• Earthquakes and Structures
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• v.3 no.2
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• pp.97-115
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• 2012

The energy-transmitting boundary, which is used in the well-known finite element method (FEM) program FLUSH, is quite efficient for the earthquake response analysis of buildings considering soil-structure interaction. However, it is applicable only in the frequency domain. The author proposed methods for transforming frequency dependent impedance into the time domain, and studied the time domain transform of the boundary. In this paper, first, the estimation methods for both the halfspace condition under the bottom of the soil model and the pseudo three-dimensional effect were studied with the time domain transmitting boundary. Next, response behavior when using the boundary was studied in detail using a practical soil and building model. The response accuracy was compared with those using viscous boundary, and the boundary that considers the excavation force. Through these studies, the accuracy and efficiency of the proposed time domain transmitting boundary were confirmed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.354-362
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• 1995

The finite element modeling is used to study the buckling and postbuckling behavior of composite laminates with an embedded delamination. Degenerated shell element and rigid beam element are utilized for the finite element modeling. In the nonlinear finite element formulation, the updated Lagrangian description method based on the second Piola-Kirchhoff stress tensor and the Green strain tensor is used. The buckling and postbuckling behavior of composite laminates with a delamination are investigated for various delamination sizes, stacking sequences, and boundary conditions. It is shown that the buckling load and postbuckling behavior of composite laminates depend on the buckling model which is determined by the delamination size, stacking sequence and boundary condition. Also, results show that introduction of couplings can reduce greatly the buckling load.

• Journal of the Earthquake Engineering Society of Korea
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• v.13 no.6
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• pp.67-86
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• 2009

In this study, a 3D transmitting boundary in water-saturated transversely isotropic soil strata has been developed based on u-w formulation for application to general 3D analysis. Behavior in the far field region is expanded in the Fourier series, and dynamic stiffness for each term is obtained based on the u-w formulation. Transformation of the dynamic stiffness is presented to combine the transmitting boundary with the 3D finite elements for the near field region formulated in a 3D Cartesian coordinate system. The developed transmitting boundary is verified through a comparison of the dynamic behavior of a rigid circular foundation with the results from the existing numerical method. In addition, the developed transmitting boundary is applied to the analysis of the dynamic behavior of rigid foundations of diverse shapes, and the effects of the level of the groundwater table on the dynamic stiffness of a rigid rectangular foundation in the water-saturated transversely isotropic layered stratum are studied.

• Tribology and Lubricants
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• v.15 no.4
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• pp.343-353
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• 1999

The role of viscosity index improver's(Ⅶ) additives for modem engine lubrication is complex. Under the condition of atmosphere or low shear rate, the characteristics of Ⅶ added lubricant is verified and quoted frequently for mathematical model of lubricant behavior. However, recent research shows that added lubricant has the characteristics of shear thinning at high shear rate condition although it performs well enough over the whole range of working temperature. At high shear rate, they show significant decrease of apparent viscosity irrespective of temperature. Many experimental researches verify that Ⅶ added lubricant shows boundary film layer formation on the solid surface as well as shear thinning effect by its polymeric molecular characteristics. The intend of our research is to verify the effects of Ⅶ from the viewpoint of continuum mechanics, because conventional Reynolds'equation with only pressure-viscosity relation cannot fully predict the lubricant behavior under the Ⅶ added condition. In these aspects, Reynolds'equation of Newtonian fluid model lacks the reflection of real fluid behavior and there is no way to explain the non-linear characteristics of Ⅶ added lubricant. In this research, we mathematically modeled the Ⅶ added lubricant behaviors which are the characteristics of non-Newtonian fluid behavior at high shear rate and boundary film formation on the solid surface. The consideration of elastic deformation in the contact region is also included in our computation and finally the converged film pressure and the film thickness with elastic deformation are obtained. The results are compared with those of Newtonian fluid model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.17-28
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• 1999

A new procedure of the boundary element method(BEM),say, singular BEM for the potential problems with singularities is presented. To obtain the numerical solution of which asymptotic behavior near the singularities is close to that of the analytic solution, we use particular elements on the boundary segments containing singularities. The Motz problem and the crack problem are taken as the typical examples, and numerical results of these cases show the efficiency of the present method.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.249-265
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• 2017

Interface problem here refers to a second order elliptic problem with a discontinuous coefficient for the second order derivatives. For the corresponding boundary value problem, the maximum principle still holds but Hopf's boundary point lemma may fail. We will give an optimal power type estimate that replaces Hopf's lemma at those boundary points, where this coefficient jumps.

• Journal of Welding and Joining
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• v.31 no.3
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• pp.31-38
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• 2013

The transition of serrated grain boundary and its effect on liquation behavior in the simulated weld heat-affected zone (HAZ) have been investigated in a wrought Ni-based superalloy Alloy 263. Recently, the present authors have found that grain boundary serration occurs in the absence of adjacent coarse ${\gamma}^{\prime}$ particles or $M_{23}C_6$ carbides when a specimen is direct-aged with a combination of slow cooling from solution treatment temperature to aging temperature. The present study was initiated to determine the interdependence of the serration and HAZ property with a consideration of this serration as a potential for the use of a hot-cracking resistant microstructure. A crystallographic study indicated that the serration led to a change in grain boundary character as special boundary with a lower interfacial energy as those terminated by low-index {111} boundary planes. It was found that the serrated grain boundaries are highly resistant to boron enrichment, and suppress effectively grain coarsening in HAZ. Furthermore, the serrated grain boundaries showed a higher resistance to susceptibility of liquation cracking. These results was discussed in terms of a significant decrease in interfacial energy of grain boundary by the serration.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.135-143
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• 2006

We consider some applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length. And we present some geometric applications of extremal length. The method of extremal length lead to simple proofs of theorems.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.495-502
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• 2004

We consider the applications of extremal length to the boundary behavior of analytic functions and derive a theorem in connection with the capacity. This theorem applies the extremal length to the analytic functions defined on the domain with a number of holes. So it shows us the usefulness of the method of extremal length.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.603-611
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• 2005

We present some geometric applications of extremal length. The method of extremal length leads a simple proofs of theorems. And we consider the applications of extremal length to the boundary behavior of analytic functions and derive theorems in connection with the conformal mappings. It shows us the usefulness of the method of extremal length.