• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• 한국전산유체공학회:학술대회논문집
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• 2008.10a
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• pp.33-41
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• 2008

This paper is an extension of previous study[9] on a development of a divergence-free element method using a hermite interpolated stream function. Divergence-free velocity bases defined on rectangles derived herein produce pointwise divergence-free flow fields. Hence the explicit imposition of continuity constraint is not necessary and the Galerkin finite element formulation for velocities does not involve the pressure. The divergence-free element of the previous study employed hermite serendipity cubic for interpolation of stream function, and it has been noted a possible discontinuity in variables along element interfaces. This deficiency can be removed by use of a hermite bicubic interpolated stream function, which requires at each element corners four degrees-of-freedom such as the unknown variable, its x- and y-derivatives and its cross derivative. Detailed derivations are presented for both solenoidal and irrotational bases from the hermite bicubic interpolated stream function. Numerical tests are performed on the lid-driven cavity flow, and results are compared with those from hermite serendipity cubics and a stabilized finite element method by Illinca et al[7].

• Geomechanics and Engineering
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• v.10 no.6
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• pp.757-774
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• 2016

Soils are usually weak in tension therefore different materials such as geosynthetics are used to address this inadequacy. Worldwide annual consumption of geosynthetics is close to $1000million\;m^2$, and the value of these materials is probably close to US$1500 million. Since the total cost of the construction is at least four or five times the cost of the geosynthetic itself, the impact of these materials on civil engineering construction is very large indeed. Nevertheless, there are several significant problems associated with geosynthetics, such as creep, low modulus of elasticity, and susceptibility to aggressive environment. Carbon fiber reinforced polymer (CFRP) was introduced over two decades ago in the field of structural engineering that can also be used in geotechnical engineering. CFRP has all the benefits associated with geosynthetics and it boasts higher strength, higher modulus, no significant creep and reliability in aggressive environments. In this paper, the performance of a CFRP reinforced retaining wall is investigated using the finite element method. Since the characterization of behavior of soils and interfaces are vital for reliable prediction from the numerical model, soil and interface properties are obtained from comprehensive laboratory tests. Based on the laboratory results for CFRP, backfill soil, and interface data, the finite element model is used to study the behavior of a CFRP reinforced wall. The finite element model was verified based on the results of filed measurements for a reference wall. Then the reference wall simulated by CFRP reinforcements and the results. The results of this investigations showed that the safety factor of CFRP reinforced wall is more and its deformations is less than those for a retaining wall reinforced with ordinary geosynthetics while their construction costs are in similar range.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.202-207
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• 2004

An elastic-plastic finite element analysis of fatigue crack closure is performed for plane strain conditions. The stabilization behavior of crack opening level and the effect of mesh size on the crack opening stress are investigated. In order to obtain a stabilized crack opening level for plane strain conditions, the crack must be advanced through approximately four times the initial monotonic plastic zone. The crack opening load tends to increase with the decrease of mesh size. The mesh size nearly equal to the theoretical plane strain cyclic plastic zone size may provide reasonable numerical results comparable with experimental crack opening data. The crack opening behavior is influenced by the crack growth increment and discontinuous opening behavior is observed. A procedure to predict the most appropriate mesh size for different stress ratio is suggested. Crack opening loads predicted by the FE analysis based on the procedure suggested resulted in good agreement with experimental ones within the error of 5 %. Effect of the distance behind the crack tip on the crack opening load determined by the ASTM compliance offset method based on the load-displacement relation and by the rotational offset method based on the load-differential displacement relation is investigated. Optimal gage location and method to determine the crack opening load is suggested.

• Journal of the Korean Ceramic Society
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• v.35 no.12
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• pp.1257-1265
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• 1998

Hertzian contact tests were used to investigate the evolution of fracturedamage in the coating layer as functions of contact load and coating thickness by studying crack patterns in porcelain on glass-infiltrated alumina bilayer system conceived to simulate the crown structure of a tooth. Cone cracks initiated at the coating top surface without delamination at interface and crack propagation to substrate. Preferentially the cracks made multi-cracks at the coating top surface rather than proceeding to interface. The cracks were highly stabilized with wide ranges between the loads to initiate first cracking and to cause final failure im-plying damage-tolerant capability. Finite element modelling was used to evaluate the stress distribution. Maximum tensile stress were responsible for the cracking at the coating layer and had a profound influence on the crack pattern and fracture damage in the layered structure materials.

• Journal of computational fluids engineering
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• v.10 no.2
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• pp.38-47
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• 2005

Substructuring methods are often used in finite element structural analyses. In this study a multi-level substructuring(MLSS) algorithm is developed and proposed as a possible candidate for finite element fluid solvers. The present algorithm consists of four stages such as a gathering, a condensing, a solving and a scattering stage. At each level, a predetermined number of elements are gathered and condensed to form an element of higher level. At the highest level, each sub-domain consists of only one super-element. Thus, the inversion process of a stiffness matrix associated with internal degrees of freedom of each sub-domain has been replaced by a sequential static condensation of gathered element matrices. The global algebraic system arising from the assembly of each sub-domain matrices is solved using a well-known iterative solver such as the conjugare gradient(CG) or the conjugate gradient squared(CGS) method. A time comparison with CG has been performed on a 2-D Poisson problem. With one domain the computing time by MLSS is comparable with that by CG up to about 260,000 d.o.f. For 263,169 d.o.f using 8 x 8 sub-domains, the time by MLSS is reduced to a value less than $30\%$ of that by CG. The lid-driven cavity problem has been solved for Re = 3200 using the element interpolation degree(Deg.) up to cubic. in this case, preconditioning techniques usually accompanied by iterative solvers are not needed. Finite element formulation for the incompressible flow has been stabilized by a modified residual procedure proposed by Ilinca et al.[9].

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.411-414
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• 2006

This paper describes a recent development on the divergence free basis function based on a hermite stream function. The well-known cavity problem has been used to compare the accuracy and the convergence of the present method with those of a modified residual method known as one of the stabilized finite e1ement methods. The comparison showed the present method performs better in the accuracy and convergence.

• Journal of the Korean Geotechnical Society
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• v.26 no.5
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• pp.15-26
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• 2010

This paper presents the results of a three-dimensional finite element analysis on a geosynthetic-reinforced bridge abutment. Examples on the use of mechanically stabilized earth bridge abutment in north America are first presented. A three-dimensional finite element analysis on a 4.8 m high, 14 m wide geosynthetic-reinforced bridge abutment was performed to investigate the 3D behavior of the geosynthetic-reinforced bridge abutment and the load carrying capacity of the bridge abutment in the three-dimensional space. The results are then presented in a way that the three-dimensional behavior of the abutment can be identified in terms of wall displacements and reinforcement forces. It is shown that the wall facing displacements as well as the reinforcement forces in the abutment are smaller than those computed based on a plane strain approximation.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.10a
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• pp.381-386
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• 2002

Recently, The machine tools have been needed for high speed and accuracy to increase productivity. The most important thing to get a more stabilized machine is to know the frequncy response which has an effect on manufacture a lot. This problem should be considered seriously by many researchers. There are many programs about FEM. but just using FEM program to get information of the object is not enough to put our confidence in the stability of the structure design. Therefore, the purpose of this research is to make a study for proving one of the ways to design to produce stabilized a machine more efficiently by comparing FRT with Simulation through FEM. At this two tests, we can learn about the frequency response area causing resonance and we can reconfirm the result to trust.

• Korean Journal of Mathematics
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• v.27 no.1
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• pp.193-219
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• 2019

The Navier-Stokes equations with variable density are challenging problems in numerical analysis community. We recently built the 2nd order stabilized Gauge-Uzawa method [SGUM] to solve the Navier-Stokes equations with constant density and have estimated theoretically optimal accuracy. Also we proved that SGUM is unconditionally stable. In this paper, we apply SGUM to the Navier-Stokes equations with nonconstant variable density and find out the stability condition of the algorithms. Because the condition is rather strong to apply to real problems, we consider Allen-Cahn scheme to construct unconditionally stable scheme.