• Structural Engineering and Mechanics
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• v.39 no.6
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• pp.767-793
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• 2011

An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.205-226
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• 2015

Finite element method (FEM) is an effective quantitative method to solve complex engineering problems. The basic idea of FEM for a complex problem is to be able to find a solution by reducing the problem made simple. If mathematical tools are inadequate to obtain precise result, even approximate result, FEM is the only method that can be used for structural analyses. In FEM, the domain is divided into a large number of simple, small and interconnected sub-regions called finite elements. FEM has been used commonly for linear and nonlinear analyses of different types of structures to give us accurate results of plane stress and plane strain problems in civil engineering area. In this paper, FEM is used to investigate stress analysis of a shear wall which is subjected to concentrated loads and fundamental principles of stress analysis of the shear wall are presented by using matrix displacement method in this paper. This study is consisting of two parts. In the first part, the shear wall is discretized with constant strain triangular finite elements and stiffness matrix and load vector which is attained from external effects are calculated for each of finite elements using matrix displacement method. As to second part of the study, finite element analysis of the shear wall is made by ANSYS software program. Results obtained in the second part are presented with tables and graphics, also results of each part is compared with each other, so the performance of the matrix displacement method is demonstrated. The solutions obtained by using the proposed method show excellent agreements with the results of ANSYS. The results show that this method is effective and preferable for the stress analysis of shell structures. Further studies should be carried out to be able to prove the efficiency of the matrix displacement method on the solution of plane stress problems using different types of structures.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.13 no.2
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• pp.10-15
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• 1984

The aims of this study are to obtain a suitable method and a proper mesh for investigation of the temperature distribution and heat transfer. The relative errors of temperature distribution and heat transfer for each mesh are acquired in accordance with linear finite element (FEM 3), square finite element (FEM 6), cubic finite element (FEM 10), and finite difference method (FDM). It has been found that FEM 10 is the most accurate measure to obtain the temperature distribution and heat transfer. However, no significant results have been obtained successfully, because when higher order finite element methods are used the more computational efforts are necessary due to the distribution of elements. The results of this study are as follows ; 1 . In case of a=b=L, meshes for less than $1\%$ relative errors (temperature distribution) acquired in various methods to exact solution are $2\times2,\;4\times4,\;8\times8\;and\;8\tiems8$ for each FEM 10, FEM 6, FEM 3 and FDM and a=L, b=1/2L are $10\times5$ for each FEM 3 and FDM. And the tendency of results acquired of heat transfer is similar to those above. 2 . In computational efforts (a=b=L), FEM 6 has taken 21 times. and FEM 10 154times FEM 3 and FDM and FEM 3 is the sane as FDM.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.590-595
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• 2001

To improve the modeling accuracy for the finite element method, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for a Timoshenko beam element are derived and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. The exact interpolation functions are used to gain more accurate mode shape functions for the finite element method. This paper also presents a combined use of finite elements and exact dynamic elements in design problems. A Timoshenko frame with tapered sections is tested to demonstrate the design procedure with the proposed method.

• Smart Structures and Systems
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• v.13 no.4
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• Journal of Power System Engineering
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• v.11 no.1
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• pp.92-97
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• 2007

It is important to compute the structural analysis of plate structures in structural design. In this paper, the author uses the finite element-transfer stiffness coefficient method (FE-TSCM) for the structural analysis of plate structures. The FE-TSCM is based on the concept of the successive transmission of the transfer stiffness coefficient method and the modeling technique of the finite element method (FEM). The algorithm for in-plane structural analysis of a rectangular plate structure is formulated by using the FE-TSCM. In order to confirm the validity of the FE-TSCM for structural analysis of plate structures, two numerical examples for the in-plane structural analysis of a plate with triangular elements and the bending structural analysis of a plate with rectangular elements are computed. The results of the FE-TSCM are compared with those of the FEM on a personal computer.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2410-2413
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• 2005

Finite element method (FEM) has been widely used as a useful numerical method that can analyze complex engineering problems in electro-magnetics, mechanics, and others. CEMTool, which is similar to MATLAB, is a command style design and analyzing package for scientific and technological algorithm and a matrix based computation language. In this paper, we present new 3D FEM package in CEMTool environment. In contrast to the existing CEMTool 2D FEM package and MATLAB PDE (Partial Differential Equation) Toolbox, our proposed 3D FEM package can deal with complex 3D models, not a cross-section of 3D models. In the pre-processor of 3D FEM package, a new 3D mesh generating algorithm can make information on 3D Delaunay tetrahedral mesh elements for analyses of 3D FEM problems. The solver of the 3D FEM package offers three methods for solving the linear algebraic matrix equation, i.e., Gauss-Jordan elimination solver, Band solver, and Skyline solver. The post-processor visualizes the results for 3D FEM problems such as the deformed position and the stress. Consequently, with our new 3D FEM toolbox, we can analyze more diverse engineering problems which the existing CEMTool 2D FEM package or MATLAB PDE Toolbox can not solve.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.2
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• pp.141-149
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• 2002

Although the finite element method has become an indispensible tool for the dynamic analysis of structures, difficulty remains to quantify the errors associated with discretization. To improve the modeling accuracy, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for the Timoshenko beam element are derived using the exact dynamic element modeling (EDEM) and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. A combined use of finite element method and exact interpolation functions is presented to gain more accurate mode shape functions. This paper also presents a combined use of finite elements and exact dynamic elements in design/reanalysis problems. Timoshenko flames with tapered sections are tested to demonstrate the design procedure with the proposed method. The numerical study shows that the combined use of finite element model and exact dynamic element model is very useful.

• Korean Journal of Mathematics
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• v.13 no.2
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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.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.326-329
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• 2002

The dc reactor type superconducting fault current limiter is composed of a power converter, magnetic core reactors and a do reactor that is a superconducting coil. When a fault occurs, the dc reactor maintains the stability of system by limiting its fault current. In this study, we focus on the design of the dc reactor using FEM(Finite Element Method). In order to design it, various elements should be considered such as magnetic field intensity, Lorentz's force, its inductance and so forth. Firstly, we forecast the values of those elements from the simulation of FEM and then measured with a copper wire magnet. Finally, verify the reliability of this FEM method by comparing with two results.