• 대한수학회보
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• 제51권3호
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 추계학술대회 논문집
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• pp.634-638
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• 1997

The objectives of this research are to develop lumber and lower-thoracic pedicle fixation system for Korean patients. To achieve the aimed goals, first, optimized shape design process is performed, and finite element methods are applied to evaluate the mechanical strength of the developed fixation system. Second, appropriate machining experiments are carried out to develop optimum machining conditions for titan~um alloys those are known as one of the most difficult-to-cut material. As the results of this research, new pedicle screw system, considering the morphological characteristics of Korean patients, is developed by applying the finite element analysis, optimum shape processing method and optimize design algorithm.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• Journal of Mechanical Science and Technology
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• 제20권3호
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• pp.319-328
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• 2006

A simple approximation method for the stress intensity factor at the tip of the axial semielliptical cracks on the cylindrical vessel is developed. The approximation methods, incorporated in VINTIN (Vessel INTegrity analysis-INner flaws), utilizes the influence coefficients to calculate the stress intensity factor at the crack tip. This method has been compared with other solution methods including 3-D finite element analysis for internal pressure, cooldown, and pressurized thermal shock loading conditions. For these, 3-D finite-element analyses are performed to obtain the stress intensity factors for various surface cracks with t/R=0.1. The approximation solutions are within $\pm2.5%$ of the those of finite element analysis using symmetric model of one-forth of a vessel under pressure loading, and 1-3% higher under pressurized thermal shock condition. The analysis results confirm that the approximation method provides sufficiently accurate stress intensity factor values for the axial semi-elliptical flaws on the surface of the reactor pressure vessel.

• Structural Engineering and Mechanics
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• 제87권2호
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• pp.191-200
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• 2023

This paper presents a mechanical model of a "tapered composite shaft" rotating at a constant speed around its axis. The spatial equations of motion are solved using the Lagrange technique, and a finite element approach is employed to construct the model. Theoretical analysis is used to compute the kinetic and strain energies. A comparison is made between conventional finite element methods and hierarchical finite element methods, indicating that the former uses fewer elements and provides higher accuracy in determining natural frequencies. Numerical calculations are performed to determine the eigen frequencies and critical speeds of the rotating composite shaft. The critical speeds of composite shaft systems are compared with existing literature to validate the proposed model.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.73-79
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• 2006

In this paper, we propose a new triangular finite element mesh generation method based on simplification of high-density mesh and adaptive Level-of-Detail (LOD) methods for efficient CAE. In our method, mesh simplification is used to control the mesh properties required for FE mesh, such as the number of triangular elements, element shape quality and size while keeping the specified approximation tolerance. Adaptive LOD methods based on vertex hierarchy according to curvature and region of interest, and global LOD method preserving density distributions are also proposed in order to construct a mesh more appropriate for CAE purpose. These methods enable efficient generation of FE meshes with properties appropriate for analysis purpose from a high-density mesh. Finally, the effectiveness of our approach is shown through evaluations of the FE meshes for practical use.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.339-350
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• 2019

This research focuses on finite element model updating and damage assessment of structures at element level based on global nondestructive test results. For this purpose, an optimization system is generated to minimize the structural dynamic parameters discrepancies between numerical and experimental models. Objective functions are selected based on the square of Euclidean norm error of vibration frequencies and modal assurance criterion of mode shapes. In order to update the finite element model and detect local damages within the structural members, modern optimization techniques is implemented according to the evolutionary algorithms to meet the global optimized solution. Using a simulated numerical example, application of genetic algorithm (GA), particle swarm (PSO) and artificial bee colony (ABC) algorithms are investigated in FE model updating and damage detection problems to consider their accuracy and convergence characteristics. Then, a hybrid multi stage optimization method is presented merging advantages of PSO and ABC methods in finding damage location and extent. The efficiency of the methods have been examined using two simulated numerical examples, a laboratory dynamic test and a high-rise building field ambient vibration test results. The implemented evolutionary updating methods show successful results in accuracy and speed considering the incomplete and noisy experimental measured data.

• 비파괴검사학회지
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• 제20권2호
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• pp.116-129
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• 2000

초음파검사에서 발생하는 물리적 현상의 복잡성을 고려할 때, 이를 이론적으로 모델링하기 위해 수치적인 기법을 이용하는 것이 효과적인 경우가 많다. 본 논문에서는 초음파검사를 수치적으로 모델링하는 기법들에 대하여 개괄적으로 살펴보고, 특히 유한차분법과 유한요소법에 대하여 상세히 알아본다. 즉, 유한차분법과 유한요소법을 이용한 해석의 개요를 설명하고, 이들의 적용시 고려사항 및 문제점에 대해 알아 본 후, 기존의 연구결과 중 중요한 것들을 참고문헌으로 열거하고 몇 가지 예를 소개한다. 계속되는 컴퓨터의 기술적 발전으로 인하여 초음파검사에 대한 수치적 모델링 기법의 신뢰성과 편의성이 지속적으로 증대될 것으로 기대된다.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.1-31
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• 2008

The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors' own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

• Structural Engineering and Mechanics
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• 제17권6호
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• pp.735-749
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• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.