• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.947-955
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• 2020

Predicting the sloshing motion of a coolant during a seismic assessment of a rectangular spent fuel pool is of critical concern. Linear theory, which provides a simple analytical method, has been used to predict the sloshing motion in rectangular pools and tanks. However, this theory is not suitable for the high-frequency excitation problem. In this study, the authors developed a simple analytical method for predicting the sloshing motion in a rectangular pool for a wide range of excitation frequencies. The correlation among the linear theory parameters, influencing on excitation and convective waves, and the excitation frequency is investigated. Sloshing waves in a rectangular pool with several liquid heights are predicted using the original linear theory, a modified linear theory and computational fluid dynamics analysis. The results demonstrate that the developed method can predict sloshing motion over a wide range of excitation frequencies. However, the developed method has the limitations of linear solutions since it neglects the nonlinear features of sloshing motion. Despite these limitations, the authors believe that the developed method can be useful as a simple analytical method for predicting the sloshing motion in a rectangular pool under various external excitations.

• The Journal of Art Theory & Practice
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• no.7
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• pp.165-188
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• 2009

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term 'vanishing point'. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of 'vanishing points'. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04b
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• pp.447-454
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• 1998

The main object of the study is that axial force-moment relationships for high strength concrete structures using reliability theory(Linear statstical method, Monte Carlo Simulation) including probability conception. And mean stress factors and centroid factors proposed to high strength concrete structures using reliability theory(Linear statstical method, Monte Carlo Simulation). Finally, The established experimental data for axial force-moment relationships are compared to the analytical data(data for Linear statstical method and Monte Carlo Simulation) for axial force-moment relationships in this analytical method.

• Advances in nano research
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• v.12 no.1
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• pp.37-47
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• 2022

In this paper, the non-linear static analysis of Timoshenko nanobeams consisting of bi-directional functionally graded material (BFGM) with immovable ends is investigated. The scratching in the FG nanobeam mid-plane, is the source of nonlinearity of the bending problems. The nonlocal theory is used to investigate the non-linear static deflection of nanobeam. In order to simplify the formulation, the problem formulas is derived according to the physical middle surface. The Hamilton principle is employed to determine governing partial differential equations as well as boundary conditions. Moreover, the differential quadrature method (DQM) and direct iterative method are applied to solve governing equations. Present results for non-linear static deflection were compared with previously published results in order to validate the present formulation. The impacts of the nonlocal factors, beam length and material property gradient on the non-linear static deflection of BFG nanobeams are investigated. It is observed that these parameters are vital in the value of the non-linear static deflection of the BFG nanobeam.

• Publications of The Korean Astronomical Society
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• v.26 no.2
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• pp.55-70
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• 2011

Cosmological linear perturbation theory has fundamental importance in securing the current cosmological paradigm by connecting theories with observations. Here we present an explanation of the method used in relativistic cosmological perturbation theory and show the derivation of basic perturbation equations.

• Selected Papers of The Society of Naval Architects of Korea
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• v.2 no.1
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• pp.79-105
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• 1994

A ship in waves is suffered from the various wave loads that comes from its motion throughout its life. Because these loads are dynamic, the analysis of a ship structure must be considered as the dynamic problem precisely. In the rationally-based design, the dynamic structural analysis is carried out using dynamic wave loads provided from the results of the ship motion calculation as a rigid body. This method is based on the linear theory assumed low wave height and small amplitude of motion. But at the rough sea condition, high wave height, compared with ship's depth, induce the large ship motion, so the ship section configuration under waterline is rapidly changed at each time. This results in a non-linear problem. Considering above situation in this paper, a strength analysis method is introduced for the hull girder among waves considering non-linear hydrodynamic forces. This paper evaluates the overall or primary level of the ship structural dynamic loading and dynamic response provided from the non-linear wave forces, and bottom flare impact forces by momentum slamming theory. For numerical calculation a ship is idealized as a hollow thin-walled box beam using thin walled beam theory and the finite element method is used. This method applied to a 40,000 ton double hull tanker and attention is paid to the influence of the response of the ship's speed, wave length and wave height compared with the linear strip theory.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.686-689
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• 2004

As the demands of X-Y linear motors increase, it becomes very important to measure flatness errors and to compensate them. In this study, in order to investigate flatness errors, a laser interferometer is used for measurement. To improve the measurement efficiency, a Union Jack method is adopted instead of a square method. The square method is frequently used because of its accuracy, but it requires many measurement points. In this study, the Union Jack method with Grey Theory is used. By using the Grey Theory, unmeasured data are predicted, and these are compared with results of the square method. The results show that the Union Jack method with Grey Theory is accurate enough to replace the square method.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.315-328
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• 2005

In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.

• Journal of the Korea Concrete Institute
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• v.14 no.6
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• pp.843-850
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• 2002

Linear transformation theory has been effectively used in the design and analysis of prestressed concrete structures. The underlying assumptions of the theory, which were often overlooked, are investigated in the respect of equivalent load method. As a result, it is found that the same equivalent loading system is produced for all the cases of the linear transformation by the assumptions of the conventional equivalent load method. On the other hand, equivalent loading systems in a strict and accurate sense do not satisfy the classical theories of the linear transformation. Also, it is shown that a little different equivalent loading system from the conventional one is obtained for each linear transformation according to the proposed equivalent load method that is derived from the self-equilibrium property of the tendon-induced forces. Therefore, it can be concluded that the linear transformation theory is valid only when referring to the conventional approximate equivalent load method. The discussions are further extended to the eccentrically located circumferential tendon in the wall of containment structures, where the problem of eccentricity is analyzed also from the view point of the linear transformation.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.481-493
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• 2011

We prove a theorem which shows the existence of at least three ${\pi}$-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.