• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.599-602
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• 2008

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.371-386
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• 2001

In this work we investigate the finite element preconditioning method for the $C^1$-cubic spline collocation discretizations for an elliptic operator A defined by $Au := -{\Delta}u + a_1u_x+a_2u_y+a_0u$ in the unit square with some boundary conditions. We compute the condition number and the numerical solution of the preconditioning system for the several example problems. Finally, we compare the this preconditioning system with the another preconditioning system.

• Journal of Sensor Science and Technology
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• v.8 no.3
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• pp.211-218
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• 1999

This paper describes the application of a coupled finite element-boundary element method (FE-BEM) to obtain the steady-state response of a piezoelectric transducer. The particular structure considered is a PZT4 disc-typed projector. The projector is three-dimensionally simulated to transduce applied electric charge on axial surfaces of the piezoelectric disc to acoustic pressure in air or in water. The directivity pattern of the acoustic field formed from the projected sound pressure is also simulated. And the displacement of the disc caused by the externally applied electric charge is shown in temporal motion. The coupled FE-BE method is described in detail.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.124-129
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• 2004

Finite element alternating method have been suggested and used for assessing the integrity of cracked structures. In the paper, in order to analyze arbitrarily shaped three dimensional cracks, the finite element alternating method is extended. The cracks are modeled as a distribution of displacement discontinuities by the displacement discontinuity method and the symmetric Galerkin boundary element method. Applied the proposed method to three dimensional crack included in the elbow, the efficiency and applicability of the method were demonstrated.

• Structural Engineering and Mechanics
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• v.43 no.6
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• pp.761-769
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• 2012

In this paper the Modified Finite Element-Transfer Matrix Method, which is the combination of Transfer Matrix Method and Finite Element Method, is applied to the static analysis of the structures. In the method, the structure is divided into substructures thus the number of unknowns that need to be worked out is reduced due to the transformation process. The static analysis of the structures can be performed easily and speedily by the proposed method. At the end of the study examples are presented for ensuring the agreement between the proposed method and classic Finite Element Method.

• Journal of the korean Society of Automotive Engineers
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• v.10 no.6
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• pp.54-60
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• 1988

During recent years, a great deal of interest has emerged on the use of adaptive approaches and a posteriori estimates in finite element method. The results are intended to be used to improve the quality of finite element solution by changing the location of the nodes within a fixed number of degrees of freedom-so called r method-, and by increasing the order of polynomial approximation with the new degrees of freedom-p method. This paper deals with error analysis that contains the basic theory and method of deriving error estimates and adaptive processes applied to finite element solutions underlying the rpm method that is the combination of r and p method of finite element. It is shown that we can obtain more accurate solution by applying the method to the 2-dimensional heat transfer problem.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.367-371
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• 2001

In the shape optimization based on the finite element method, the accuracy of finite element analysis of a given structure is important to determine the final shape. In case of a bending dominant problem, finite element solutions by the full integration scheme are not reliable because of the locking phenomenon. Furthermore, in the process of shape optimization, the mesh distortion is large due to the change of the structure outline: therefore, we cannot guarantee the accurate result unless the finite element itself is accurate. We approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two-dimensional simple beam. Results show that the modified finite element have improved the optimization results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.7 s.238
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• pp.990-997
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• 2005

The objective of this paper is to present the element connectivity parameterization (ECP) fur three dimensional problems. In the ECP method, a continuum structure is viewed as discretized finite elements connected by zero-length elastic links whose stiffness values control the degree of inter-element connectivity. The ECP method can effectively avoid the formation of the low-density unstable elements. These elements appear when the standard element density method is used for geometrical nonlinear problems. In this paper, this ECP method developed fur two-dimensional problems is expanded to the design of three-dimensional geometrical nonlinear structures. Among others, the automatic procedure converting standard finite element models to the models suitable for the ECP approach is developed and applied for optimization problems defined on general three-dimensional design domains.

• East Asian mathematical journal
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• v.35 no.5
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• pp.569-587
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• 2019

In this paper, we consider a split least-squares characteristic mixed element method for Sobolev equations with a convection term. First, to manipulate both convection term and time derivative term efficiently, we apply a characteristic mixed element method to get the system of equations in the primal unknown and the flux unknown and then get a least-squares minimization problem and a least-squares characteristic mixed element scheme. Finally, we obtain a split least-squares characteristic mixed element scheme for the given problem whose system is uncoupled in the unknowns. We prove the optimal order in $L^2$ and $H^1$ normed spaces for the primal unknown and the suboptimal order in $L^2$ normed space for the flux unknown.