• 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.

• The Pure and Applied Mathematics
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• v.23 no.1
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• pp.13-19
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• 2016

In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.

• Proceedings of the Korea Society for Simulation Conference
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• 2001.10a
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• pp.373-379
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• 2001

There is a big issue to generate 3D hexahedral finite element (FE) model, since a process to divide the whole domain into several simple-shaped sub-domains is required before generating a continuous mesh with mapped mesh generators. In general, it is nearly impossible to set up proper division numbers interactively to keep mesh connectivity between sub-domains on a complicated arbitrary-shaped domain. If mesh continuity between sub-domains is not required in an analysis, this complicated process can be omitted. Element-free Galerkin method (EFGM) can accept discontinuous meshes, which only requires nodal information. However it is difficult to choose a reasonable influenced domain in moving least squares scheme with non-uniformly distributed nodes in discontinuous FE models. A new FE scheme fur discontinuous mesh is proposed in this paper by applying improved EFGM with some modification to derive FE approximated function in discontinuous parts. Its validity is evaluated on linear elastic problems.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.535-550
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• 2005

The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.

• Structural Engineering and Mechanics
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• v.48 no.6
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• pp.775-789
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• 2013

The current paper proposes a boundary element formulation, applicable to 2-D and 3-D elastostatics problems using a unified approach for transformations of the domain integrals into boundary integrals. The method is applicable to linear problems encompassing both finite and infinite multi-region domains allowing non-vanishing body forces. Numerical results agree quite well with the analytical solutions; while the present method offers easy formulation with less numerical efforts in comparison to FEM or some BEM which need interior points to treat arbitrary body forces. It is demonstrated that the method has the potential to have profound impact on engineering design, notably in dam-foundation interaction.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.5
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• pp.49-58
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• 2013

Appropriate random variables and probability density functions based on statistical analysis should be defined to execute reliability analysis. Most studies have focused on only normal distributions or assumed that the variables showing non-normal characteristics follow the normal distributions. In this study, the reliability problem with non-normal probability distribution was dealt with using the convolution method in the case that the integration domains of variables are limited to a finite range. The results were compared with the traditional method (linear transformation of normal distribution) and Monte Carlo simulation method to verify that the application was in good agreement with the characteristics of probability density functions with peak shapes. However it was observed that the reproducibility was slightly reduced down in the tail parts of density function.

• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.613-626
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• 2021

In this paper, an enhanced Violation-based Sensitivity analysis and Border-Line Adaptive Sliding Technique (ViS-BLAST) will be utilized for optimization of some well-known structural and mechanical engineering problems. ViS-BLAST has already been introduced by the authors for solving truss optimization problems. For those problems, this method showed a satisfactory enactment both in speed and efficiency. The Enriched ViS-BLAST or EVB is introduced to be vastly applicable to any solvable constrained optimization problem without any specific initialization. It uses one-directional step-wise searching technique and mostly limits exploration to the vicinity of FNF border and does not explore the entire design space. It first enters the feasible region very quickly and keeps the feasibility of solutions. For doing this important, EVB groups variables for specifying the desired searching directions in order to moving toward best solutions out or inside feasible domains. EVB was employed for solving seven numerical engineering design problems. Results show that for problems with tiny or even complex feasible regions with a larger number of highly non-linear constraints, EVB has a better performance compared to some records in the literature. This dominance was evaluated in terms of the feasibility of solutions, the quality of optimum objective values found and the total number of function evaluations performed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Journal of Photoscience
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• v.5 no.1
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• pp.11-15
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• 1998

The texture change of non-linear optical molecules at the air/water interface was investigated as a function of surface pressure with Brewster angle microscopy. The texture change resulted from the aggregation of dye molecules is important to understand the film uniformity and grain formation process. The 4-Octadecylhydroxy-4'-nitrostilbene (OHNS) generated the small spots of size around 1$\mu$m. The spots exhibit high contrast with other film area and do not show angle dependent reflectivity change. It is interesting to observe that the size of the domain stays the same as the film pressure increases. At high surface pressure, the contrast ratio of domains becomes high, which means dense packing of OHNS. And, the size of domain grows. In the middle of domain, highly contrasted domains are formed. The first and the second order transitions of OHNS observed from surface pressure-area isotherm result from the two types of grains. The N,N-Dihexadecylcyanoaniline (DHCA) formed highly contrasted gains over entire region, and the grains are the double layers. The difference in Langmuir film of OHNS and DHCA at the air/water interface is consistent with the small tilt angle from the surface normal for OHNS and the large tilt angle for DHCA in the Langmuir-Blodgett films.

• The Korean Journal of Ceramics
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• v.7 no.1
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• pp.30-35
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• 2001

The contribution of the non-$180^{\circ}C$ domains to the electric-field-induced strains (EFI-strains) of PZT ceramics was evaluated by an XRD method and by an interferometric method. The XRD intensity ratio of 200 and 002 diffraction peaks of tetragonal PZT was measured under strong electric fields. The amount of the $90^{\circ}$ domain reorientation was evaluated and the strain due to the domain reorientation was calculated. It was confirmed that the EFI-strain of PZT ceramics was equal to the sum of the strain calculated from the d$_33$ constant determined by the resonance-antiresonance method and the strain due to the $90^{\circ}$ domain reorientation. The amount of the $90^{\circ}$domain reorientation has a linear relation with the c/a ratio in the "soft" PZT ceramics. A Mech-Zehnder interferometer was constructed to measure the EFI-strains vs. electric-field curves of PZT ceramics as a function of frequency. The EFI-strain vs. electric-field curve showed a hysteresis due to the effect of the non-$180^{\circ}$ domain reorientation when the applied voltage was high and its frequency was low. The apparent piezoelectric constant increased from the d$_33$ value determined by the resonance-antiresonance method with decreasing frequency. This deviation was attributed to the non-$180^{\circ}$ domain contribution.tribution.