design sensitivity analysis of the buckling load in the continuous elastic body. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Though the buckling problem is more efficiently solved by the structural elements such as beam and shell, the elastic solids are considered in this paper because the solid elements can be used in general for any kind of structures whether they are thick or thin. The initial stress and buckling analysis is carried out by the commercial analysis code ANSYS. The sensitivity is computed by using the mathematical package MATLAB using the results of ANSYS. Several problems including straight and curved beams under compressive load, ring under pressure load, thin-walled section are chosen to illustrate the efficiency of the presented method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1989.10a
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• pp.34-39
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• 1989

Recent trends in design standards development have encouraged the use of probabilistic limit sate design concepts. Reliability analysis adopted in those advanced countries have the potentials that they afford for symplifying the design Process arid placing it on a consistent reliability based for various construction materials. This study is proposed in the reliability analysis of plane frame structures using second-order moment method(Level-II they). Lind-Hasofer's minimum distance method is use in the derivation of an mathematical algorithm as well as an determination of Correlation cofficients, reliability index and total reliability index depending on the multiple failure modes. In addition. This study is employed as a practical tool for the approximate reliability analysis. Results of the numerincal analysis showed that the difference between the reliability index of the failure probability of the multiple failure modes and the total reliability index of the failure probability with the simultaneous failure modes deviated nearly 3∼10% depending on tile performance functions.

• Journal of the Speleological Society of Korea
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• no.71
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• pp.13-17
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• 2006

New methods of nano sized material and composite coating preparations have been considered on the base of mathematical model of abrasion reaction interaction of milling and grinding bodies in planetary centrifugal mill. The essence of the method is the abrasive and oxidative wear of the milling bodies and amorphous (better inert) additives. Interactions between them has been supplied the necessary impulse of pressure and temperature on the impact frictional contacts and promoted chemical processes. The offered method can find application for such processing as sintering and geological minerals opening.