• Steel and Composite Structures
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• v.46 no.5
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• pp.649-658
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• 2023

Although some scholars have studied the thermal post-buckling of graphene platelets strengthened metal foams (GPLRMFs) plates, they have not considered the influence of initial geometrical imperfection. Inspired by this fact, the present paper studies the thermal post-buckling characteristics of GPLRMFs plates with initial geometrical imperfection. Three kinds of graphene platelets (GPLs) distribution patterns including three patterns have been considered. The governing equations are derived according to the first-order plate theory and solved with the help of the Galerkin method. According to the comparison with published paper, the accuracy and correctness of the present research are verified. In the end, the effects of material properties and initial geometrical imperfection on the thermal post-buckling response of the GPLRMFs plates are examined. It can be found that the presence of initial geometrical imperfection reduces the thermal post-buckling strength. In addition, the present study indicates that GPL-A pattern is best way to improve thermal post-buckling strength for GPLRMFs plates, and the presence of foams can improve the thermal post-buckling strength of GPLRMFs plates, the Foam- II and Foam- I patterns have the lowest and highest thermal post-buckling strength. Our research can provide guidance for the thermal stability analysis of GPLRMFs plates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.1
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• pp.95-103
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• 2015

This paper presents the effects of the tool shape on the geometrical characteristics of flat end-milled side walls. A tool shape is characterized by such parameters as helix angle, number of cutting edges, and diameter. The geometrical characteristics of the side walls are represented by the surface profiles in the feed and axial directions, which are orthogonal to each other. The geometrical defects in each direction are estimated based on the instantaneous apparent cutting areas, which are represented by the interference area between the tool and workpiece and that between the cutting edge and workpiece. It is confirmed that a geometrical defect in the feed direction is formed when the tool leaves the workpiece and the curvature of the tool path changes. Defects in the axial direction are also found in the side walls, except for the defect zone in the feed direction. An up-cut using an end-mill with a steeper helix angle, a greater number of cutting edges, and a smaller diameter are thus found to improve the geometrical accuracy of end-milled side walls.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.52.1-52.1
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• 2012

It is often said that there is little geometrical mind in Korean history. However, a method to project the surface of a sphere onto 2-dimensional plain was applied to the representative Korean star chart or Cheonsang Yeolcha Bunyajido (天象列次分野之圖). The method, called the equi-distant polar projection, was explained in detail in ancient Chinese history book of the Tang dynasty, which was originated from older history. Another method of the Mercator projection was introduced by the famous engineer Su Song (蘇頌) of the Song dynasty. The description has quite geometrical thoughts, especially the concept of infinity or convergence appears, However, this type of sky projection method was not widely used in east Asia. When the European Jesuits came to China to evangelize the Chinese people, they found that the Chinese people paid much attention to advanced European astronomical knowledge. Thus, they introduced the European astronomical knowledges into China, and the star chart was one of them. The projection method of the new charts were quite different from the Chinese tradition. When the Koreans brought those new star chart from China, they must have known the geometrical description of the method. The method was described in detail in a volume of Chongzhen Lishi (崇禎曆書) or Xiyang Xinfa Lishu (西洋新法曆書). The explanation consists of three part. One is the quantitative way; another is a geometrical way using axiomatic systems; and the other is the practical method to draw star chart with the geometical projection. However, when we see the Honcheon Jeondo (渾天全圖) that is thought to be duplicated by Kim Jeongho (金正浩), the new geometrical method was not so widely known to the Koreans. I will discuss the reason why the geometrical minds have not been widely adopted in the Korean civilization.

• School Mathematics
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• v.11 no.1
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• pp.147-164
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• 2009

This study investigated the development of geometrical thinking levels of the under achievers at mathematics through supplementary classes according to van Hiele's learning process by stages using mathematical journal writing. We selected five under achievers at mathematics among the fourth graders. We examined their geometrical thinking levels in advance and interviewed them to collect basic data related to their family backgrounds and their attitude toward mathematics and their characteristics. Supplementary classes for the under achievers were conducted a couple of times a week during 12 weeks. Each class was conducted through five learning stages of van Hiele and journal writing was applied to the last consolidating stage. After 12th class had been finished, posttest on geometrical thinking levels was conducted and the journals written by the pupils were analyzed to find out changes in their geometrical thinking levels. The result is that three out of five under achievers showed one or two level-up in their geometrical thinking levels, though the other two pupils remained at the same level as the results by the pretest. Moreover we found that mathematical journal writing could provide the pupils with opportunities to restructure the content which they study through their class.

• 전기의세계
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• v.14 no.1
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• pp.5-12
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• 1965

In the designs of the sensitive electronic devices such as phase sensitive detector, X-ray diffractometer, and neutron diffractometers, we must take into account the geometrical factors in a coil systems and extraneous stray fields. Input wave forms in such a sensitive electronic devices are often altered by the influence of these factors. Since the magnitude of the stray fields is generally very small, this affection may be removed by applying a good shielding but it is not ease to remove the affection from a geometrical factor. This affection must be however calculated by the theoretical methods and analytical solution in the equation of these factors. The fundamental purpose of this paper lie in the theoretical calculations and practical measurements of the geometrical factor in the coil systems, finite solenoid, and four point prove. In the heoretical calculations, the geometrical factors in the coil systems were calculated by applying the elliptic functions and in the contact points were calculated by applying the elliptic functions and in the contact points were calculated by applying the eigen functions and the infinite series. The measurements were carried out by using the sensitive electronic device made from author's design, as shown in the Fig. 9. The result of this work has verified the essential correctness of theoretical investigations and measuring techniques of geometrical factors on the design of sensitive electronic devices. It also has several advantages such that: (1) all the data obtained may give effective data to designer to work on the field of sensitive electronic devices or microelectronic devices, (2) it has evidently explained the characteristics of electrical investigations and physical definition, and has removed the conventional error of geometrical factors in the coil systems and contact points.

• Journal of the Korean Society of Costume
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• v.61 no.8
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• pp.85-99
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• 2011

Geometrical figures have been used as artwork motifs from the ancient times to the present day. The area of fashion, being a part of modern art, is also largely influenced by geometry and geometrical shapes are being used as a motif for fashion design now more than ever before. However, studies about geometry in the fashion field are not yet done enough and further research is necessary. This research will therefore investigate the usages of round, square and triangular design in contemporary fashion. The main scope of this research is to look at the type of expression and analyze the intrinsic meanings of these shapes in modern fashion. This research will look profoundly into the general characteristics of these geometrical figures and analyze the effects and uniqueness found in the world collection introduced since 2007. As a result from this study, it was found that round and square objects were perceived in such a straightforward and positive way and these designs, when worn, really completed the final look. On the other hand, the triangular design was used mainly for spatial expansion and was interpreted in a more metaphorical, indirect and abstract way. The intrinsic meaning of round, square and triangle figures in contemporary fashion consists of the informal features that really steps out of the formative clothing structure. The topological changes that is formed from the interactive functions and the wholism that creates a new system through integration of the human body and clothing contains the intrinsic meaning of these geometrical figures. Based on the research results, the method of expression and the characteristics of modern day fashion's geometrical figures was able to be easily understood. This work provides the useful information on the development of fashion design and the extended interpretation of clothing structure.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.10a
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• pp.106-110
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• 2001

The ball-end milling process is widely used in the die/mold industries, and it is very suitable for the machining of free-form surfaces. However, this process is inherently inefficient process to compared with the end-milling or face milling process, since it relays upon the machining at the cutter/surface contact point. The machined part is the result of continuous point-to-point machining on the free-form surface. And cusps (or scallops) remain at the machined part along the cutter paths and they give the geometrical roughness of the workpiece. Thus, for the good geometrical roughness of the workpiece, it is required very tightly spaced cutter paths in this ball-endmilling process. However, with the tight cutter paths, the geometrical roughness of the workpiece is not regular on the workpiece since the cusp height is variable in the previously developed ISO-parametric or Cartesian machining methods. This paper suggests a method of tool path generation which makes the geometrical roughness of workpiece be constant through the machined surface. In this method, Ferguson Surface design Model is used and cusp height is derived from the instantaneous curvatures. And, to have constant cusp height, an increment of parameter u or v is estimated along the reference cutter path. In ball-end milling experiments, the cusp pattern was examined, and it was proved that the geometrical roughness could be regular by suggested tool path generation method.

• Korean Institute of Interior Design Journal
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• no.26
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• pp.95-103
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• 2001

This study was performed to search for the geometrical principles in modern architecture and design based on Frobel's educational idea and Kindergarten system. Especially, it studies on the geometrical principles of Froebel's building gifts and it's types, and then illustrates applied examples in modern architecture and design. As the architectural scope, the architecture and design theory of Frank Lloyd Wright and Bauhaus in early 20th century is analyzed. The conclusions of this study that starts these purpose are as follows. First, Froebel's educational theory is based on principles and rules which are perceived through the observation of nature, and Froebel's Kindergarten system consists of geometrical building gifts and categories of geometrical forms. Second, the characteristics of Froebel's building gifts are mathematical size, proportion, symmetry and the rules of spatial relation. Third, the influence of Froebel's kindergarten system on Bauhaus is that it based on the rational rules of $\bigtriangleup\square\bigcirc$ organized by geometrical basic forms as like Froebel's educational idea. And the influence of Froebel's Kindergarten system on Frank Lloyd Wright is that he used unit system, unity of space and structure and modular system as like the Froebel's building gifts.

• Journal of the Korean Solar Energy Society
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• v.29 no.2
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• pp.39-46
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• 2009

Heliostat, as a mirror system tracking the sun's movement, is the most important subsystem determining the efficiency of solar thermal power plant. Thus the accurate sun tracking performance under the various hazardous operating condition, is required. This study presents a methodology of development of the solar ray tracing technique and the application of it in the analysis of sun tracking error due to the heliostat geometrical errors. The geometrical errors considered here are the azimuth axis tilting error and the elevation axis tilting error. We first analyze the geometry of solar ray reflected from the heliostat. Then the point on the receiver, where the solar ray reflected from the heliostat is landed, is computed and compared with the original intended point, which represents the sun tracking error. The result obtained shows that the effect of geometrical error on the sun tracking performance is varying with time(season) and the heliostat location. It also shows that the heliostat located near the solar tower has larger sun tracking error than that of the heliostat located farther.

• Korean Institute of Interior Design Journal
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• v.14 no.3 s.50
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• pp.95-102
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• 2005

Guarini's architectural contribution has simply focused on the dome structure that has been known to us; however, his geometric and spatial construction has been overlooked so far Through this study, it has been demonstrated that the dome structure was simply part of geometrical forms that Guarini wanted to express ultimately and it functioned as a geometrical element such as the network combined with the entire spatial structure. The purpose of this study is to reevaluate Guarini's architectural thought by means of investigating the ultimate principles of spatial composition appeared in the late Baroque architecture through the analysis of the principles of spatial composition and organized formal Idioms by Guarini's geometrical concepts. Besides, it has been assumed that such geometrical concepts by Guarini's mathematical proportion and his reiteration and change of diagrams could be clearly distinguished from the Classical geometry in the Renaissance and Guarini. suggested a way to create a new space through more active and amusing application and transformation. In this aspect, Guarini's principles of geometric composition will be one of the role models that need to be seriously reconsidered in chaotic reality of modern architecture.