• Title/Summary/Keyword: rotation matrix

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A Geometrically Nonlinear Analysis of the Curved Shell Considering Large Displacements and Large Rotation Increments (대변위 및 대회전을 고려한 만곡된 쉘의 기하학적 비선형 해석)

  • Jae-Wook Lee;Young-Tae Yang
    • Journal of the Society of Naval Architects of Korea
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    • v.29 no.2
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    • pp.132-139
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    • 1992
  • This paper presents geometrically nonlinear formulation of shell problems using the three-dimensional curved shell element, which includs large displacements and large rotations. Formulations of the geometrically nonlinear problems can be derived in a variety of ways, but most of them have been obtained by assuming that nodal rotations are small. Hence, the tangent stiffness matrix is derived under the assumptions that rotational increments are infinitesimal and the effect of finite rotational increments have to be considered during the equilibrium iterations. To study the large displacement and large rotation problems, the restrictions are removed and the formulations of the curved shell element including the effect of large rotational increments are developed in this paper. The displacement based finite element method using this improved formulation are applied to the analyses of the geometrically nonlinear behaviors of the single and double curved shells, which are compared with the results by others.

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A Bifurcation Analysis of Space Structures by Using 3D Beam-Column Element Considering Finite Deformations and Bowing Effect (유한변형과 굽힘효과가 고려된 3차원 보-기둥요소에 의한 공간구조물의 분기좌굴해석)

  • Lee, Kyung-Soo;Han, Sang-Eul
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.4
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    • pp.307-314
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    • 2009
  • The present paper briefly describes the space frame element and the fundamental strategies in computational elastic bifurcation theory of geometrically nonlinear, single load parameter conservative elastic spatial structures. A method for large deformation(rotation) analysis of space frame is based on an eulerian formulation, which takes into consideration the effects of large joint translations and rotations with finite deformation(rotation). The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing are taken into account. and the derived geometric stiffness matrix is unsymmetric because of the fact that finite rotations are not commutative under addition. To detect the singular point such as bifurcation point, an iterative pin-pointing algorithm is proposed. And the path switching mode for bifurcation path is based on the non-negative eigen-value and it's corresponding eigen-vector. Some numerical examples for bifurcation analysis are carried out for a plane frame, plane circular arch and space dome structures are described.

Float Zone Growth of Superconduction $Bi_2Sr_2CaCu_2O_8$ Fiber with Halogen Lamp (할로겐 램프 열원을 이용한 초전도성 $Bi_2Sr_2CaCu_2O_8$ Fiber의 Float Zone 성장)

  • 김철진;정준기
    • Korean Journal of Crystallography
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    • v.7 no.2
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    • pp.147-155
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    • 1996
  • Floating Zone Image furnace with halogen lamps as heat source has been made and applied to the growth of high-Tc superconductor Bi2Sr2CaCu2O8. The manufactured crystal growth equipment is composed of holder unit for setting the halogen lamps at the focal point of the elliptical mirror, image furnace with maximum temperature of 1800℃ with 1kW halogen lamps, cooling unit, feeding unit for supplying source material to the molten zone, pulling unit for crystal growth, and the control unit in the range of 2mm/hr -40 mm/hr vertical movement and 15rpm - 12rpm rotation. Bi2Sr2CaCu2O8 fibers have been grown with 300W halogen lamps and characterized with XRD, SEM and EDS. The growth condition was air atmosphere, growth speed 3∼4mm/hr, rotation speed of upper and lower part 20∼25 rpm. The fiber was composed of 20∼25 rpm matrix phase and secondary phases such as (Sr,Ca)CuO2 and (Sr,Ca)2CuO3.

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An Interference Coordination Technique Utilizing Sub-Arrays and Its Performance in Cellular Systems (부 어레이 빔포밍을 활용하는 간섭 제어 기법 및 셀룰러 시스템에서의 성능 평가)

  • Kang, Hosik;Lee, Donghyun;Sung, Wonjin
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.25 no.6
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    • pp.653-663
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    • 2014
  • To cope with an increasing amount of data traffic, research efforts are being made to maximize the data rate by reducing the interference between the transmission nodes. This paper also focuses on interference control schemes utilizing antenna sub-array beam-forming. The first scheme relies on horizontal beam rotation which utilizes three types of narrow beam patterns. Different beam patterns are applied to transmit signals in rotating fashion to control the interference. The second scheme is based on user-specific sub-array beamforming, which uses the precoding matrix based on users' location and controls the amount of interference in the multi-user environment. The performance of the proposed schemes is evaluated using the computer simulation to demonstrate the performance enhancement.

The Study on the Implementation of the X-Ray CT System Using the Cone-Beam for the 3D Dynamic Image Acquisition (3D 동영상획득을 위한 Cone-Beam 형 X-Ray CT 시스템 구현에 관한 연구)

  • Jeong, Chan-Woong;Jun, Kyu-Suk
    • The Journal of the Acoustical Society of Korea
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    • v.28 no.4
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    • pp.370-374
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    • 2009
  • In this paper, we presents a new cone beam computerized tomography (CB CT) system for the reconstruction of 3 dimensional dynamic images. The system using cone beam has less the exposure of radioactivity than fan beam, relatively. In the system, the reconstruction 3-D image is reconstructed with the radiation angle of X-ray in the image processing unit and transmitted to the monitor. And in the image processing unit, the Three Pass Shear Matrices, a kind of Rotation-based method, is applied to reconstruct 3D image because it has less transcendental functions than the one-pass shear matrix to decrease a time of calculations for the reconstruction 3-D image in the processor. The new system is able to get 3~5 3-D images a second, reconstruct the 3-D dynamic images in real time.

Comparison of Misalignment and Retardation Errors of Dual Rotating Quarter-Wave Plates in Muller-Matrix Ellipsometry (타원편광 분석기에서 정렬오차와 사분파장판의 지연오차로 인한 뮬러 매트릭스 오차 분석)

  • Cheong, Hai Du;Kim, Dukhyeon
    • Korean Journal of Optics and Photonics
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    • v.25 no.5
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    • pp.262-272
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    • 2014
  • Using an ellipsometer with dual rotating quarter-wave plates, we have analyzed the relationship between Fourier coefficients and Mueller matrices in the cases of an error-free optical system and of five systematic errors (alignment errors and retardation errors in the quarter-wave plates, and alignment error in the analyzer). In the case with five systematic errors, simulation results show that retardation errors cause more error in the diagonal elements of the Mueller matrix than do alignment errors. We have found that errors in the Mueller matrix caused by initial misalignment of the dual quarter-wave plates were the same. We have chosen the rotation rates of two quarter-wave plates such that the rotational frequencies ${\omega}_1$ and ${\omega}_2$ differ by a factor of 5, i.e. ${\omega}_2=5{\omega}_1$. The simulation results show 0.18% relative error in the diagonal elements ($m_{22}$ and $m_{33}$) and 200% relative error in the off-diagonal elements ($m_{23}$ and $m_{32}$), when we compare errors caused by misalignment of the analyzer to those caused by initial misalignment of the quarter-wave plates. We can use these results in measuring accurate Mueller matrices of optical materials.

Out-of-plane Buckling Analysis of Doubly Symmetric Thin-walled Circular Arch (이축 대칭단면을 갖는 박벽 원형아치의 면외좌굴해석)

  • Kim, Moon Young;Min, Byoung Cheol;Kim, Sung Bo
    • Journal of Korean Society of Steel Construction
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    • v.10 no.3 s.36
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    • pp.509-523
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    • 1998
  • A consistent finite element formulation and analytic solutions are presented for stability of thin-walled circular arch. The total potential energy is derived by applying the principle of linearized virtual work and including second order terms of finite semitangential rotations. As a result, the energy functional corresponding to the semitangential moment is newly derived. Analytic solutions for the out-of-plane buckling of symmetric thin-walled curved beam subjected to pure bending or uniform compression with simply supported boundary conditions are obtained. For finite element analysis, the cubic Hermitian polynomials are utilized as shape functions and $16{\times}16$ stiffness matrix for curved beam elements and $14{\times}14$ stiffness matrix for straight beam elements are evaluated, respectively. In order to illustrate the accuracy of this study, analytical and numerical results for lateral buckling problems of circular arch are presented and compared with available analytical solutions.

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Evaluation of Compressive Strength of Assembled Column System Reinforced with Cross-Arms and Stayed Struts (수평재 및 사재로 보강된 조립기둥시스템의 압축강도 평가)

  • Kim, Kyung Sik;Park, Hyun Yong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.33 no.6
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    • pp.2169-2179
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    • 2013
  • The compressive strengths of simply supported columns may be significantly increased by reinforcing them with an assemblage of cross-arms and stayed struts connecting both ends of the columns and the cross-arm members. The purpose of the stayed struts and cross-arms is to introduce partial restraints against translation and rotation, thereby decreasing the effective buckling length of the column. In this study, buckling strengths of the assembled column system have been quantitatively evaluated from the theoretical methods based on both the equivalent spring model and the stiffness matrix formulation. And the results were compared with those from elastic/inelastic analysis using a finite element analysis package program, ABAQUS, for verification purpose. Expected compressive strength curves have been proposed for the assembled column system as a function of slenderness ratio of the simply supported column.

A David Star Magic Square Algorithm for Efficient LED Control (효율적인 LED 제어를 위한 다윗 스타 마방진 알고리즘)

  • Lee, Kyung-Min;Lin, Chi-Ho
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.16 no.3
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    • pp.109-113
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    • 2016
  • In this paper, we propose efficient LED lighting control algorithm using a David star magic square. Such algorithms increases the power reduction, the heat efficiency and LED life cycle and the efficiency of the LED lighting control consumption. Lighting system using existing Magic square algorithm could be reduced to increase the heat efficiency of the LED because the LED lighting time of the reduced cross-lighting. but it has a limit to the lighting control. If should apply the this proposed algorithm, can reduces power consumption and increases LED life-cycle, heat efficiency of LED lighting module and efficiency of the lighting control of the LED. This paper proposed that algorithm is by using a David star magic square on the LED Matrix. Divided into twelve areas to move the pattern in constant time interval, to perform the cross rotation and inversion techniques to thereby light up. In this paper proposed algorithm of this paper was compared with existing Magic square approach. As a result, power consumption and heat-value and luminous flux was reduced as the conventional lighting system. And, the LED lighting control increase the efficiency.

Calculation of Dose Distribution for SBRT Patient Using Geant4 Simulation Code (Geant4 전산모사 코드를 이용한 SBRT 환자의 선량분포 계산)

  • Kang, Jeongku;Lee, Jeongok;Lee, Dong Joon
    • Progress in Medical Physics
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    • v.26 no.1
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    • pp.36-41
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    • 2015
  • The Monte Carlo based dose calculation program for stereotactic body radiotherapy was developed in this study. The Geant4 toolkit widely used in the radiotherapy was used for this study. The photon energy spectrum of the medical linac studied in the previous research was applied for the patient dose calculations. The geometry of the radiation fields defined by multi-leaf collimators were taken into account in the PrimaryGeneratorAction class of the Geant4 code. The total of 8 fields were demonstrated in the patient dose calculations, where rotation matrix as a function of gantry angle was used for the determination of the source positions. The DicomHandler class converted the binary file format of the DICOM data containing the matrix number, pixel size, endian type, HU number, bit size, padding value and high bits order to the ASCII file format. The patient phantom was constructed using the converted ASCII file. The EGSnrc code was used to compare the calculation efficiency of the material data.