• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.59-71
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• 2018

We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.

• Computers and Concrete
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• v.33 no.3
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• pp.275-284
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• 2024

This work presents a comprehensive investigation of buckling behavior of bidirectional functionally graded imperfect beams exposed to several thermal loading with general boundary conditions. The nonlinear governing equations are derived based on 2D shear deformation theory together with Von Karman strain-displacement relation. The beams are composed of two different materials. Its properties are porosity-dependent and are continuously distributed over the length and thickness of the beams following a defined law. The resulting equations are solved analytically in order to determine the thermal buckling characteristics of BDFG porous beams. The precision of the current solution and its accuracy have been proven by comparison with works previously published. Numerical examples are presented to explore the effects of the thermal loading, the elastic foundation parameters, the porosity distribution, the grading indexes and others factors on the nonlinear thermal buckling of bidirectional FG beam rested on elastic foundation.

• Wind and Structures
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• v.24 no.5
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• pp.465-480
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• 2017

Modelling an equilibrium atmospheric boundary layer (ABL) in computational wind engineering (CWE) and relevant areas requires the boundary conditions, the turbulence model and associated constants to be consistent with each other. Among them, the inflow boundary conditions play an important role and determine whether the equations of the turbulence model are satisfied in the whole domain. In this paper, the idea of modeling an equilibrium ABL through specifying proper inflow boundary conditions is extended to the SST $k-{\omega}$ model, which is regarded as a better RANS model for simulating the blunt body flow than the standard $k-{\varepsilon}$ model. Two new sets of inflow boundary conditions corresponding to different descriptions of the inflow velocity profiles, the logarithmic law and the power law respectively, are then theoretically proposed and numerically verified. A method of determining the undetermined constants and a set of parameter system are then given, which are suitable for the standard wind terrains defined in the wind load code. Finally, the full inflow boundary condition equations considering the scale effect are presented for the purpose of general use.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.6
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• pp.673-678
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• 2011

This paper analyzes the standing balance of four-legged robots which are useful for delivering objects or investigating of information. For this, we specify an effective model of general four-legged robots and propose a boundary condition based on the standing stability of the four-legged walking. To verify such a standing balance, we consider some exemplary free motions at the standing mode of the robot and discuss on the robot's balance margin. The analysis specified in this paper will be applicable for effective balancing control of various quadruped robotic walking.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.4
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• pp.290-295
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• 2001

Subsets pipelines are exposed to several potential risks of damage due to corrosion, soil instability, anchor impact and other hazards. One of the main risk factors for the safety of a subsea pipeline is its free spanning. This paper examines the safety of subsea pipelines with free span under axial compressive load. The variation of allowable lengths of dynamic free span is examined for generalized boundary conditions. The free span is modelled as a beam with an elastic foundations and the boundary condition is replaced by linear and rotational springs at each end. A dynamic free span curve is obtained with a function of non-dimensional parameters and can be used usefully for the design of subsea pipelines with a free span. A case study is carried out to introduce the application method of the curve.

• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.57-62
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• 2008

Finite difference method using not general SSG(standard staggered grid) but RSG(rotated staggered grid) was applied to simulation of elastic wave propagation. Special free surface boundary condition such as imaging method is needed in finite difference method using SSG in elastic wave propagation but free surface boundary condition in finite difference method using RSG is easily solved with adding air layer. Recently PML(Perfectly Matched layer) is widely used to eliminate artificial reflection waves from finite boundary because of its' greate efficiency. Absorbing ability of CPML(convolutional Perfectly Matched Layer) that is more efficient than that of PML was applied to FDM using RSG in this study. The results of CPML eliminated artificial boundary waves very effectively in FDM using RSG in being compared with that of Cerjan's absorbing method.

• Ocean and Polar Research
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• v.28 no.3
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• pp.245-258
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• 2006

We investigated seasonal variations of the upper ocean temperature and the mixed layer depth (MLD) in an eddy-permitting global ocean general circulation model (OGCM) to assess the OGCM perfermance. The OGCM is based on the GFDL MOM3 which has a horizontal resolution of 0.5 degree and 30 vertical levels. The OGCM was integrated for 68 years using a monthly-mean climatological wind stress forcing. The model sea surface temperature (SST) and sea surface salinity were restored to the Levitus climatology with a time scale of 30 days. Annual-mean model SST shows a cold bias $(<\;-2^{\circ}C)$ in the summer hemisphere and a warm bias $(>\;1^{\circ}C)$ in the winter hemisphere mainly due to the restoring boundary condition of temperature. The model MLD captures well the observed features in most areas, with a slightly deep bias. However, in the Ross Sea and Weddell Sea, the model shows significantly deeper MLD than the climatology-mainly due to weak salinity stratifications in the model. For amplitude of seasonal variation, the model SST is smaller $(1{\sim}3^{\circ}C)$ than the observation largely due to the restoring surface boundary condition while the model MLD has larger seasonal variation $({\sim}50m)$. It is suggested that for more realistic simulation of the upper ocean structure in the present eddy-permitting ocean model, more refinements in the surface boundary condition for the thermohaline forcing and parameterization for vertical mixing are required, together with the incorporation of a sea-ice model.

• Journal of Advanced Research in Ocean Engineering
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• v.1 no.3
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• pp.157-167
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• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1349-1353
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• 2003

CEMTool is a command style design and analyzing package for scientific and technological algorithm and a matrix based computation language. In this paper, we present a compiler based approach to the implementation of the command mode generalized PDE solver in CEMTool. In contrast to the existing MATLAB PDE Toolbox, our proposed FEM package can deal with the combination of the reserved words such as "laplace" and "convect". Also, we can assign the border lines and the boundary conditions in a very easy way. With the introduction of the lexical analyzer and the parser, our FEM toolbox can handle the general boundary condition and the various PDEs represented by the combination of equations. That is why we need not classify PDE as elliptic, hyperbolic, parabolic equations. Consequently, with our new FEM toolbox, we can overcome some disadvantages of the existing MATLAB PDE Toolbox.

• Journal of Magnetics
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• v.18 no.2
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• pp.95-104
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• 2013

This paper presents a general analytical method for predicting the magnetic fields of different Halbach magnet arrays with or without back iron mounted on slotless permanent magnet (PM) linear machines. By using Fourier decomposition, the magnetization components of four typical Halbach magnet arrays are determined. By applying special synthetic boundary conditions on the PM surfaces, the expressions of their magnetic field distributions are derived based on the magnetic scalar potential (MSP), which are simpler than those based on the magnetic vector potential (MVP). The correctness of the method is validated by finite element analysis. The harmonics of airgap flux density waveforms of these Halbach magnet arrays with or without back iron are also compared and optimized.