• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.363-376
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• 2002

Stability result is obtained for the approximation of the stationary Stokes problem with nonconforming elements proposed by Douglas et al [1] for the velocity and discontinuous piecewise constants for the pressure on qudrilateral elements. Optimal order $H^1$and $L^2$error estimates are derived.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.153-160
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• 1995

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babufka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. It is shown that the pressure solutions, although stable, exhibit sensitivity to the stabilization parameters.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.110-118
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• 2001

In many areas of finite element analysis, elements with special properties are required to achieve maximal accuracy. As examples, we may mention infinite elements for the representation of spatial domain that extend to special and singular elements for modeling point and line singularities engendered by geomeric features such as reentrant corners and cracks. In this paper, we study on modified shape function representing singular properties and algorigthm for the pollution adaptive mesh generation. We will also show that the modified shape function reduces pollution error and local error.

• East Asian mathematical journal
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• v.21 no.2
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• pp.205-217
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• 2005

In this paper we consider the fuzzy ideals of N-group G where N is a near-ring. We introduce the concepts: minimal elements, fuzzy linearly independent elements, and fuzzy basis of an N-group G and obtained fundamental related results.

• Structural Engineering and Mechanics
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• v.3 no.2
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• pp.193-199
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• 1995

Two kinds of special 3-dimensional 12-node finite elements-each one contains a traction-free planar surface-have been developed based on Hellinger-Reissner principle by assumed stress hybrid method. Example solutions have demonstrated the advantage of using these special elements for analyzing plates and solids with rectangular holes.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.15 no.3
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• pp.190-195
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• 2003

For many coastal problems, such as wave transformation, tidal circulation, sediment transports and diffusion phenomena, we resort to numerical techniques. The representative numerical techniques are the method of finite differences and finite elements. The approximate algebraic equations, referred to as finite difference equations(FDEs), are subsequently solved at discrete grid points within the domain of interests. Therefore, a set of grid points within the domain, as well as the boundaries of the domain, must be specified. The generation of grids for FDEs, with uniform spacing, is very simple compared to that of finite elements. However, within a very complex domain, there are few grid generation tools we can use conveniently. Unfortunately, most of the commercial grid generation programs are developed only for finite element method. In this paper, grid generation method using digitizer, with uniform rectangular spacing, are introduced in detail. Didger and Surfer programs by Golden Software are necessary to produce comparatively accurate and simple depth data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.10
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• pp.1139-1146
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• 2012

An alternative approach for topology optimization of steady incompressible Navier-Stokes flow problems is presented by using P1 nonconforming finite elements. This study is the extended research of the earlier application of P1 nonconforming elements to topology optimization of Stokes problems. The advantages of the P1 nonconforming elements for topology optimization of incompressible materials based on locking-free property and linear shape functions are investigated if they are also valid in fluid equations with the inertia term. Compared with a mixed finite element formulation, the number of degrees of freedom of P1 nonconforming elements is reduced by using the discrete divergence-free property; the continuity equation of incompressible flow can be imposed by using the penalty method into the momentum equation. The effect of penalty parameters on the solution accuracy and proper bounds will be investigated. While nodes of most quadrilateral nonconforming elements are located at the midpoints of element edges and higher order shape functions are used, the present P1 nonconforming elements have P1, {1, x, y}, shape functions and vertex-wisely defined degrees of freedom. So its implentation is as simple as in the standard bilinear conforming elements. The effectiveness of the proposed formulation is verified by showing examples with various Reynolds numbers.

• Journal of Biomedical Engineering Research
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• v.3 no.2
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• pp.65-70
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• 1982

This paper presents a new method of solving the electric potential distribution using the finite element method. The thoracic region surrounded by the body surface and the heart is discretized into finite elements and the Continuous Laplace-equation is transformed into one of the finite degrees of freedom. The current source density, the conductivity, and the excitable range is obtained by the references. From the result of simulation, it was revealed that the potential pattern of in homogeneity was much different from that of homogeneity.

• Structural Engineering and Mechanics
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• v.23 no.4
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• pp.431-447
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• 2006

A new incremental finite element model is developed to simulate the frictional contact of elastic bodies. The incremental convex programming method is exploited, in the framework of finite element approach, to recast the variational inequality principle of contact problem in a discretized form. The non-classical friction model of Oden and Pires is adopted, however, the friction effect is represented by an equivalent non-linear stiffness rather than additional constraints. Different parametric studies are worked out to address the versatility of the proposed model.

• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.383-390
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• 1995

A 2-D four-noded finite element which contains a ${\lambda}$ singularity is developed. The new element is compatible with quadratic standard isoparametric elements. The element is tested on two different examples. In the first example, an edge crack problem is analyzed using two different meshes and different integration orders. The second example is a crack perpendicular to the interface problem which is solved for different material properties and in turn different singularity order ${\lambda}$. The results of those examples illustrate the efficiency of the proposed element.