• Steel and Composite Structures
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• 재36권6호
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• pp.711-727
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• 2020

In the present research, the free vibration analysis of functionally graded (FG) nanocomposite deep spherical shells reinforced by graphene platelets (GPLs) on elastic foundation is performed. The elastic foundation is assumed to be Winkler-Past ernak-type. It is also assumed that graphaene platelets are randomly oriented and uniformly dispersed in each layer of the nanocomposite shell. Volume fraction of the graphene platelets as nanofillers may be different in the layers. The modified HalpinTsai model is used to approximate the effective mechanical properties of the multilayer nanocomposite. With the aid of the first order shear deformation shell theory and implementing Hamilton's principle, motion equations are derived. Afterwards, the generalized differential quadrature method (GDQM) is utilized to study the free vibration characteristics of FG-GPLRC spherical shell. To assess the validity and accuracy of the presented method, the results are compared with the available researches. Finally, the natural frequencies and corresponding mode shapes are provided for different boundary conditions, GPLs volume fraction, types of functionally graded, elastic foundation coefficients, opening angles of shell, and thickness-to-radius ratio.

• Geomechanics and Engineering
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• 제13권4호
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• pp.585-600
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• 2017

This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.

• 한국광학회지
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• 제13권3호
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• pp.266-271
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• 2002

구면수차와 Stiles-Crawford 효과를 기준으로 4개의 굴절비구면을 가지는 모형안을 최적화 기법으로 설계하였다. 구속조건으로는 측정된 안구의 곡률반경 , 중심두께, 비구면도, 구면수차를 사용하였다. 또한 동공에서의 Stiles-Crawford 효과를 고려하여 최적화하였다 최적화의 결과로 얻은 모형안의 근축영역값들은 유효초점거리 20.8169mm, 상측정점초점거리 15.4820mm, 물측정점초점거리 -13.8528mm, 상거리 15.7150mm이다. 본 논문의 모형안은 한국인 정시 75안을 대상으로 측정되어진 자료를 바탕으로 국내에서 처음으로 제작된 정밀모형안이다.

• International Journal of Precision Engineering and Manufacturing
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• 제4권3호
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• pp.48-54
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• 2003

This paper deals with mirror grinding of a small-sized aspherical lens by a resin bonded diamond spherical wheel. Up to now, a spherical lens has been used for the lens of the optical communication optical part. However, recently, aspherical optical parts are mainly used in order to attempt the improvement in image quality and miniaturization of the optical device. It is possible to manufacture the aspherical lens which is presently being used in optical instrument through ultra-precision machining technology. Also, to realize compactness, efforts are being made to produce a micro aspherical lens, fur which the development of a high-precision, micro molding die is inevitable. Therefore, extensive research is being done on methods of producing a micro aspherical surface by high-precision grinding. In this paper, the spherical wheel was trued by cup-shaped truer and tool path was calculated by the radius of curvature of the wheel after truing and dressing. Then in the aspherical grinding experiment, WC material which is used as a melding die for the small-sized aspherical lens was ground. The results showed that a form accuracy of 0.1918 $\mu\textrm{m}$ P-V and a surface roughness of 0.064 $\mu\textrm{m}$ Rmax could be achieved.

• 한국정밀공학회지
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• 제18권12호
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• pp.82-87
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• 2001

This paper deals with mirror grinding of a small-sized aspherical lens by the resin bonded diamond spherical wheel. Up to now, a spherical lens has been used for the lens of the optical communication optical part. However, recently, the aspherical optical parts are mainly used in order to attempt the improvement in image quality and miniaturization of the optical device. It is possible to manufacture the aspherical lens which is presently being used in optical instrument through ultra-precision machinery technology. Also, to realize compactability, efforts are being made to produce a micro aspherical lens, for which the development of a high-precision, micro molding die is inevitable. Therefore, extensive research is being done on methods of producing an micro aspherical surface by high-precision grinding. In this paper, the spherical wheel was trued by cup-type truer and tool path was calculated by the radius of curvature of wheel after truing and dressing. And then in the aspherical grinding experiment, WC material which is used as a molding die for the small-sized aspherical lens was ground. It results was that a form accuracy of 0.1918${\mu}m$ P-V and a surface roughness of 0.064${\mu}m$ Rmax.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• 한국안광학회지
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• 제4권2호
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• pp.23-31
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• 1999

본 연구에서는 안과적 질환이 없는 한국인 성인 남녀의 안광학적요소를 측정하여, 안축의 길이를 각막 양주경선의 평균곡률반경으로 나눈 값(Al/CR비)과 눈의 굴절이상과의 상관성을 분석하였다. 눈의 굴절이상과 안축의 길이, 각막곡률반경과는 각각 -0.77(0.001>p), 0.29(0.01>p)의 상관관계가 있었으나, AL/CR비와는 이것들보다 훨씬 높은 -0.89(0.001>p)의 상관성을 보였다. 그러므로 눈의 굴절이상의 대부분은 AL/CR비에 의해서 결정된다고 할 수 있다. 또한 Al/CR비에 기여하는 안광학 요소를 알아보기 위해 AL/CR비와 안광학요소와의 상관성을 분석한 결과, 안축의 길이와는 0.82(0.001>p), 유리체의 깊이와는 0.80(0.001>p), 전방의 깊이와는 0.57(0.001>p), 각막굴절력과는 0.40(0.001>p), 각막골률반경과는 0.39(0.001>p), 수정체의 굴절력과는 -0.35(0.01>p) 등의 순서로 나타났다. 그러므로 눈의 굴절이상은 안광학요소 중 안축의 길이와 각막곡률반경의 비에 의해서 가장 많은 영향을 받으며, 이 AL/CR비는 안축의 길이, 초자처의 깊이, 전방의 깊이 등이 밀접한 관련성이 있으나, 수정체의 두께는 유의할 만한 상관성이 없음을 알았다.

• Korean Chemical Engineering Research
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• 제58권4호
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• pp.618-623
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• 2020

구형 페놀수지 입자 및 상대적으로 가교밀도가 낮은 구형 페놀-크레졸 공중합체 수지를 페놀, ortho-크레졸, 및 포름알데히드로부터 염기성 촉매인 트리에틸아민(triethylamine)의 존재 하에 98 ℃에서 현탁중합을 통하여 합성하였다. 페놀은 두 개의 ortho 및 한 개의 para 위치에서 포름알데히드와 반응하여 가교구조를 형성하지만 ortho-크레졸은 선점된 하나의 ortho 위치의 methyl 기로 인하여 공중합 시 가교 밀도를 저하시킨다. 그 영향으로 700 ℃ 질소 환경에서의 탄화 시 구형 페놀수지 비드에 비해 구형 페놀-크레졸 공중합체 수지의 경우 겉보기 밀도의 감소와 함께 수축율의 증가 현상이 일어나는 것을 확인할 수 있었다. 크레졸 올리고머의 분자량이 증가함에 따라 탄화 된 공중 합체 비드의 기공 반경이 감소하여 밀도 및 수축 결과와 일치 하였으며, 크레졸을 이용하여 구형 페놀수지 입자의 가교도를 조절함으로써 탄화과정에서의 밀도 감소율이 약 3~6%포인트 증가되고, 수축율은 약 6~20%포인트 증가함을 확인하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회B
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• pp.3015-3020
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• 2007

An experimental study of the dynamic characteristics of the free rising oblate spherical bubble is investigated. As noted by Saffman, the characteristics of the spiral motion are defined with parameters of the spiral frequency, spiral radius, and rising velocity. High speed camera recorded every detail information of free rising bubble. The spiral number, the bubble rise velocity, and the angular velocities were measured for the bubble size between 1.0mm to 20.0mm in diameter. In order to make clear trajectory, we employed the Fast Fourier Transformation for the normal digital camera data to synchronize with the high speed camera data. It was found that the spiral number suggested here was monotonically decreased as the bubble size increases. The present observation, however tells us that previous Saffman's formulation shows a good agreement with the trend, but over estimated spiral number. Therefore, it is recommended that Saffman's theoretical study is needed to be improved.

• The Korean Journal of Ecology
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• 제19권5호
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• pp.403-416
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• 1996

Global natural vegetation mapping (GNVM) system was developed for estimating potential forest area of the globe. With input of monthly mean temperature and monthly precipitation observed at weather stations, the system spherically interpolates them into 1°×1°grid points on a blobe, converts them into vegetation types, and produces a potential vegetation map and a potenital vegetation area. The spherical interpolation was based on negative exponential function fed from the constant radius stations with oval weighing method which is latitudinally elongated weighing in temperature and longitudinally elongated weighing in precipitation. The temperature values were corrected for altitude by applying a linear lapse-rate (0.65℃ / 100m) with reference to a built-in digital terrain map of the globe. The vegetation classification was based upon Koppen’s sKDICe. The potential forest area is estimated for 6.96 Gha (46.24％) of the global land area (15.05 Gha).