• Proceedings of the KSME Conference
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• 2005.11a
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• pp.67.2-67.2
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• 2005

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.549-558
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• 2012

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

• Steel and Composite Structures
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• v.47 no.5
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• pp.569-585
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• 2023

This paper proposes an efficient approach for the structural topology optimization of bi-directional functionally graded structures by incorporating popular radial basis functions (RBFs) into an implicit level set (ILS) method. Compared to traditional element density-based methods, a level set (LS) description of material boundaries produces a smoother boundary description of the design. The paper develops RBF implicit modeling with multiquadric (MQ) splines, thin-plate spline (TPS), exponential spline (ES), and Gaussians (GS) to define the ILS function with high accuracy and smoothness. The optimization problem is formulated by considering RBF-based nodal densities as design variables and minimizing the compliance objective function. A LS-RBF optimization method is proposed to transform a Hamilton-Jacobi partial differential equation (PDE) into a system of coupled non-linear ordinary differential equations (ODEs) over the entire design domain using a collocation formulation of the method of lines design variables. The paper presents detailed mathematical expressions for BiDFG beams topology optimization with two different material models: continuum functionally graded (CFG) and mechanical functionally graded (MFG). Several numerical examples are presented to verify the method's efficiency, reliability, and success in accuracy, convergence speed, and insensitivity to initial designs in the topology optimization of two-dimensional (2D) structures. Overall, the paper presents a novel and efficient approach to topology optimization that can handle bi-directional functionally graded structures with complex geometries.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.41 no.11
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• pp.759-765
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• 2017

In this study, a three-dimensional least-square, level-set-based two-phase flow code was developed for the simulation of three-dimensional sloshing problems using finite element discretization. The code was validated by solving some benchmark problems. The proposed method was found to provide improved results against other existing methods, by using a coarser mesh. The results of the numerical experiments conducted during the course of this study showed that the proposed method was both robust and accurate for the simulation of three-dimensional sloshing problems. Using a substantially coarse grid, historical results of the dynamic pressure at a selected position corresponded with existing experimental data. The pressure history with a finer grid was similar to that of a coarse grid; however, a fine grid provided higher peak pressures. The present method could be extended to the analysis of a sloshing problem in a complex geometrical configuration using unstructured meshes owing to the features of FEM.

• Journal of computational fluids engineering
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• v.7 no.4
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• pp.28-34
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• 2002

A general purpose program for computing 3-D flows has been extended for two-phase flows with topologically complex interfaces. The 3-D interfaces are tracked by employing a coupled level set and volume-of-fluid (CLSVOF) method which not only can calculate an interfacial curvature accurately but also can achieve mass conservation well. The program has been tested through the computations of bubbles rising in a liquid. The numerical results are found to compare well with the results reported in the literature.

• International Journal of Control, Automation, and Systems
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• v.4 no.5
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• pp.660-667
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• 2006

This paper presents a novel region-based snake method for vessel segmentation. According to geometric shape analysis of the vessel structure with different scale, an efficient statistical estimation of vessel branches is introduced into the energy objective function, which applies not only the vessel intensity information, but also geometric information of line-like structure in the image. The defined energy function is minimized using the gradient descent method and a new region-based speed function is obtained, which is more accurate to the vessel structure and not sensitive to the initial condition. The narrow band algorithm in the level set framework implements the proposed method, the solution of which is steady. The segmentation experiments are shown on several images. Compared with other geometric active contour models, the proposed method is more efficient and robust.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.391-396
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• 2008

A level set based topological shape optimization using extended B-spline basis functions is developed for steady state heat conduction problems. The only inside of complicated domain is identified by the level set functions and taken into account in computation. The solution of Hamilton-Jacobi equation leads to an optimal shape according to the normal velocity field determined from the sensitivity analysis, minimizing a thermal compliance while satisfying a volume constraint. To obtain exact shape sensitivity, the precise normal and curvature of geometry need to be determined using the level set and B-spline basis functions. The nucleation of holes is possible whenever and wherever necessary during the optimization using a topological derivative concept.

• Applied Science and Convergence Technology
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• v.25 no.5
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• pp.98-102
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• 2016

The level set method has recently become popular in the simulation of semiconductor processes such as etching, deposition and photolithography, as it is a highly robust and accurate computational technique for tracking moving interfaces. In this research, full three-dimensional level set simulation has been developed for the investigation of focused ion beam processing. Especially, focused ion beam induced nanodot formation was investigated with the consideration of three-dimensional distribution of redeposition particles which were obtained by Monte-Carlo simulation. Experimental validations were carried out with the nanodots that were fabricated using focused $Ga^+$ beams on Silicon substrate. Detailed description of level set simulation and characteristics of nanodot formation will be discussed in detail as well as surface propagation under focused ion beam bombardment.

• Journal of Advanced Marine Engineering and Technology
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• v.28 no.2
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• pp.200-209
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• 2004

The fuzzy control based on $\alpha$-level fuzzy set decomposition. It is known to produce quick response and calculating time of fuzzy inference. This paper derived the embodiment computational algorithm for defuzzification by min-max fuzzy inference and the center of gravity method based on $\alpha$-level fuzzy set decomposition. It is easy to realize the fuzzy controller hardware. based on the calculation formula. In addition. this study proposed a circuit that generates PWM actual signals ranging from fuzzy inference to defuzzification. The fuzzy controller was implemented with mixed analog-digital logic circuit using the computational fuzzy inference algorithm by min-min-max and defuzzification by the center of gravity method. This study confirmed that the fuzzy controller worked satisfactorily when it was applied to the position control of a dc servo system.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.416-418
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• 2004

Tracking of evolving solid-fluid interfaces is treated using level set method and MLS-based finite element with variable nodes. Several applications will be illustrated to demonstrate the effectiveness of the present scheme