• Korean Journal of Mathematics
• /
• v.16 no.1
• /
• pp.25-40
• /
• 2008

We are concerned with a free boundary problem for the 2D Stokes channel flows, which determines the profile of the wing for the channel, so that the given traction force is to be distributed along the wing of the channel. Using the domain embedding technique, the free boundary problem is transferred into the shape optimization problem through the compliant formulation by releasing the traction condition along the variable boundary. The justification of the formulation will be discussed.

• Smart Structures and Systems
• /
• v.29 no.2
• /
• pp.279-286
• /
• 2022

In this article, a novel propagation formulation of Rayleigh waves in a compressible isotropic half-space with impedance boundary condition is proposed by embedding the normal stress. In a two-dimensional case, it is assumed that a design boundary is free of normal traction and a shear traction depends on linearly a normal component of displacements multiplied by frequencies. Therefore, impedance boundary conditions affect the normal stress, where the impedance parameters correspond to dimensions of stresses over velocity. On the other hand, vanished impedance values are traction-free boundary conditions. The main purpose of this article is to present theoretically the existence and uniqueness of a Rayleigh wave formulation relying on secular equation's mathematical analyses. Its velocity varies along with the impedance parameters. Moreover, numerical experiments with different values for the velocity of Rayleigh waves are carried out. The present Rayleigh waves study is a fundamental step in analyzing the cause and effect of physical states such as building or structure damages resulting from natural dynamics. The results of the study generate a basic design formulation theory to test the effects of Rayleigh waves affecting structures when an earthquake occurs. The presence and uniqueness of the proposed formulation is verified by mutual comparisons of several numerical examples.

• Korea-Australia Rheology Journal
• /
• v.19 no.4
• /
• pp.211-219
• /
• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.11
• /
• pp.1595-1600
• /
• 2012

This paper shows an improvement of the WRSM (Wound Rotor Synchronous Motor) by satisfying the voltage limit condition at high speed. After that, it compares the performance of the improved WRSM to that of the IPMSM (Interior Permanent Magnet Synchronous Motor). The comparison has been made under the condition where the dimension of the motor is identical to that of the IPMSM, having the rotor switched to a wounded rotor form. Moreover, this paper compares the Basic Model of the two motor, and estimates the parameters of the WRSM, thereby proposing the method to improve high speed performance. Furthermore, this paper presents the feasibility of switching the conventional motor into rare-earth-free motors for traction purpose.

• Smart Structures and Systems
• /
• v.19 no.2
• /
• pp.203-211
• /
• 2017

This paper provides a numerical solution for multiple confocal elliptic dissimilar cylinders. In the problem, the inner elliptic notch is under the traction free condition. The medium is composed of many confocal elliptic dissimilar cylinders. The transfer matrix method is used to study the continuity condition for the stress and displacement along the interfaces. Two cases, or the infinite matrix case and the finite matrix case, are studied in this paper. In the former case, the remote tension is applied in y- direction. In the latter case, the normal loading is applied along the exterior elliptic contour. For two cases, several numerical results are provided.

• Proceedings of the KSME Conference
• /
• 2000.04b
• /
• pp.698-703
• /
• 2000

In a computational fluid dynamics, the imposition of open boundary condition has an important part of the accuracy but it is not easy to find the optimal boundary rendition. This difficult is introduced by making artificial boundary in unbounded domairs. Such open boundary requires us to ensure the continuity of all primitive variables because the nature is in continuum. Here we introduce a revised well-conditioned open boundary condition particularly in FEM and apply it to various problems-entrainment, body force, short domains.

• Computational Structural Engineering
• /
• v.10 no.3
• /
• pp.185-193
• /
• 1997

The order of the stress singularity that occurs at the termination of an interface between materials exhibiting bilinear stress-strain response under plane strain conditions has been calculated, The governing equation of elasticity together with traction-free boundary condition and interface continuity condition defines a two-point boundary value problem. The stress components near the free edge are assumed to be proportional to r/sup s-1/, with solutions existing only for certain values of s. Finding these values entails the solution of an eigenvalue problem. Because it has been impossible to integrate the differential equations analytically, the integration has been performed numerically with a shooting method coupled with a Newton improvement scheme.

• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 1998.04a
• /
• pp.98-105
• /
• 1998

In this study, the boundary element analysis in dynamics for the multilayered semi-infinite plane is developed using the fundamental solution for moving loads. Also the indirect method and superposition method are introduced to consider the multilayered systems and moving loads. At each layer the fundamental solution can be obtained by solving the governing equation which is transformed by the Fourier transform. The governing equation can be solved by three conditions; continuity conditions of displacement and stress, the traction free condition at the surface and the radiation condition at the surface and the radiation condition at the infinite distance. To verify the solution and the developed algorithm, the theoretical solution for the homogeneous layer and commercial FEM program is compared with the results of this study.

• Geomechanics and Engineering
• /
• v.9 no.5
• /
• pp.631-644
• /
• 2015

This article considers the problems of cylindrical bending of functionally graded plates in which material properties vary through the thickness. The variation of the material properties follows two power-law distributions in terms of the volume fractions of constituents. In addition, this paper considers orthotropic materials rather than isotropic materials. The traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. Numerical results are presented to show the effect of the material distribution on the deflections and stresses. Results show that, all other parameters remaining the same, the studied quantities (stress, deflection) of P-FGM and E-FGM plates are always proportional to those of homogeneous isotropic plates. Therefore, one can predict the behaviour of P-FGM and E-FGM plates knowing that of similar homogeneous plates.

• Smart Structures and Systems
• /
• v.19 no.3
• /
• pp.237-241
• /
• 2017

The present study deals with the propagation of Love wave (a type of surface wave) in crustal layer having temperature dependent inhomogeneity. It is assumed that the inhomogeneity in the crustal layer arises due to linear temperature variation in rigidity and density. The upper boundary of the crustal layer is traction free. Numerical results for Love wave are discussed by plotting analytical curves between phase velocity against wave number and stress against depth in the presence of inhomogeneity and temperature parameters. The effects boundary condition on the Love wave propagation in the crustal layer is also analyzed. The results presented in this study would be useful for seismologists and geologists.