• Title/Summary/Keyword: Nodal Solution

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Iterative Cell-wise Solution Method for the Adaptive Analysis of a Meshless Method (무요소법의 적응해석을 위한 반복격자해법)

  • 석병호;임장근
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 2002.10a
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    • pp.607-614
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    • 2002
  • For the accurate analysis of crack problems, considerable nodal refinement near the crack tip to capture singular stress field with sufficient accuracy to provide a useful computation of stress intensity factor is required. So, in this paper, adaptive nodal refinement scheme is proposed where nodes in restricted cell regions centered at crack tip are arranged in array for enhanced spatial resolution and adaptivity. With only cell-wise adaptive refinement scheme around crack tip fields, singularity of crack tip is sufficiently described to expect a successive crack propagate direction. Through numerical tests, accuracy of the proposed adaptive scheme is investigated and compared with the finite element and experimental results. By this implementation, it is shown that high accuracy is achieved by using iterative cell-wise solution method fur analyzing crack propagation problems.

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An exact finite element for a beam on a two-parameter elastic foundation: a revisit

  • Gulkan, P.;Alemdar, B.N.
    • Structural Engineering and Mechanics
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    • v.7 no.3
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    • pp.259-276
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    • 1999
  • An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters.

Structure Analysis of Vehicle Air Compressor (자동차용 공기압축기의 구조해석)

  • 원종진;이종선;흥석주;이현곤
    • Proceedings of the Korean Society of Machine Tool Engineers Conference
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    • 1999.05a
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    • pp.45-50
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    • 1999
  • The object of this study is structure analysis of vehicle air compressor. Structure analysis is compose to nodal solution and element solution using ANSYS code. Then analysis is partition to head part, cylinder and piston part of vehicle air compressor. Stress and strain results are satisfy to Von Mises yield criterion.

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A response matrix method for the refined Analytic Function Expansion Nodal (AFEN) method in the two-dimensional hexagonal geometry and its numerical performance

  • Noh, Jae Man
    • Nuclear Engineering and Technology
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    • v.52 no.11
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    • pp.2422-2430
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    • 2020
  • In order to improve calculational efficiency of the CAPP code in the analysis of the hexagonal reactor core, we have tried to implement a refined AFEN method with transverse gradient basis functions and interface flux moments in the hexagonal geometry. The numerical scheme for the refined AFEN method adopted here is the response matrix method that uses the interface partial currents as nodal unknowns instead of the interface fluxes used in the original AFEN method. Since the response matrix method is single-node based, it has good properties such as good calculational efficiency and parallel computing affinity. Because a refined AFEN method equivalent nonlinear FDM response matrix method tried first could not provide a numerically stable solution, a direct formulation of the refined AFEN response matrix were developed. To show the numerical performance of this response matrix method against the original AFEN method, the numerical error analyses were performed for several benchmark problems including the VVER-440 LWR benchmark problem and the MHTGR-350 HTGR benchmark problem. The results showed a more than three times speedup in computing time for the LWR and HTGR benchmark problems due to good convergence and excellent calculational efficiency of the refined AFEN response matrix method.

FUNDAMENTALS AND RECENT DEVELOPMENTS OF REACTOR PHYSICS METHODS

  • CHO NAM ZIN
    • Nuclear Engineering and Technology
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    • v.37 no.1
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    • pp.25-78
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    • 2005
  • As a key and core knowledge for the design of various types of nuclear reactors, the discipline of reactor physics has been advanced continually in the past six decades and has led to a very sophisticated fabric of analysis methods and computer codes in use today. Notwithstanding, the discipline faces interesting challenges from next-generation nuclear reactors and innovative new fuel designs in the coming. After presenting a brief overview of important tasks and steps involved in the nuclear design and analysis of a reactor, this article focuses on the currently-used design and analysis methods, issues and limitations, and current activities to resolve them as follows: (1) Derivation of the multi group transport equations and the multi group diffusion equations, with representative solution methods thereof. (2) Elements of modem (now almost three decades old) diffusion nodal methods. (3) Limitations of nodal methods such as transverse integration, flux reconstruction, and analysis of UO2-MOX mixed cores. Homogenization and related issues. (4) Description of the analytic function expansion nodal (AFEN) method. (5) Ongoing efforts for three-dimensional whole-core heterogeneous transport calculations and acceleration methods. (6) Elements of spatial kinetics calculation methods and coupled neutronics and thermal-hydraulics transient analysis. (7) Identification of future research and development areas in advanced reactors and Generation-IV reactors, in particular, in very high temperature gas reactor (VHTR) cores.

Effects of Ethanol Extract of Rehmanniae Radix(RREE) on Resting and Action Potential of Rabbit Sinoatrial Node and Papillary Muscle (Rehmanniae Radix에 의한 가토 동방결절 및 유두근의 활동전압의 변동)

  • Hwang, Bo-Sang;Koh, Sang-Don;Shin, Hong-Kee;Kim, Kee-Soon
    • The Korean Journal of Physiology
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    • v.19 no.2
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    • pp.127-137
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    • 1985
  • The present study was undertaken in order to investigate effect of ethanol extract of Rehmanniae radix(RREE) on electrophysiology of sinus node and papillary muscle. Rehmanniae radix is a herbal medicine which has been known to have diuretic, antipyretic, hemopoietic and cardiotonic effects. Action potentials were recorded by means of glass capillary microelectrode(technique) in rabbit sinoatrial nodal cells and papillary muscle cells which were superperfused with either tyrode solution or tyrode solutions containing different amount of RREE. The results obtained were as follows ; 1) In both central and peripheral nodal cells maximum diastolic potential (MDP) and amplitude of action potential (APA) were not affected by RREE. 2) Action potential duration as expressed $APD_{60}$(time to 60% repolarization) of central and peripheral pacemaker cells were significantly prolonged following perfusion with tyrode solution containing 0.1% RREE. 3) The rates of spontaneous firing from central pecemaker cell were decreased by RREE at concentration of 0.05% and 0. 1% while spontaneous rhythm of perinodal cell was decreased by 0.1% RREE. 4) The action potential duration of papillary muscle as expressed $APD_{60}$ were prolonged by 0.1% RREE.

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Comparison of Interpolation Methods for Reconstructing Pin-wise Power Distribution in Hexagonal Geometry

  • Lee, Hyung-Seok;Yang, Won-Sik
    • Nuclear Engineering and Technology
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    • v.31 no.3
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    • pp.303-313
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    • 1999
  • Various interpolation methods have been compared for reconstruction of LMR pin power distributions in hexagonal geometry. Interpolation functions are derived for several combinations of nodal quantities and various sets of basis functions, and tested against fine mesh calculations. The test results indicate that the interpolation functions based on the sixth degree polynomial are quite accurate, yielding maximum interpolation errors in power densities less than 0.5%, and maximum reconstruction errors less than 2% for driver assemblies and less than 4% for blanket assemblies. The main contribution to the total reconstruction error is made tv the nodal solution errors and the comer point flux errors. For the polynomial interpolations, the basis monomial set needs to be selected such that the highest powers of x and y are as close as possible. It is also found that polynomials higher than the seventh degree are not adequate because of the oscillatory behavior.

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ELEMENTARY PROOF OF THE NONEXISTENCE OF NODAL SOLUTIONS FOR SOME QUASILINEAR ELLIPTIC EQUATIONS

  • Soo Hyun Bae;Dae Hyeon Pahk
    • Communications of the Korean Mathematical Society
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    • v.10 no.4
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    • pp.925-929
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    • 1995
  • Consider the problem $-div($\mid$\bigtriangledown_u$\mid$^{p-2}\bigtriangledown_u) = $\mid$u$\mid$^{p^*-2}u + \lambda$\mid$u$\mid$^{q-2}u$ in B, u = 0 on $\partial B$; where $B \subset R^n$ is a ball, $\lambda < 0, 1 < p < n$ and $p^* = \frac{np}{n-p}$ is the critical Sobolev exponent. For given $\lambda > 0$, we show that there exists $k = k(\lambda) \in N$ such that any radial solutions to this problem have at most k noda curves when $p \leq q \leq p^* - 1$.

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PRECONDITIONING FOR THE p-VERSION BOUNDARY ELEMENT METHOD IN THREE DIMENSIONS WITH TRIANGULAR ELEMENTS

  • Cao, Wei-Ming;Guo, Benqi
    • Journal of the Korean Mathematical Society
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    • v.41 no.2
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    • pp.345-368
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    • 2004
  • A preconditioning algorithm is developed in this paper for the iterative solution of the linear system of equations resulting from the p-version boundary element approximation of the three dimensional integral equation with hypersingular operators. The preconditioner is derived by first making the nodal and side basis functions locally orthogonal to the element internal bases, and then by decoupling the nodal and side bases from the internal bases. Its implementation consists of solving a global problem on the wire-basket and a series of local problems defined on a single element. Moreover, the condition number of the preconditioned system is shown to be of order $O((1+ln/p)^{7})$. This technique can be applied to discretization with triangular elements and with general basis functions.

A Study on the Application of Macro Air-gap Element for Magnetic Flux Distribution Analysis of Electric Machinery by F.E.M. (유한요소법에 의한 전기기계의 자속분포해석을 위한 MACRO 공선요소 적용에 관한 연구)

  • Dal-Ho Im
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.35 no.11
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    • pp.479-486
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    • 1986
  • It is necessary to consider a rotor movement in dynamic analysis on the flux distribution of electric machinery by FEM. Therefore, if air-gap domain was subdivided into triangular elements, computation results contain errors due to variation of element shape in air-gap because the nodal points corresponding to the rotor are displaced in analyzing domain for the time difference. In order to reduce this errors, the paper presents a application of a Macro Air-gap Element that interpolation function is obtained analytically and a means to join it with linear triangular elements in the rotating machine or in the linear machine. At the end of paper, setting up analytic domain model, it compares analytic solution with the computation results of Macro Air-gap Element appliction and that of linear triangular element subdivision only to each cases of nodal displacement. And it carries out that errors due to variation of element shape are reduced effectively by application of a Macro air-gap element.

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