• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.849-866
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• 2024

In this paper, we study the rectifying curves in multiplicative Euclidean space of dimension 3, i.e., those curves for which the position vector always lies in its rectifying plane. Since the definition of rectifying curve is affine and not metric, we are directly able to perform multiplicative differential-geometric concepts to investigate such curves. By several characterizations, we completely classify the multiplicative rectifying curves by means of the multiplicative spherical curves.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.71-80
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• 2007

Recently, feature-based solid modeling systems have been widely used in product design. However, for engineering analysis of a product model, an ed CAD model composed of mid-surfaces is desirable for conditions in which the ed model does not affect analysis result seriously. To meet this requirement, a variety of solid ion methods such as MAT (medial axis transformation) have been proposed to provide an ed CAE model from a solid design model. The algorithm of the MAT approach can be applied to any complicated solid model. However, additional work to trim and extend some parts of the result is required to obtain a practically useful CAE model because the inscribed sphere used in the MAT method generates insufficient surfaces with branches. On the other hand, the mid-surface ion approach supports a practical method for generating a two-dimensional ed model, even though it has difficulties in creating a mid-surface from some complicated parts. In this paper, we propose a dimension reduction approach on solid models based on the midsurface abstraction approach. This approach simplifies the solid model by abbreviating or removing trivial features first such as the fillet, mounting, or protrusion. The geometry of each face is replaced with mid-patches from the simplified model, and then unnecessary topological entities are deleted to generate a clean ed model. Also, additional work, such as extending and stitching mid-patches, completes the generation of a mid-surface model from the patches.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.997-1009
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• 1999

Silica particle formation and growth process including chemical reaction, coagulation and sintering was studied in a counterflow diffusion flame burner. The counterflow geometry provides a one dimensional flow field, along the stagnation point streamline, which greatly simplifies interpretation of the particle growth characteristics. $SiCl_4$ has been used as the source of silicon in hydrogen/oxygen/argon flames. The temperature profiles obtained by calculation showed a good agreement with experiment data. Using one and two dimensional sectional method, aerosol dynamics equation in a flame was solved, and these two results were compared. The two dimensional section method can consider sintering effect and growth of primary particle during synthesis, thus it showed evolution of morphology of non-spherical particles (aggregates) using surface fractal dimension. The effects of flame temperature and chemical loading on particle dynamics were studied. Geometric mean diameter based on surface area and total number concentration followed the trend of experiment results, especially, the change of diameters showed the sintering effect in high temperature environment.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.7 s.166
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• pp.1094-1103
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• 1999

Ice-plugging of tube in nuclear power plant has been widely used for the purpose of preventing flow of the tube temporarily like a valve. Most common plugging method employs Liquid Nitrogen Gas of $-196^{\circ}C$. According to the change of tube materials and its dimension, the thermal stress caused from the application of the frozen gas can be varied. In this research, a series of experiments have been carried out to inspect the effect of tube geometry on thermal stresses induced due to ice-plugging. Two typical dimension of stainless and mild steels of 3 and 6 inch diameters were used for the experiments. Each critical spots were checked using strain rosette gages. Another inspection was made on the pressure and temperature of the fluid. It is shown that significant thermal stress level which can cause plastic deformation of failure has not been noticed in this series of experiments.

• Geomechanics and Engineering
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• v.3 no.3
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• pp.219-231
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• 2011

Waste fills resulting from coal mining should consist of large, free-draining sedimentary rocks fragments. The successful performance of these fills is related to the strength and durability of the individual rock fragments. When fills are made of shale fragments, some fragments will be durable and some will degrade into soil particles resulting from slaking and inter-particle point loads. The degraded material fills the voids between the intact fragments, and results in settlement. A laboratory program with point load and slake durability tests as well as thin section examination of sixty-eight shale samples from the Appalachian region of the United States revealed that pore micro-geometry has a major influence on degradation. Under saturated and unsaturated conditions, the shales absorb water, and the air in their pores is compressed, breaking the shales. This breakage was more pronounced in shales with smooth pore boundaries and having a diameter equal to or smaller than 0.060 mm. If the pore walls were rough, the air-pressure breaking mechanism was not effective. However, pore roughness (measured by the fractal dimension) had a detrimental effect on point load resistance. This study indicated that the optimum shales to resist both slaking as well as point loads are those that have pores with a fractal dimension equal to 1.425 and a diameter equal to or smaller than 0.06 mm.

• Geomechanics and Engineering
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• v.14 no.1
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• pp.51-60
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• 2018

The foundations are classified into shallow and deep, which have important differences: in terms of geometry, the behavior of the soil, its structural functionality, and its constructive systems. The shallow foundations may be of various types according to their function; isolated footings, combined footings, strip footings, and slabs foundation. The isolated footings are of the type rectangular, square and circular. The combined footing may be rectangular, trapezoidal or T-shaped in plan. This paper presents a new model for T-shaped combined footings to obtain the most economical contact surface on the soil (optimal dimensioning) to support an axial load and moment in two directions to each column. The new model considers the soil real pressure, i.e., the pressure varies linearly. The classical model uses the technique of test and error, i.e., a dimension is proposed, and subsequently, the equation of the biaxial bending is used to obtain the stresses acting on each vertex of the T-shaped combined footing, which must meet the conditions following: The minimum stress should be equal or greater than zero, and maximum stress must be equal or less than the allowable capacity that can withstand the soil. To illustrate the validity of the new model, numerical examples are presented to obtain the minimum area of the contact surface on the soil for T-shaped combined footings subjected to an axial load and moments in two directions applied to each column.

• The KSFM Journal of Fluid Machinery
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• v.14 no.6
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• pp.91-95
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• 2011

This paper deals with the detail rotordynamic analysis for the assembly rotor composed of turbine wheel, turbine shaft, connecting arbor, and flange & spindle in order to perform the spin test of turbocharger turbine. Prior to rotordynamic analysis, the 1st spin test was performed but the test was failed by excess vibration in the neighborhood rated speed. It is the reason for this fail that the separation margin between the rated speed and critical speed is not enough, confirmed by rotordynamic analysis results. Since then, the dimension of turbine shaft was modified and the critical speeds were again reviewed for modified assmebly rotor. In results, the separation margin between the rated speed and critical speed is over 20% and then the 2nd spin test was performed successfully. In preparing spin test for turbine, compressor wheels and etc., the geometry design of connecting arbor and dimension of rough machining should be reviewed by considering rotordynamic results, and the separation margin should be enough for successful spin test.

• Water Engineering Research
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• v.6 no.2
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• pp.49-61
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• 2005

This paper presents the numerical study to examine characteristics of fluid flow and solute transport in a rough fracture subject to effective normal stresses. The aperture distribution is generated by using the self-affine fractal model. In order to represent a nonlinear relationship between the supported normal stress and the fracture aperture, we combine a simple mechanical model with the local flow model. The solute transport is simulated using the random walk particle following algorithm. Results of numerical simulations show that the flow is significantly affected by the geometry of aperture distribution varying with the effective normal stress level while it is slightly affected by the fractal dimension that determines the degree of the fracture surface roughness. However, solute transport is influenced by the effective normal stress as well as the fracture surface roughness.

• Journal of the Optical Society of Korea
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• v.18 no.5
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• pp.531-537
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• 2014

Through-silicon vias (TSVs) are fine, deep holes fabricated for connecting vertically stacked wafers during three-dimensional packaging of semiconductors. Measurement of the TSV geometry is very important because TSVs that are not manufactured as designed can cause many problems, and measuring the critical dimension (CD) of TSVs becomes more and more important, along with depth measurement. Applying white-light scanning interferometry to TSV measurement, especially the bottom CD measurement, is difficult due to the attenuation of light around the edge of the bottom of the hole when using a low numerical aperture. In this paper we propose and demonstrate four bottom CD measurement methods for TSVs: the cross section method, profile analysis method, tomographic image analysis method, and the two-dimensional Gaussian fitting method. To verify and demonstrate these methods, a practical TSV sample with a high aspect ratio of 11.2 is prepared and tested. The results from the proposed measurement methods using white-light scanning interferometry are compared to results from scanning electron microscope (SEM) measurements. The accuracy is highest for the cross section method, with an error of 3.5%, while a relative repeatability of 3.2% is achieved by the two-dimensional Gaussian fitting method.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.