• Korean Journal of Mathematics
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• 제13권2호
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• pp.127-137
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• 2005

The objective of numerical analysis is to devise and analyze efficient algorithms or numerical methods for equations arising in mathematical modeling for science and engineering. In this article, we present some recent topics in computational mathematics, specially in the finite element method and overview the development of the mixed finite element method in the context of second order elliptic and parabolic problems. Multiscale methods such as MsFEM, HMM, and VMsM are included.

• 대한수학회지
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• 제56권3호
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• pp.739-750
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• 2019

We proved that finite p-groups in the title coincide with finite p-groups all of whose non-abelian subgroups are generated by two elements. Based on the result, finite p-groups all of whose subgroups of class 2 are minimal non-abelian (of the same order) are classified, respectively. Thus two questions posed by Berkovich are solved.

• 한국정밀공학회지
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• 제11권1호
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• pp.157-165
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• 1994

A general-purpose program for automatic two-dimensional finite-element modelling with quadrilateral elements was developed in this research. The conventional looping method employed in the program was introduced with emphasis on a new splitting criterion and a splitting scheme developed for improving the method. Some application examples were given, which show versatility and applicability of the developed program.

• Structural Engineering and Mechanics
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• 제23권6호
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• pp.691-711
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• 2006

This paper uses the finite element method to simultaneously consider the coupled cable-deck vibrations and the parametric vibrations of stay cables in dynamic analysis of a cable-stayed bridge. The stay cables are represented by some cable finite elements, which can consider the parametric vibration of the cables. In addition to modeling stay cables using multiple link cable elements, a procedure for removing the self-weight term of cable element is proposed. A eigenvalue analysis process using dynamic condensation method for sorting out the natural modes of the girder-tower vibrations and the Rayleigh damping considering element damping for damping matrix are also proposed for dynamic analyses of cable-stayed bridges. The possibilities of using cable elements and of using global and local vibrations to evaluate the parametric vibrations of stay cables in a cable-stayed bridge are confirmed, respectively.

• 한국해양공학회지
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• 제13권1호통권31호
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• pp.11-17
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• 1999

A three dimensional finite element generation code has been developed attaching simple blocks. Block can be either a quadrature or a cube depending on the dimension of a subject considered. Finite element serendipity basis functions are employed to map elements between the computational domain and the physical domain. Elements can be generated with wser defined progressive ratio for each block. For blocks to be connected properly, a block should have a consistent numbering scheme for vertices, side nodes, edges and surfaces. In addition the edge information such as the number of elements and the progressive ratio for each direction should also be checked for interfaces to have unique node numbers. Having done so, user can add blocks with little worry about the orientation of blocks, Since the present the present code has been written by a Visual Basic language, it can be developed easily for a user interactive manner under a Windows environment.

• Interaction and multiscale mechanics
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• 제3권3호
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• pp.235-255
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• 2010

This paper investigates the heat equation for domains subjected to an internal source with a sharp spatial gradient. The solution is first approximated using linear finite elements, and sufficiently small time-step sizes to yield stable simulations. The main area of interest is then in the ability to approximate the solution using Generalized Finite Elements, and again explore the time-step limitations required for stable simulations. Both high order elements, as well as elements with special enrichments are used to generate solutions. When compared to linear finite elements, the high order elements deliver better accuracy at a given level of mesh refinement, but do not offer an increase in critical time-step size. When special enrichment functions are used, the solution can be approximated accurately on very coarse meshes, while yielding solutions which are both accurate and computationally efficient. The major conclusion of interest is that the significantly larger element size yields larger allowable time-step sizes while still maintaining stability of the time-stepping algorithm.

• 전산구조공학
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• 제8권3호
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• pp.91-102
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• 1995

지하터널은 그 경계가 반무한영역에서 설정되고 재료나 형상의 복잡성을 갖고 있기 때문에, 동적하중에 대하여 정확한 거동을 해석하기 위해서는 3차원 동적해석이 필요하다. 이때 일반적인 수치해석기법인 유한요소만을 이용한 방법은 인위적 경계에서의 파의 반사, 입력자료의 방대함 등으로 인하여 효율적이지 못하게 된다. 본 연구는 이러한 점을 고려하여 지하터널에 직접 가해지는 동적하중에 대한 효율적인 해석기법을 개발하는데 그 목적이 있다. 개발된 프로그램에서 지반의 반무한성은 3차원 경계요소로 고려되었으며, 구조물에는 3차원 동적해석을 수행한 결과 기존의 2차원 터널해석에서 고려가 곤란했던 차량의 진행하중으로 인한 반복효과가 합리적으로 반영되는 것으로 분석되었다.

• 동력기계공학회지
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• 제4권1호
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• pp.68-73
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• 2000

A mixed degree finite element solutions using hierarchical elements are investigated for convergences on a 2-D simple cases. Elements are generated block by block and each block is assigned an arbitrary solution degree. The numerical study showed that a well constructed blocks can increase the convergence and accuracy of finite element solutions. Also, it has been found that for higher order elements, the convergence trends can be deteriorated for smaller mesh sizes. A procedure for a variable fixed boundary condition has been included.

• 대한기계학회논문집
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• 제19권3호
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• pp.647-660
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• 1995

Given the tetrahedron-based octree approximation of a solid as described in part(I) of this thesis, in this part(II) a systematic procedure of 'boundary moving' is developed for the fully automatic generation of 3D finite element meshes. The algorithm moves some vertices of the octants near the boundary onto the exact surface of a solid without transforming the topology of octree leaf elements. As a result, the inner octree leaf elements can be used as exact tetrahedral finite element meshes. In addition, as a quality measure of a tetrahedral element, 'shape value' is propopsed and used for the generation of better finite elements during the boundary moving process.

• 한국철도학회:학술대회논문집
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• 한국철도학회 2008년도 추계학술대회 논문집
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• pp.1379-1388
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• 2008

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be accurately analyzed. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk which is rotating at constant angular velocity are determined by non-linear equations formulated using 1-dimensional finite elements in radial direction. The equations of the in-plane vibrations at disturbed state are also formulated using 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 the annular disk are used as the interpolation functions of 1-dimensional finite elements in radial direction. 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.