• 대한수학회지
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• 제49권4호
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• pp.765-778
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• 2012

We construct a symmetric finite volume element (SFVE) scheme for a self-adjoint elliptic problem on tetrahedron grids and prove that our new scheme has optimal convergent order for the solution and has superconvergent order for the flux when grids are quasi-uniform and regular. The symmetry of our scheme is helpful to solve efficiently the corresponding discrete system. Numerical experiments are carried out to confirm the theoretical results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1997년도 추계 학술대회논문집
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• pp.49-54
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• 1997

Rice's monotone streamline upwind finite element method, which was proposed to treat convection-dominated flows, is applied to the linear triangular element. An alignment technique of unstructured grids with given velocity fields is used to prevent the interpolation error produced in evaluating the convection term in the upwind method. The alignment of grids is accomplished by optimizing a target function defined with the inner-product of a properly chosen side vector in the element with the velocity field. Two pure advection problems are considered to demonstrate the superiorities of the present approach in solving the convection-dominated flow on the unstructured grid. Solutions obtained with aligned grids are much closer to the exact solutions than those with initial regular grids. The capability of the present approach in predicting the appearance of the secondary vortex in the laminar confined jet impingement is shown by comparing streamlines to those produced by SIMPLE on a highly stretched grid toward the impingement plate.

• 한국자동차공학회논문집
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• 제6권4호
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• pp.141-150
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• 1998

The measurement of strains in stamped sheet metal is essential to the design and manufacture of sound sheet metal products. The measured strains can also be used in verifying the reliability of the computer analysis such as finite element analysis. In most engineering applications, strains are measured from the deformed square grids or deformed circular grids in comparison with the initial undeformed grids. In such a case, however, strains are averaged in each grid and the localized strain in a region smaller than a grid size can not be measured. In the present study, the B-spline surface interpolation technique is introduced in order to measure the strains more exactly and effectively. The strains calculated by using the surface interpolation technique are compared with the strains calculated from the three-noded grids as well as with the finite element analysis.

• 한국전산유체공학회지
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• 제4권2호
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• pp.39-46
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• 1999

The FVM(Finite Volume Method) have been used mainly for the flow analyses in the piston-cylinder. The objective of the present study is to analyze numerically the piston-driven intake flows using the FEM(Finite Element Method). The FEM algorithm used in this study is 4-step time-splitting method which requires much less execution time and computer storage than the velocity-pressure integrated method and the penalty method. And the explicit Lax-Wendroff scheme is applied to nonlinear convective term in the momentum equations to prevent checkerboard pressure oscillations. Also, the ALE(arbitrary Lagrangian Eulerian) method is adopted for the moving grids. The calculated results show good agreement in comparison with those by the FVM and the experimental results by the LDA.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제48권3호
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• pp.200-208
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• 1999

In this paper, the corona discharge is analyzed by Finite Element Method(FEM) combined with Flux-corrected Transport(FCT) algorithm. In the previous papers, Finite Difference Method(FDM) combined with FCT was used. Usually in the FDM, the regionof interest is discretized with structured grids. But to refine local regions with same resolution, much more grids are required for the structured grids than for unstructured grids than for unstructured grids. Therefore, we propose the FEM-FCT method to simulate the corona discharge. The proposed method has good flexibility in model shape and can reduce the computational cost by the local refinement where the physical quantities have steep gradients. Using the proposed method, we study the streamer growth of parallel plate electrodes which is initiated by the low and high perturbation density. We find that the varying the initial density of perturbation has very little effect on the streamer propagation. And the corona discharge of the rod-to-plane electrode is simulated. On the surface of the rod electrode, the high concentration of the electric field gives rise to many number of streamer seeds. The strong axial streamer propagate to the plane electrode. The weaker non-axial streamer repel each other and stop growing more. The results are very similar to those of the papers which used the FDM-FCT method on structured grids. Thus we can conclude that the proposed FEM-FCT method is more efficient than the conventional FDM-FCT method by virtue of the reduction in computational grids number.

• 한국전산구조공학회논문집
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• 제18권4호통권70호
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• pp.405-416
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• 2005

본 연구에서는 경수로용 핵연료집합체의 전체지지격자(Full Size Grid)와 부분지지격자(Small Size Grid)에 대한 정적 좌굴강도 실험과 전체 지지격자와 부분지지격자를 구성하는 지지격자판(Grid Strap)에 대한 정적 좌굴해석을 수행하여 지지격자의 좌굴특성을 분석하였으며, 분석결과를 이용하여 전체지지격자와 부분지지격자에 대한 좌굴하중값의 예측 가능성을 평가하였다. 좌굴강도 실험은 웨스팅하우스형 연료의 $17{\times}17$셀을 갖는 전체지지격자와 $1{\times}1,\;1{\times}2,\;1{\times}3,\;1{\times}4,\;1{\times}5,\;1{\times}17\;,2{\times}1,\;2{\times}2,\;2{\times}3,\;2{\times}9,\;2{\times}17,\;3{\times}17$ 등의 셀을 갖는 부분지지격자에 대하여 수행하였으며, 실험결과를 이용하여 지지격자의 좌굴강도와 지지격자의 행(rows)과 열(columns) 사이의 관계식을 제시하였다. 좌굴강도 해석은 범용 유한요소해석코드인 ANSYS를 이용하여 수행하였으며, 해석결과를 이용하여 지지격자의 좌굴특성을 분석하고 실험결과와 비교평가 하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권2호
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• pp.65-92
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• 2019

We survey a recently developed immersed finite element method (IFEM) for the interface problems. The IFEM uses structured grids such as uniform grids, even if the interface is a smooth curve. Instead of fitting the curved interface, the bases are modified so that they satisfy the jump conditions along the interface. The early versions of IFEM [1, 2] were suboptimal in convergence order [3]. Later, the consistency terms were added to the bilinear forms [4, 5], thus the scheme became optimal and the error estimates were proven. For elasticity problems with interfaces, we modify the Crouzeix-Raviart based element to satisfy the traction conditions along the interface [6], but the consistency terms are not needed. To satisfy the Korn's inequality, we add the stabilizing terms to the bilinear form. The optimal error estimate was shown for a triangular grid. Lastly, we describe the multigrid algorithms for the discretized system arising from IFEM. The prolongation operators are designed so that the prolongated function satisfy the flux continuity condition along the interface. The W-cycle convergence was proved, and the number of V-cycle is independent of the mesh size.

• 대한수학회지
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• 제44권5호
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• pp.1103-1119
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• 2007

We consider multiscale mortar mixed finite element discretizations for slightly compressible Darcy flows in porous media. This paper is an extension of the formulation introduced by Arbogast et al. for the incompressible problem [2]. In this method, flux continuity is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. Optimal fine scale convergence is obtained by an appropriate choice of mortar grid and polynomial degree of approximation. Parallel numerical simulations on some multiscale benchmark problems are given to show the efficiency and effectiveness of the method.

• 대한기계학회논문집A
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• 제27권3호
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• pp.424-431
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• 2003

The spacer grid is one of the main structural components in the fuel assembly, which supports the fuel rods and maintains coolable geometry from an external load. A vibration test and a finite element analysis using ABAQUS on a dummy fuel rod continuously supported by Optimized H type(OHT) and New Doublet (ND) spacer grids arc performed to obtain the vibration characteristics such as natural frequencies and mode shapes an(1 to verify a finite element model. The results from the test and the finite element analysis are compared by modal assurance criteria (MAC) values. It is resulted that MACs for the first, the third and the fifth mode shapes are relatively good as compared with those of the second an(1 fourth ones. The natural frequency differences between two methods as well as the mode comparison results for the rod with OHT spacer grid are better than those with ND spacer grid. It is judged that the FE model for the ND spacer grid spring should be modified to consider the long contact length which actually happen when the spring supports the rod.

• Steel and Composite Structures
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• 제9권3호
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• pp.239-253
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• 2009

This paper reviews the concept of tensegrity structures and proposes a new type of dismountable steel tensegrity grids for possible deployment as light-weight roof structures. It covers the fabrication of the prototype structures followed by their instrumentation, destructive testing and numerical analysis. First, a single module, measuring $1m{\times}1m$ in size, is fabricated based on half-cuboctahedron configuration using galvanised iron (GI) pipes as struts and high tensile stranded cables as tensile elements. Detailed instrumentation of the structure is carried out right at the fabrication stage. The structure is thereafter subjected to destructive test during which the strain and the displacement responses are carefully monitored. The structure is modelled and analyzed using finite element method (FEM) and the model generated is updated with the experimental results. The investigations are then extended to a $2{\times}2$ grid, measuring $2m{\times}2m$ in size, fabricated uniquely by the cohesive integration of four single tensegrity modules. After updating and validating on the $2{\times}2$ grid, the finite element model is extended to a $8{\times}8$ grid (consisting of 64 units and measuring $8m{\times}8m$) whose behaviour is studied in detail for various load combinations expected to act on the structure. The results demonstrate that the proposed tensegrity grid structures are not only dismountable but also exhibit satisfactory behaviour from strength and serviceability point of view.