• Title/Summary/Keyword: Matrix Equation

Search Result 1,081, Processing Time 0.024 seconds

Application of Hermite-Collocation Method for Unsteady Flow Analysis (부정류 해석을 위한 Hermite-Collocation 기법의 적용)

  • Han, Geon-Yeon;Lee, Eul-Rae;Park, Jae-Hong
    • Journal of Korea Water Resources Association
    • /
    • v.32 no.3
    • /
    • pp.237-246
    • /
    • 1999
  • A finite element model is studied to simulate unsteady free surface flow based on dynamic wave equation and collocation method. The collocation method is used in conjunction with Hermite polynomials, and resulting matrix equations are solved by skyline method. The model is verified by applying to hydraulic jump, nonlinear disturbance propagation and dam-break flow in a horizontal frictionless channel. The computed results are compared with those by Bubnov-Galerkin and Petrov-Galerkin methods. It is also applied to the North Han River to simulate the floodwave propagation. The computed results have good agreements with those of DWOPER model in terms of discharge hydrographs. The suggested model has proven to be one of the promising scheme for simulating the gradually and rapidly varied unsteady flow in open channels.

  • PDF

The Effect of Internal Flow on Vortex-Induced Vibration of Marine Riser (Riser의 내부유체 흐름이 소용돌이로 인한 Riser 동적반응에 미치는 영향)

  • Hong, Nam-Seeg;Hsiang Wang
    • Journal of Korean Society of Coastal and Ocean Engineers
    • /
    • v.7 no.2
    • /
    • pp.198-208
    • /
    • 1995
  • Combining Iwan-Blevin's model into the approximated form of the nonlinear model derived for the dynamic analysis of the riser system with the inclusion of internal flow, current-vortex model is developed to investigate the effect of internal flow on vortex-induced vibration due to inline current The riser system includes a steadly flow inside the pipe which is modeled as an extensible or inextensible tubular beam. Galerkin's finite element approximation are implemented to derive the matrix equation of equilibrium for the finite element system. The investigations of the effect of internal flow on vibration due to inline current are performed according to the change of various parameters such as top tension, infernal flow velocity. current velocity, and so on. It is found that the effect of internal flow on vibration due to vortex shedding can be controlled by the increase of top tension. However, careful consideration has to be given, in design point in order to avoid the resonance band occurding near vortex shedding frequency, particularly for the long riser.

  • PDF

Structural Analysis of Two-dimensional Continuum by Finite Element Method (유한요소법에 의한 이차원연속체의 구조해석)

  • 이재영;고재군
    • Magazine of the Korean Society of Agricultural Engineers
    • /
    • v.22 no.2
    • /
    • pp.83-100
    • /
    • 1980
  • This study was intended to computerize the structural analysis of two-dimensional continuum by finite element method, and to provide a preparatory basis for more sophisticated and more generalized computer programs of this kind. A computer program, applicable to any shape of two-dimensional continuum, was formulated on the basis of 16-degree-of- freedom rectangular element. Various computational aspects pertaining to the implementation of finite element method were reviewed and settled in the course of programming. The validity of the program was checked through several case studies. To assess the accuracy and the convergence characteristics of the method, the results computed by the program were compared with solutions by other methods, namely the analytical Navier's method and the framework method. Through actual programming and analysis of the computed results, the following facts were recognized; 1) The stiffness matrix should necessarily be assembled in a condensed form in order to make it possible to discretize the continuum into practically adequate number of elements without using back-up storage. 2) For minimization of solution time, in-core solution of the equilibrium equation is essential. LDLT decomposition is recommended for stiffness matrices condensed by the compacted column storage scheme. 3) As for rectangular plates, the finite element method shows better performances both in the accuracy and in the rate of convergence than the framework method. As the number of elements increases, the error of the finite element method approaches around 1%. 4) Regardless of the structural shape, there is a uniform tendency in convergence characteristics dependent on the shape of element. Square elements show the best performance. 5) The accuracy of computation is independent of the interpolation function selected.

  • PDF

3D Reconstruction using vanishing points (소실점을 이용한 3차원 재구성)

  • Kim, Sang-Hoon;Choi, Jong-Soo;Kim, Tae-Eun
    • The KIPS Transactions:PartB
    • /
    • v.10B no.5
    • /
    • pp.515-520
    • /
    • 2003
  • This paper proposes a calibration method from two images. Camera calibration is necessarily required to obtain 3D Information from 2D images. Previous works to accomplish the camera calibration needed the calibration object or required more than three images to calculate the Kruppa equation, however, we use the geometric constraints of parallelism and orthogonality can be easily presented in man-made scenes. The task of it is to obtain intrinsic and extrinsic camera parameters. The intrinsic parameters are evaluated from vanishing points and then the extrinsic parameters which are consisted of rotation matrix and translation vector of the camera are estimated from corresponding points of two views. From the calibrated parameters, we can recover the projection matrices for each view point. These projection matrices are used to recover 3D information of the scene and can be used to visualize new viewpoints.

Probabilistic Behavior of In-plane Structure due to Multiple Correlated Uncertain Material Constants (상호 상관관계가 있는 다중 재료상수의 불확실성에 의한 평면구조의 확률론적 거동)

  • Noh Hyuk-Chun
    • Journal of the Computational Structural Engineering Institute of Korea
    • /
    • v.18 no.3
    • /
    • pp.291-302
    • /
    • 2005
  • Due to the importance of the parameter in structural response, the uncertain elastic modulus was located at the center of stochastic analysis, where the response variability caused by the uncertain system parameters is pursued. However when we analyze the so-called stochastic systems, as many parameters as possible must be included in the analysis if we want to obtain the response variability that can reach a true one, even in an approximate sense. In this paper, a formulation to determine the statistical behavior of in-plane structures due to multiple uncertain material parameters, i.e., elastic modulus and Poisson's ratio, is suggested. To this end, the polynomial expansion on the coefficients of constitutive matrix is employed. In constructing the modified auto-and cross-correlation functions, use is made of the general equation for n-th moment. For the computational purpose, the infinite series of stochastic sub-stiffness matrices is truncated preserving required accuracy. To demons4rate the validity of the proposed formulation, an exemplary example is analyzed and the results are compared with those obtained by means of classical Monte Carlo simulation, which is based on the local averaging scheme.

Conjugate Gradient Least-Squares Algorithm for Three-Dimensional Magnetotelluric Inversion (3차원 MT 역산에서 CG 법의 효율적 적용)

  • Kim, Hee-Joon;Han, Nu-Ree;Choi, Ji-Hyang;Nam, Myung-Jin;Song, Yoon-Ho;Suh, Jung-Hee
    • Geophysics and Geophysical Exploration
    • /
    • v.10 no.2
    • /
    • pp.147-153
    • /
    • 2007
  • The conjugate gradient (CG) method is one of the most efficient algorithms for solving a linear system of equations. In addition to being used as a linear equation solver, it can be applied to a least-squares problem. When the CG method is applied to large-scale three-dimensional inversion of magnetotelluric data, two approaches have been pursued; one is the linear CG inversion in which each step of the Gauss-Newton iteration is incompletely solved using a truncated CG technique, and the other is referred to as the nonlinear CG inversion in which CG is directly applied to the minimization of objective functional for a nonlinear inverse problem. In each procedure we only need to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector, significantly reducing the computational requirements needed to do large-scale inversion.

A Method for the Preliminary Estimation of Vertical Natural Vibations of High Speed Boats (고속선(高速船) 선체고유상하진동(船體固有上下振動)의 초기추정(初期推定) 방법(方法))

  • K.C.,Kim;H.B.,Kim
    • Bulletin of the Society of Naval Architects of Korea
    • /
    • v.17 no.1
    • /
    • pp.25-29
    • /
    • 1980
  • For the preliminary estimation of the vertical hull natural frequency, the Schlick's or Schlick-type formulae have been traditional ones and are still in common use today. Some investigators have made their efforts, based on statistical data of ships' system parameters, to extend the applicability of Schlick-type formulae to higher modes, or to utilize the Rayleigh method. For instance, the work done by Dinsenbacher et al.[5] belongs to the former and that of Nagamoto et al.[6] to the latter. In a part of his previous paper[7], the author, investigating the case of a cargo ship of medium size, suggested that provided statistically simplified curves such as trapezoid of system parameter distributions are available in hands, direct utlization of an ordinary computer program can be also an another convenient method by which we can obtain both natural frequencies and normal mode shapes. In this paper, to confirm the feasibility of the above suggestion, four high speed boats are investigated. The system parameters of them are originally given in [5]. The computer program used here is one confiled based on a calculation method derived from Myklestal-Prohl modeling of hull, transfer matrix formulation and an extended Gumbel's initial value method for solving frequency equation. The results of the investigation show that the direct calculation based on statistically oriented and reasonably assumed trapezoidal mean curves of system parameter distributions can give us natural frequencies within about 5% deviation up to several-noded modes and normal mode shapes serviceable at least up to 4- or 5-noded modes in comparision with those based on actual distributions of system parameters. For this simplified method the actual data required for input are only of ship length, displacement, total added mass, bending and shear rigidity at amidship. They are available at the early stage of design. By this method we can also easily trace variations of vibration characteristics in the course of ship design cycles.

  • PDF

Conductivity Image Reconstruction Using Modified Gauss-Newton Method in Electrical Impedance Tomography (전기 임피던스 단층촬영 기법에서 수정된 가우스-뉴턴 방법을 이용한 도전율 영상 복원)

  • Kim, Bong Seok;Park, Hyung Jun;Kim, Kyung Youn
    • Journal of IKEEE
    • /
    • v.19 no.2
    • /
    • pp.219-224
    • /
    • 2015
  • Electrical impedance tomography is an imaging technique to reconstruct the internal conductivity distribution based on applied currents and measured voltages in a domain of interest. In this paper, a modified Gauss-Newton method is proposed for conductivity image reconstruction. In the proposed method, the dimension of the inverse term is reduced by replacing the number of elements with the number of measurement data in the conductivity updating equation of the conventional Gauss-Newton method. Therefore, the computation time is greatly reduced as compared to the conventional Gauss-Newton method. Moreover, the regularization parameter is selected by computing the minimum-maximum from the diagonal components of the Jacobian matrix at every iteration. The numerical experiments with several scenarios were carried out to evaluate the reconstruction performance of the proposed method.

Preparation and Characterization of BCB Resin-BNT Composite Substrate Materials (BCB Resin-BNT 복합 기판 소재의 제조 및 특성 평가)

  • Kim, Un-Yong;Chun, Myoung-Pyo;Cho, Jung-Ho;Kim, Byung-Ik;Lee, Yong-Hyun;Myoung, Sung-Jae;Han, Ik-Hyun;Shin, Dong-Uk
    • Journal of the Korean Ceramic Society
    • /
    • v.44 no.5 s.300
    • /
    • pp.179-183
    • /
    • 2007
  • BCB $Resin-BaNd_2Ti_4O_{12}$(BNT) composites with BNT contents were prepared by tape casting method and epoxy resin-BNT composites were prepared by using heating press. Their dielectric properties and microstructures were investigated. The dielectric properties such as dielectric constant and dielectric loss at 1 MHz for epoxy resin-BNT composites and BCB resin-BNT composites are improved with an increase of BNT volume fraction. The dielectric constant of the Epoxy-BNT composite increased from 5.9 to 7.8 as the volume fraction of BNT increased from 15 to 25. The dielectric constant of the BCB-BNT composite increased from 9.1 to 15.5 as the volume fraction of BNT increased from 30 to 50. The dielectric behavior of BCB-BNT system can be explained by Lichtenecker's equation. The dielectric constant of epoxy resin-BNT composite is smaller than that of BCB resin-BNT composite. These results are considered to be related with the dispersion of BNT filler in polymer matrix from the result of SEM photograph.

Analysis of the Axisymmetric Hydro-Mechanical Deep Drawing Process by Using the Finite Element Method (유한 요소법을 이용한 축대칭 하이드로 미케니칼 디프 드로잉 공정의 해석)

  • 양동열;김한경;이항수;김경웅
    • Transactions of the Korean Society of Mechanical Engineers
    • /
    • v.16 no.5
    • /
    • pp.873-882
    • /
    • 1992
  • The study is concerned with the rigid-plastic element analysis for axisymmetric hydromechanical deep drawing in which the fluid flow influences the metal deformation. Due to the fluid pressure acting on the sheet material hydromechanical deep drawing is distinguished from the conventional deep drawing processes. In considering the pressure effect, the governing equation for fluid pressure is solved and the result is reflected on the global stiffness matrix. The solution procedure consists of two stages ; i.e., initial bulging of the sheet surface before the initiation of steady fluid flow in the flange and fluid-lubricated stage. The problem is decoupled between fluid analysis and analysis of solid deformation by deformation by iterative feedback of mutual computed results. The corresponding experiments are carried out for axisymmetric hydro-mechanical deep drawing of annealled aluminium sheet as well as for deep drawing. It has been shown from the experiments that the limit drawing ratio for hydro-mechanical deep drawing is improved as compared with deep drawing. The computed results are in good agreement with the experiment for variation of punch head and chamber pressure with respect to the punch travel and for distribution of thicknees strain. It is thus shown that the present method of analysis can be effectively applied to the analysis of axisymmetric hydro-mechanical deep drawing processes.