• 한국정밀공학회지
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• 제13권12호
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• pp.86-98
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• 1996

An combined implicit/explicit scheme for the analysis of sheet forming problems has been proposed in this work. In finite element simulation of sheet metal forming processes, the robustness and stability of computation are important requirements since the computation time and convergency become major points of consideration besides the solution accuracy due to the complexity of geometry and boundary conditions. The implicit scheme dmploys a more reliable and rigorous scheme in considering the equilibrium at each step of deformation, while in the explict scheme the problem of convergency is elimented at thecost of solution accuracy. The explicit approach and the implicit approach have merits and demerits, respectively. In order to combine the merits of these two methods a step-wise combined implici/explicit scheme has been developed. In the present work, the rigid-plastic finite element method using bending energy augmented membraneelements(BEAM)(1) is employed for computation. Computations are carried out for some typical sheet forming examples by implicit, combined implicit/explicit schemes including deep drawing of an oil pan, front fender and fuel tank. From the comparison between the methods the advantages and disadvantages of the methods are discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.271-287
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• 2008

This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here, the Jamshidian equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.

• 전산구조공학
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• 제6권3호
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• pp.125-137
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• 1993

최근 유한요소해석에서 보다 정확한 해를 위한 적응해석법에 대해 많은 연구가 이루어지고 있다. 본 논문은 요소 면적당의 오차를 균일화하여 절점을 최적의 위치로 변화시키는 r법과 오차가 큰 요소를 같은 모양의 요소로 세분시키는 h법을 혼합한 rh형 적응해석법을 사용하였다. 그 결과 같은 자유도에서 h법과 rh법의 오차감소율과 수렴속도는 거의 같에 나타났지만, rh법은 h법만 사용했을 때보다 전체 자유도 증가를 최대한 억제한 상태에서 정확한 유한요소해를 얻을 수 있었다.

• Structural Engineering and Mechanics
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• 제53권4호
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• pp.625-644
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• 2015

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

• 전산구조공학
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• 제6권4호
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• pp.107-118
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• 1993

3차원적인 고체의 유한요소해석 결과를 컴퓨터 그래픽스를 이용하여 시각화하는 후처리 방법들을 고안하고, 유한요소해석 소프트웨어의 개발에 응용하여 그 실용성과 효율성을 검토하였다. 이 연구에서는 고체 구조물의 후처리에서 가장 어려운 문제인 입체 내부의 데이타를 표현하는 방법을 중점적으로 다루었으며, 이를 위하여 공간 내부의 절단면을 표시하는 방법, 입체를 절단하여 분리하는 방법, 등가곡면으로 데이타 값의 범위를 표시하는 방법을 제안하였다.

• 대한기계학회논문집A
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• 제21권11호
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• pp.1912-1920
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• 1997

In the analysis of metal forming process, ALE(Arbitrary Lagrangian Eulerian) finite element methods have been increasingly used for the capability to control mesh independently from material flow. The methods can be divided into two groups i.e., coupled and split formulations. In the present work, the split ALE formulation is used for computational efficiency. A split ALE finite element method developed for rigid-viscoplastic materials and applied to the analysis of hot square die extrusion. Since thermal state greatly affects the product quality, an ALE scheme for temperature analysis is also presented. As computational examples, profile shapes as square and cross-like sections are chosen.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권2호
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• pp.23-38
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• 2004

We consider finite element methods applied to a class of quasi parabolic integro-differential equations in $R^d$. Global strong superconvergence, which only requires that partitions are quasi-uniform, is investigated for the error between the approximate solution and the Sobolev-Volterra projection of the exact solution. Two order superconvergence results are demonstrated in $W^{1,p}(\Omega)\;and\;L_p(\Omega)$, for $2\;{\leq}p\;<\;{\infty}$.

• 대한수학회보
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• 제35권2호
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.535-539
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• 2001

In these days. the finite element method(FEM) is a very common method for not only a simple vibration analysis but also the optimization of structures. Since the finite element model may contain thousands of degree of freedom, the eigensolutions require extreme computing power, which will result in a serious time-consuming problem. Thus, many researchers have challenged to find more improved modeling techniques and calculating methods to overcome such problems. The Guyan reduction method and the substructure synthesis method are typical examples of such methods. Of the substructure synthesis method, the component mode synthesis method (CMS) is widely used for dynamic analysis of structure. In this study. for the efficient analysis of jet loom structure. Component Mode Synthesis was carried out. The results of the finite element program developed are compared with those of the commercial package program ANSYS for the validation of the program. The results obtained by the program showed a good agreement with those of ANSYS. The program will be further refined and verified by test to yield more accurate results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권4호
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• pp.337-350
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• 2014

In this paper, we consider discontinuous Galerkin finite element methods with interior penalty term to approximate the solution of nonlinear parabolic problems with mixed boundary conditions. We construct the finite element spaces of the piecewise polynomials on which we define fully discrete discontinuous Galerkin approximations using the Crank-Nicolson method. To analyze the error estimates, we construct an appropriate projection which allows us to obtain the optimal order of a priori ${\ell}^{\infty}(L^2)$ error estimates of discontinuous Galerkin approximations in both spatial and temporal directions.