• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.3
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• pp.195-202
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• 2012

Two nonlinear frame elements taking into account geometric nonlinearity is presented and compared based on the Lagrangian co-rotational formulation. The first frame element is believed to be geometrically-exact because not only tangent stiffness matrices is exactly evaluated including stiffness matrices due to initial deformation but also total member forces are directly determined from total deformations in the deformed state. Particularly two exact tangent stiffness matrices based on total Lagrangian and updated Lagrangian formulation, respectively, are verified to be identical. In the second frame element, the deformed curved shape is regarded as the polygon and current flexural deformations in iteration process are neglected in evaluating tangent stiffness matrices and total member forces. Two numerical examples are given to demonstrate the accuracy and the good performance of the first frame element compared with the second element. Furthermore it is shown that the first frame element can be used in tracing nonlinear behaviors of cable members.

• Journal of the Earthquake Engineering Society of Korea
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• v.9 no.2 s.42
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• pp.71-80
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• 2005

The solution to a liquid sloshing problem is challenge to the field of engineering. This is not only because the dynamic boundary condition at the free surface is nonlinear, but also because the position of the free surface varies with time in a manner not known a priori. Therefore, this nonlinear phenomenon, which is characterized by the oscillation of the unrestrained free surface of the fluid, is a difficult mathematical problem to solve numerically and analytically. In this study, three-dimensional boundary element method(BEM), which is based on the so-called an arbitrary Lagrangian-Eulerian(ALE) approach for the fluid flow problems with a free surface, was formulated to solve the behavior of the nonlinear free surface motion. An ALE-BEM has the advantage to track the free surface along any prescribed paths by using only one displacement variable, even for a three-dimensional problem. Also, some numerical examples were presented to demonstrate the validity and the applicability of the developed procedure.

• Journal of Korea Water Resources Association
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• v.32 no.2
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• pp.99-110
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• 1999

The method of moments, a Lagrangian scheme, considers the zeroth, first, and second moments of the grid cell spatial distributions of the concentration and then advects the concentration by maintaining conservation of the moments. The reasonable inital description of the first and second moments as well as the mean concentration, the zeroth moments, in grid element is important in the method of moments. In this study, the description methods of each initial moment are reviewed, and the method of moments is extended to overcome the restrictions of Courant number. Its performance is compared with those of available Eulerian and Lagrangian schemes. As the results, the method is successfully extended to overcome the stability restriction and is an accurate scheme for the advection simulation of concentration distribution, especially of which the gradient is steep. In addition, the method is very promising scheme in terms of computational efficiency when the mixing is confined in a relatively small region to the entire domain in two-dimensional problem.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.11a
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• pp.185-186
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• 2008

• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.55-59
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• 1991

We consider perturbation problems and Lagrangians for convex set function optimization problems. In particular, we prove that the Lagrangian $L({\Omega},y)$ is a convex set function in ${\Omega}$ for each y if the perturbation function is convex.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.67.1-67.1
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• 2005

• Proceedings of the Korea Air Pollution Research Association Conference
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• 2009.10a
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• pp.549-550
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• 2009

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.647-654
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• 2017

Duality methods based on modified Lagrangian functional for solving a model crack problem is considered. Without additional assumptions of regularity of the solution of an initial problem duality ratio is established for initial and dual problem.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.2
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• pp.105-112
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• 2007

Sediment transport model based on the Lagrangian concept considering the grain size distribution(GSD) was setup and the change of the sediment diffusion range was analysed in the condition of considering and not considering the GSD. The GSD curve is assumed as the Log-normal distribution function in order to consider the GSD with respect to the Lagrangian concept and the random numbers, i.e. sediment particles, are generated based on the distribution function. The sediment particles is assumed as the spherical type and the random numbers based on the sediment weight is converted to the sediment diameters. Sediment transport patterns are analysed by the settling simulation, in which the settling velocity is computed by the van Rijn formulae and the horizontal diffusion coefficient is used as the constant parameter. The diffusion patterns are very similar to the patterns with GSD condition. The diffusion range defined as the range including 90%, 99% sediment weight of the total sediment weight, however, is larger than without considering GSD condition in 90%-option and shorter than with considering GSD condition in 99-option, respectively. The diffusion range is defined as tile p-percentage of the cumulative sediment weight region with reference to the 50% region, 90%- option, 99%-option, respectively.

• Computational Structural Engineering
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• v.5 no.4
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• pp.103-111
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• 1992

In this paper, liquid sloshing effects in rectangular storage structures for spent fuel under earthquake loadings are investigated. Eulerian and Lagrangian approaches are presented. The Eulerian approach is carried out by solving the boundary value problem for the fluid motion. In the Lagrangian approach, the fluid as well as the storage structure is modelled by the finite element method. The fluid region is discretized by using fluid elements. The (1*1)-reduced integration is carried out for constructing the stiffness matrices of the fluid elements. Seismic analysis of the coupled system is carried out by the response spectra method. The numerical results show that the fluid forces on the wall obtained by two approaches are in good agreements. By including the effect of the wall flexibility, the hydrodynamic forces due to fluid motion can be increased very significantly.