• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.853-862
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• 2014

In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.

• Journal of Information Processing Systems
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• v.5 no.1
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• pp.1-4
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• 2009

Level set methods are the numerical techniques for tracking interfaces and shapes. They have been successfully used in image segmentation. A new variational level set evolving algorithm without re-initialization is presented in this paper. It consists of an internal energy term that penalizes deviations of the level set function from a signed distance function, and an external energy term that drives the motion of the zero level set toward the desired image feature. This algorithm can be easily implemented using a simple finite difference scheme. Meanwhile, not only can the initial contour can be shown anywhere in the image, but the interior contours can also be automatically detected.

• Proceedings of the KSR Conference
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• 2002.10b
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• pp.1100-1105
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• 2002

The elasticity of the contact wire is one of important static parameters for the catenary system. This paper presents how to analyse the elasticity of the catenary system using both simple string model method and finite element method with their formula. Analysis results obtained by these two methods for KTX catenary system are compared. A measurement of the elasticity for the KTX catenary under construction which is located near Kumkang bridge is made for the comparison with the analysis results. Both a dynamic and a static methods are tried for the measurement. Because of wave propagation, the dynamic method with 5 km/h running presented an asymmetric variational pattern of the elasticity while the static method presented a symmetric pattern of the elasticity in the span. Measured elasticity using the static method is found to be a little higher than the analysis results. But, the static method can presented us a variational pattern of the elasticity in the span similar to the analysed results. Therefore, the static method can be used for evaluating the elasticity of the catenary system

• Steel and Composite Structures
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• v.27 no.6
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• pp.789-801
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• 2018

A weak-form formulation of finite annular prism methods (FAPM) based on Reissner's mixed variational theorem (RMVT), is developed for the quasi three-dimensional (3D) static analysis of two-directional functionally graded (FG) circular plates with various boundary conditions and under mechanical loads. The material properties of the circular plate are assumed to obey either a two-directional power-law distribution of the volume fractions of the constituents through the radial-thickness surface or an exponential function distribution varying doubly exponentially through it. These FAPM solutions of the loaded FG circular plates with both simply-supported and clamped edges are in excellent agreement with the solutions obtained using the 3D analytical approach and two-dimensional advanced plate theories available in the literature.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.97-108
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• 2020

This study presents a 4 node, 11 DOF/node plate element based on higher order shear deformation theory for lamina composite plates. The theory accounts for parabolic distribution of the transverse shear strain through the thickness of the plate. Differential field equations of composite plates are obtained from energy methods using virtual work principle. Differential field equations of composite plates are obtained from energy methods using virtual work principle. These equations were transformed into the operator form and then transformed into functions with geometric and dynamic boundary conditions with the help of the Gâteaux differential method, after determining that they provide the potential condition. Boundary conditions were determined by performing variational operations. By using the mixed finite element method, plate element named HOPLT44 was developed. After coding in FORTRAN computer program, finite element matrices were transformed into system matrices and various analyzes were performed. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Steel and Composite Structures
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• v.39 no.3
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• pp.291-306
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• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.

• Journal of IKEEE
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• v.26 no.3
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• pp.475-482
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• 2022

Signal pre-processing and post-processing are some areas of study around electrical resistance tomography due to the low spatial resolution of pixel-based reconstructed images. In addition, methods that improve integrity and noise reduction are candidates for application in ERT. Lately, formulations of image processing methods provide new implementations and studies to improve the response against noise. For example, compact variational mode decomposition has recently shown good performance in image decomposition and segmentation. The results from this first approach of C-VMD to ERT show an improvement due to image segmentation, providing filtering of noise in the background and location of the target.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Journal of the Korean Society of Systems Engineering
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• v.19 no.2
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• pp.145-156
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• 2023

Trajectory of ballistic missile is defined by inherent flight dynamics, which decided range and maneuvering characteristics. It is crucial to predict range and maneuvering characteristics of ballistic missile in KAMD (Korea Air and Missile Defense) to minimize damage due to ballistic missile attacks, Nowadays, needs for applying AI(Artificial Intelligence) technologies are increasing due to rapid developments of DNN(Deep Neural Networks) technologies. To apply these DNN technologies amount of data are required for superviesed learning, but trajectory data of ballistic missiles is limited because of security issues. Trajectory data could be considered as multivariate time series including many variables. And augmentation in time series data is a developing area of research. In this paper, we tried to augment trajectory data of ballistic missiles using recently developed methods. We used TimeVAE(Time Variational AutoEncoder) method and TimeGAN(Time Generative Adversarial Networks) to synthesize missile trajectory data. We also compare the results of two methods and analyse for future works.