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Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

  • Xiang, Ping;Wu, Minger;Zhou, Rui Q.
    • Structural Engineering and Mechanics
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    • v.54 no.6
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    • pp.1153-1174
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    • 2015
  • Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

Free Vibration of EllllIipticall and Circular Plates (타원형 및 원형 평판의 자유 진동)

  • 김찬수
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.8
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    • pp.1485-1492
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    • 1992
  • While the vibration of circular plates were considered by many researchers, rather less attention is given to elliptical plates. In the present paper, the Rayleigh-Ritz mothod is used to obtain an eigenvalue equation for the free flexural vibration of thin elliptical plates having the classical free, simply suported or clmped boundary condition. Circular plates are included as a special case of the elliptical plates. Products of simple polynomials are used as the admissible functions and a recurrence relationship facilitates the evaluation of the necessary integrals. The analysis is developed for rectilinear orthotropic plates but the numerical results are given for isotropic plates with various aspect ratios.

On the Reconstruction of Pinwise Flux Distribution Using Several Types of Boundary Conditions

  • Park, C. J.;Kim, Y. H.;N. Z. Cho
    • Nuclear Engineering and Technology
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    • v.28 no.3
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    • pp.311-319
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    • 1996
  • We reconstruct the assembly pinwise flux using several types of boundary conditions and confirm that the reconstructed fluxes are the same with the reference flux if the boundary condition is exact. We test EPRI-9R benchmark problem with four boundary conditions, such as Dirichlet boundary condition, Neumann boundary condition, homogeneous mixed boundary condition (albedo type), and inhomogeneous mixed boundary condition. We also test reconstruction of the pinwise flux from nodal values, specifically from the AFEN [1, 2] results. From the nodal flux distribution we obtain surface flux and surface current distributions, which can be used to construct various types of boundary conditions. The result show that the Neumann boundary condition cannot be used for iterative schemes because of its ill-conditioning problem and that the other three boundary conditions give similar accuracy. The Dirichlet boundary condition requires the shortest computing time. The inhomogeneous mixed boundary condition requires only slightly longer computing time than the Dirichlet boundary condition, so that it could also be an alternative. In contrast to the fixed-source type problem resulting from the Dirichlet, Neumann, inhomogeneous mixed boundary conditions, the homogeneous mixed boundary condition constitutes an eigenvalue problem and requires longest computing time among the three (Dirichlet, inhomogeneous mixed, homogeneous mixed) boundary condition problems.

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Development of Optimal Blank Shape Design Program Using the Initial Velocity of Boundary Nodes (초기 속도법을 이용한 최적 블랭크 설계 프로그램의 개발)

  • 심현보;이상헌;손기찬
    • Transactions of Materials Processing
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    • v.11 no.6
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    • pp.487-494
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    • 2002
  • A new method of optimal blank shape design using the initial nodal velocity (INOV) has been proposed for the drawings of arbitrary shaped cups. With the given information of tool shape and the final product shape, corresponding initial blank shape has been found from the motion of boundary nodes. Although the sensitivity method, the past work of the present authors, has been proved to be excellent method to find optimal blank shapes, the method has a problem that a couple of deformation analysis is required at each design step and it also exhibits an abnormal behaviors in the rigid body rotation prevailing region. In the present method INOV, only a single deformation analysis per each design stage is required. Drawings of practical products as well as oil-pan, have been chosen as the examples. At every case the optimal blank shapes have been obtained only after a few times of modification without predetermined deformation path. The deformed shape with predicted optimal blank almost coincides with the target shape at every case. Through the investigation the INOV is found to be very effective in the arbitrary shaped drawing process design.

In-plane Natural Vibration Analysis of a Rotating Annular Disk (회전하는 환상 디스크의 면내 고유진동 해석)

  • Song, Seung-Gwan;Kwak, Dong-Hee;Kim, Chang-Boo
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.2
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    • pp.208-216
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    • 2009
  • In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

Analysis of PSC Box Girder Anchorage Zone using FEM and 2D SUB-3D STM Approach (유한요소법 및 유사 3 차원 스트릿-타이 모델 방법을 이용한 PSC 박스거더 정착부의 해석)

  • Yun, Young-Mook;Kim, Seung-Eock;Oh, Jin-Woo;Park, Jung-Woong
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.4 no.2
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    • pp.113-129
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    • 2000
  • This study evaluates the behavior and strength of an anchorage zone of the prestressed concrete box girder bridge on the Kyungboo highway railroad using the 2D SUB-3D STM approach and a linear elastic finite element analysis. The 2D SUB-3D STM approach utilizes several two-dimensional sub strut-tie models that represent the compressive and tensile stress flows of each projected plane of the three-dimensional structural concrete in the selection of a three dimensional strut-tie model, evaluation of the effective strengths of the concrete struts, and verification of the geometric compatibility condition and bearing capacity of the critical nodal zones in the selected three-dimensional strut-tie model. The finite element analysis uses an 8-node brick element and the longitudinal prestressing force is considered as the equivalent nodal force. Analysis results show that the 2D SUB-3D STM approach and linear elastic finite element method can be effectively applied to the analysis and design of three-dimensional structural concrete including a prestressed concrete box girder anchorage zone.

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Liquid boundary effect on free vibration of an annular plate coupled with a liquid

  • Kyeong-Hoon Jeong
    • Coupled systems mechanics
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    • v.12 no.2
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    • pp.127-149
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    • 2023
  • A theoretical method is developed to analyze the free vibration of an elastic annular plate in contact with an ideal liquid. The displacement potential functions of the contained liquid are expressed as a combination of the Bessel functions that satisfy the Laplace equation and the liquid boundary conditions. The compatibility condition along the interface between the annular plate and the contained liquid is taken into account to consider the fluid-structure coupling. The dynamic displacement of the wet annular plate is assumed to be a combination of dry eigenfunctions, allowing for prediction of the natural frequencies using the Rayleigh-Ritz method. The study investigates the effect of radial liquid boundary conditions on the natural frequencies of the wet annular plate, considering four types of liquid bounding: outer container bounded, outer and inner bounded, inner bounded, and radially unbounded. The proposed theoretical method is validated by comparing the predicted wet natural frequencies with those obtained from finite element analysis, showing excellent accuracy. The results indicate that the radial liquid bounding effect on the natural frequencies is negligible for the axisymmetric vibrational mode, but relatively significant for the mode with one nodal diameter (n =1) and no nodal circle (m' = 0). Furthermore, the study reveals that the wet natural frequencies are the largest for the plate with an inner bounded cylinder among the radial liquid boundary cases, regardless of the vibration mode.

Development and validation of transient analysis module in nodal diffusion code RAST-V with Kalinin-3 coolant transient benchmark

  • Jaerim Jang;Deokjung Lee
    • Nuclear Engineering and Technology
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    • v.56 no.6
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    • pp.2163-2173
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    • 2024
  • This study introduces a transient analysis module developed for RAST-V and validates it using the Kalinin-3 benchmark problem. For the benchmark analysis, RAST-V standalone and STREAM/RAST-V calculations were performed. STREAM supplies the few-group constants and RAST-V conducts a 3D core simulation utilizing few-group cross-sectional data. To improve accuracy, the main solver was developed based on the advanced semi-analytic nodal method. To evaluate the computational capability of the transient analysis module in RAST-V, Kalinin-3 benchmark is employed. Kalinin-3 represents a coolant transient benchmark that offers experimental data during the deactivation of the Main Circulation Pumps. Consequently, the transient calculations reflected the changes in the reactor flow rate. Benchmark comprising steady-state and transient calculations. During the steady state, the STREAM/RAST-V combination demonstrated a 30 ppm root mean square difference from 0 to 128.50 EFPD. For the transient calculations, STREAM/RAST-V showed power differences within ±7 % over a range of 0-300 s. Axial offset differences were within ±3 %, and the RMS difference in radial power ranged within 2.596 % at both 0 and 300 s. Overall, this study effectively demonstrated the newly developed transient solver in RAST-V and validated it using the Kalinin-3 benchmark problem.

The Role of Pelvic Irradiation after Hysterectomy in Early Stage Cervical Carcinoma with Pelvic Nodal Metastasis (림프절 전이를 동반한 초기 자궁경부암에서 수술 후 방사선치료의 역할)

  • Suh, Hyun-Suk
    • Radiation Oncology Journal
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    • v.16 no.4
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    • pp.469-475
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    • 1998
  • Purpose : To determine the role of Pelvic irradiation in stage I or IIA cervical carcinoma with pelvic nodal metastasis after hysterectomy and bilateral pelvic lymphadenectomy. Materials and Methods : This is a retrospective study of 68 cervical carcinoma patients who were found to have pelvic nodal metastasis at hysterectomy and received pelvic irradiation from 1983 to 1996 at Inje University Seoul Paik Hospital. External beam radiation therapy to pelvis was delivered using 4 MeV Linac and intracavitary irradiation was given via vaginal ovoids or cylinders. Five-year survival and disease-free survival were estimated by Kaplan-Meier Method and prognostic factors related to survival were analysed by log-rank test and Cox proportional hazards regression model. Results : Median length of follow-up was 52months. Five-year overall survival and disease-free survival (DFS) were 81.8$\%$ and 81.7$\%$ respectively. Patients with endometrial invasion had a 57.1$\%$ 5-year DFS compared to 87.5$\%$ for those without endometrial invasion (p=0.0074). Multivariate analysis revealed endometrial invasion as an only statistically significant prognostic factor for 5-year DFS. Among total 15 (22$\%$) recurrences. pelvic recurrences occurred in 4 cases and distant metastases occurred in 13 cases. Conclusion : We have been able to confirm previous results demonstrating marked decrease in local recurrence after pelvic irradiation. In view of the high proportion of distant metastasis found in this study, a trial of aggressive adjuvant systemic therapy and irradiation in early stage cervical carcinoma patients with pelvic nodal metastasis, especially with endometrial invasion, appears to be warranted.

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Investigation and Processing of Seismic Reflection Data Collected from a Water-Land Area Using a Land Nodal Airgun System (수륙 경계지역에서 얻어진 육상 노달 에어건 탄성파탐사 자료의 고찰 및 자료처리)

  • Lee, Donghoon;Jang, Seonghyung;Kang, Nyeonkeon;Kim, Hyun-do;Kim, Kwansoo;Kim, Ji-Soo
    • The Journal of Engineering Geology
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    • v.31 no.4
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    • pp.603-620
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    • 2021
  • A land nodal seismic system was employed to acquire seismic reflection data using stand-alone cable-free receivers in a land-river area. Acquiring reliable data using this technology is very cost effective, as it avoids topographic problems in the deployment and collection of receivers. The land nodal airgun system deployed on the mouth of the Hyungsan River (in Pohang, Gyeongsangbuk Province) used airgun sources in the river and receivers on the riverbank, with subparallel source and receiver lines, approximately 120 m-spaced. Seismic data collected on the riverbank are characterized by a low signal-to-noise (S/N) and inconsistent reflection events. Most of the events are represented by hyperbola in the field records, including direct waves, guided waves, air waves, and Scholte surface waves, in contrast to the straight lines in the data collected conventionally where source and receiver lines are coincident. The processing strategy included enhancing the signal behind the low-frequency large-amplitude noise with a cascaded application of bandpass and f-k filters for the attenuation of air waves. Static time delays caused by the cross-offset distance between sources and receivers are corrected, with a focus on mapping the shallow reflections obscured by guided wave and air wave noise. A new time-distance equation and curve for direct and air waves are suggested for the correction of the static time delay caused by the cross-offset between source and receiver. Investigation of the minimum cross-offset gathers shows well-aligned shallow reflections around 200 ms after time-shift correction. This time-delay static correction based on the direct wave is found essential to improving the data from parallel source and receiver lines. Data acquisition and processing strategies developed in this study for land nodal airgun seismic systems will be readily applicable to seismic data from land-sea areas when high-resolution signal data becomes available in the future for investigation of shallow gas reservoirs, faults, and engineering designs for the development of coastal areas.