• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.3
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• pp.255-260
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• 2002

This paper describes a fuzzy-based system for analyzing the stress intensity factors (SIFs) of three-dimensional (3D) cracks. A geometry model, i.e. a solid containing one or several 3D cracks is defined. Several distributions of local node density are chosen, and then automatically superposed on one another over the geometry model by using the fuzzy knowledge processing. Nodes are generated by the bucketing method, and ten-coded quadratic tetrahedral solid elements are generated by the Delaunay triangulation techniques. The singular elements such that the mid-point nodes near crack front are shifted at the quarter-points, and these are automatically placed along the 3D crack front. The complete finite element(FE) model is generated, and a stress analysis is performed. The SIFs are calculated using the displacement extrapolation method. To demonstrate practical performances of the present system, semi-elliptical surface cracks in a inhomogeneous plate subjected to uniform tension are solved.

• Journal of Educational Research in Mathematics
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• v.17 no.3
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• pp.253-270
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• 2007

by A.C. Clairaut was written based on the historico-genetic principle such as his . In this paper, by analyzing his we can induce six principles that Clairaut adopted to teach algebra: necessity and curiosity as a motive of studying algebra, harmony of discovery and proof, complementarity of generalization and specialization, connection of knowledge to be learned with already known facts, semantic approaches to procedural knowledge of mathematics, reversible approach. These can be considered as strategies for teaching algebra accorded with beginner's mind. Some of them correspond with characteristics of , but the others are unique in the domain of algebra. And by comparing Clairaut's approaches with school algebra, we discuss about some mathematical subjects: setting equations in relation to problem situations, operations and signs of letters, rule of signs in multiplication, solving quadratic equations, and general relationship between roots and coefficients of equations.

• Economic and Environmental Geology
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• v.27 no.5
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• pp.451-458
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• 1994

Geochemical studies on gold-bearing quartz veins and granitic wallrocks from the Mugeug mine were carried out in order to investigate primary dispersion patterns of elements and to quantify primary dispersion widths of elements with distance from the gold-bearing quartz veins. The best fitting model of dispersion pattern in altered wallrock around the gold-bearing quartz veins is an exponential function for Au, As, Sb, $Na_2O$ and Sr, and a quadratic function for CaO, $K_2O$, MnO, Ba, Rb and Cs. The primary dispersion widths are 15~343 cm in the hanging wall, and 33~173 cm in the footwall. The width of primary dispersion in the hanging wall is twice as thick as that in the footwall mainly due to the thermal effect and volatile components. The primary dispersion width is increased as the increase of gold-bearing quartz vein width and contents of As and Sb in gold-bearing quartz veins, but is not related to Au content in gold-bearing quartz veins.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.8 no.6
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• pp.84-91
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• 1999

The goal of this study is to analyse the stress and the strain occurring within the work piece at the fine-blanking process and hence to assume the size direction and a distribution chart of the shearing stress as the penetration of the punch is being increased trough the application of the FEM. For this analysis we introduced the piece-wise linear method in the non linear structural analysis program for large deformation sheet metal forming and we defined it as the problem of the non linear contact. Therefore we modeled the above problems as quadratic-nodded axi-symmetrical elements for the character-istics of the work piece. From the result of this analysis it was found that the shearing stress is a great deal occurred on the surface of the work piece during the beginning process of the punch penetration and it's effect is expected to influence importantly for the formation of burnish because the deeper is the penetration of the punch in the narrow clearance zone. the greater is the degree of the strain stress.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.6
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• pp.411-416
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• 2016

This paper presents the design methodology of an unknown input observer for Lipschitz nonlinear systems with unknown inputs in the framework of convex optimization. We use an unknown input observer (UIO) to consider both nonlinearity and disturbance. By deriving a sufficient condition for exponential stability in the linear matrix inequality (LMI) form, existence of a stabilizing observer gain matrix of UIO will be assured by checking whether the quadratic stability margin of the error dynamics is greater than the Lipschitz constant or not. If quadratic stability margin is less than a Lipschitz constant, the coordinate transformation may be used to reduce the Lipschitz constant in the new coordinates. Furthermore, to reduce the maximum singular value of the observer gain matrix elements, an object function to minimize it will be optimally designed by modifying its magnitude so that amplification of sensor measurement noise is minimized via multi-objective optimization algorithm. The performance of UIO is compared to a nonlinear observer (Luenberger-like) with an application to a flexible joint robot system considering a change of load and disturbance. Finally, it is validated via simulations that the estimated angular position and velocity provide true values even in the presence of unknown inputs.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.755-770
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• 2009

This study proposes a new smart base isolation system that employs Magneto-Rheological Elastomers (MREs), a class of smart materials whose elastic modulus or stiffness can be varied depending on the magnitude of an applied magnetic field. It also evaluates the dynamic performance of the MRE-based isolation system in reducing vibrations in structures subject to various seismic excitations. As controllable stiffness elements, MREs can increase the dynamic control bandwidth of the isolation system, improving its vibration reduction capability. To study the effectiveness of the MRE-based isolation system, this paper compares its dynamic performance in reducing vibration responses of a base-isolated single-story structure (i.e., 2DOF) with that of a conventional base-isolation system. Moreover, two control algorithms (linear quadratic regulator (LQR)-based control and state-switched control) are considered for regulating the stiffness of MREs. The simulation results show that the MRE-based isolation system outperformed the conventional system in suppressing the maximum base drift, acceleration, and displacement of the structure.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.677-697
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• 2010

This paper focuses on geometrically non-linear static analysis of a simply supported beam made of hyperelastic material subjected to a non-follower transversal uniformly distributed load. As it is known, the line of action of follower forces is affected by the deformation of the elastic system on which they act and therefore such forces are non-conservative. The material of the beam is assumed as isotropic and hyperelastic. Two types of simply supported beams are considered which have the following boundary conditions: 1) There is a pin at left end and a roller at right end of the beam (pinned-rolled beam). 2) Both ends of the beam are supported by pins (pinned-pinned beam). In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element. The considered highly non-linear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. In order to use the solution procedures of Newton-Raphson type, there is need to linearized equilibrium equations, which can be achieved through the linearization of the principle of virtual work in its continuum form. In the study, the effect of the large deflections and rotations on the displacements and the normal stress and the shear stress distributions through the thickness of the beam is investigated in detail. It is known that in the failure analysis, the most important quantities are the principal normal stresses and the maximum shear stress. Therefore these stresses are investigated in detail. The convergence studies are performed for various numbers of finite elements. The effects of the geometric non-linearity and pinned-pinned and pinned-rolled support conditions on the displacements and on the stresses are investigated. By using a twelve-node quadratic element, the free boundary conditions are satisfied and very good stress diagrams are obtained. Also, some of the results of the total Lagrangian finite element model of two dimensional continuum for a twelve-node quadratic element are compared with the results of SAP2000 packet program. Numerical results show that geometrical nonlinearity plays very important role in the static responses of the beam.

• Smart Structures and Systems
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• v.13 no.4
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.42-57
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• 1995

An efficient and accurate scheme has been constructed by taking advantages of the hi-quadratic spline scheme and the higher-order boundary element method selectively depending on computation domains. Boundary surfaces are represented by 8-node boundary elements to describe curved surfaces of a ship and its neighboring free surface more accurately. The variation of the velocity potential complies with the characteristics of the 8-node element on the body surface. But on the free surface, it is assumed to follow that of the hi-quadratic spline scheme. By which, the free surface solution is free from numerical damping and has better numerical dispersion property. As numerical examples, steady and unsteady Neumann-Kelvin problems are considered. Numerical results for a submerged spheroid, Series 60($C_B=0.6$) and a modified support the proposed method. Finally, a new upstream radiation condition is derived using a wave equation operator in order to deal with problems for subcritical reduced frequency. The relevance of this operator has been confirmed in the case of unsteady Kelvin source potential.

• Ocean and Polar Research
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• v.39 no.4
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• pp.269-277
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• 2017

Medium compositions for the hyperthermophilic archaeon, Thermococcus onnurineus NA1 was statistically optimized to enhance formate-driven hydrogen ($H_2$) production by using response surface methodology. From the Plackett-Burman design-based experiment, it was confirmed that among the minor components of medium such as KCl, $MgSO_4$, $NH_4Cl$, Cystein-HCl, trace elements, Fe-EDTA and $CaCl_2$, the trace elements were screened as the only positively effective components with respect to $H_2$ production. Subsequently, the optimal concentrations of the trace elements and the major components of a medium such as NaCl, yeast extract and sodium formate were determined from the five-level central composite design (CCD)-based experiment. The resulting quadratic model predicted the maximum $H_2$ production of 46.6 mmol/L in serum bottle and it was validated experimentally using the optimal medium initially supplemented with 26.70 g/L of NaCl, 9.81 g/L of sodium formate, 3.50 g/L of yeast extract and 4.59 mL/L of trace elements. From the duplicate batch cultivations in the fermentor using the optimized medium, the a maximum $H_2$ production rate up to 71.8 mmol/L/h could be obtained, which was a 65% enhanced value compared with that obtained using the control medium, showing the high efficiency of the optimized medium.