• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.565-568
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• 2011

NURBS는 매개변수를 이용하여 3차원에서 곡면을 표현한 방법으로서 노트벡터, 조정점, 가중치로 구성된다. 레벨셋은 공간을 음함수로 정의된 장으로 형성하여 음함수의 일정한 값을 추적하여 곡면을 표현한 방법이다. 본 논문에서는 스캔 데이터를 NURBS 형태로 추출한 뒤 이를 정밀한 레벨셋 모델로 변환하였다. 레벨셋 모델을 구성하기 위해서 형성된 음함수는 부호를 갖는 거리함수를 사용하였고, 거리함수를 정밀하게 나타내기 위해 Newton 순환법을 이용하였다. 변환된 레벨셋 모델을 이용하여 형상의 몰핑을 수행하였다. 몰핑은 초기 형상을 목표 형상으로 변화시켜 나가는 과정으로서 레벨셋 모델을 이용한 몰핑은 용이성과 질적인 측면에서 우수하다. 수치 예제에서는 스캔 데이터의 레벨셋 모델 변환과 변환된 형상이 자연스럽게 목표형상으로 변화하는지를 확인한다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.1
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• pp.79-87
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• 2013

An isogeometric topological shape optimization method is developed using the level sets and Heaviside enrichments. 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 functions, which facilitates to handle complicated topological shape changes. The Heaviside enrichment improves the isogeometric analysis by adding some enrichment functions to model the internal boundaries. The proposed topological shape optimization method has several benefits: exact geometric models can be obtained using the isogeometric approach and the limitation of tensor-product patches can be overcome using the Heaviside enrichments to represent the internal voids. Even in a single patch, discontinuous displacement fields as well as smooth stress field can be obtained. Since the level sets offer the implicit moving boundary inside the domain, it is easy to represent the topological shape variations in the isogeometric analysis using Heaviside enrichments.

• 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

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.239-245
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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 identified by the level set functions is taken into account in computation, so we can remove the effects of domain outside parts in heat conduction problem. 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. Using topological derivative concept, the nucleation of holes for topological changes can be made whenever and wherever necessary during the optimization.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.1-8
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• 2014

Using the level set and the meshfree methods, we develop a topological shape optimization method applied to linear elasticity problems. Design gradients are computed using an efficient adjoint design sensitivity analysis(DSA) method. The boundaries are represented by an implicit moving boundary(IMB) embedded in the level set function obtainable from the "Hamilton-Jacobi type" equation with the "Up-wind scheme". Then, using the implicit function, explicit boundaries are generated to obtain the response and sensitivity of the structures. Global nodal shape function derived on a basis of the reproducing kernel(RK) method is employed to discretize the displacement field in the governing continuum equation. Thus, the material points can be located everywhere in the continuum domain, which enables to generate the explicit boundaries and leads to a precise design result. The developed method defines a Lagrangian functional for the constrained optimization. It minimizes the compliance, satisfying the constraint of allowable volume through the variations of boundary. During the optimization, the velocity to integrate the Hamilton-Jacobi equation is obtained from the optimality condition for the Lagrangian functional. Compared with the conventional shape optimization method, the developed one can easily represent the topological shape variations.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.1
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• pp.16-27
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• 2002

A level-set method is used for analyzing the behaviors of gas bubbles in two fluids incompressible viscous flow domain. The governing equations are solved by using a finite volume method. The numerical results are verified by comparing with the experimental and other computational results. Computations for the deformations and motions of one or multi-bubbles in the flow domain with the initial undisturbed free interface are conducted. It can be seen that numerical results for different surface tension and density ratio arise very different behaviors of bubbles. When bubbles rise near the free interface, the free interface gives some great influence on the behaviors of bubbles. The present results computed by a level-set method give useful information about the properties of bubble motions and deformations.

• Journal of the Korea Computer Graphics Society
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• v.18 no.2
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• pp.9-15
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• 2012

In this paper, we propose a method to segment a color image into several meaningful regions. We suppose that the meaningful region has a set of colors with high frequency in the color image. To find these colors, the color image is represented as several sets of color points in RGB space. And when we use the density of points defined in this method, color belonging to a dense region of color points in RGB space refers to the color that appeared frequently in the image. Eventually, we can find meaningful regions by looking for regions with high density of color points using our level set function in RGB space. However, if a meaningful region does not have a contiguous region of the sufficient size in the image, this is not a meaningful region but meaningless region. Thus, the pixels in the meaningless region are assigned to the biggest meaningful region belonging to its neighboring pixels in the color image. Our method divides the color image into meaningful regions by applying the density of color points to level set function in RGB space. This is different from the existing level set method that is defined only in 2D image.

• Journal of the Society of Naval Architects of Korea
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• v.39 no.3
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• pp.18-27
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• 2002

In order to improve the accuracy of the solution near the boundary in an analysis of viscous flow around an arbitrary boundary which move and be deformed using an Eulerian concept, a level-set based grid deformation method is introduced to concentrate grid points near the boundary. This paper presents a new monitor function which can easily control the level of the concentration of grid points along the boundary. Computations for steady flow around a semi-circular cylinder mounted on the bottom of the flow domain were carried out to check the improvement of the solution using the adaptive grid system with an immersed boundary method. The present numerical results show a good agreement with the solutions obtained by a body fitted grid system and more accurate solutions than those computed with non-adaptive grid system. For the validation of mechanical usefulness of the present method, an expanded analysis of flow around multi-body fixed in the flow domain was carried out. Finally, the present moving adaptive grid method was applied to a two-dimensional bubble rise problem. The computed results show well adapted grid points around the boundary of the bubble at every time and a good agreement with the result calculated by fixed grid system.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.10
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• pp.1223-1228
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• 2011

A moving-coil type linear actuator has been widely used in the system reciprocating short stroke because of its several advantages, such as the structural simplicity, low weight and a fast control response speed. This paper presents a design approach for improving the actuating performance with a clear expression of optimal configuration represented by a level set function. The optimization problem is formulated to minimize the variation of magnetic force at every moving displacement of the mover for fast and easy control. To consider the manufacturability of actuator, the concept of phase-field model is incorporated to control the complexity of structural boundaries. To verify the usefulness of the proposed method, the core design example of cylindrical linear actuator is performed.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.354-359
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• 2007

A new level set based topology optimization employing inner-front creation algorithm is presented. In the conventional level set based topology optimization, the optimum topology strongly depends on the initial level set distribution due to the incapability of inner-front creation during optimization process. In the present work, an inner-front creation algorithm is proposed, in which the sizes, positions, and number of new inner-fronts during the optimization process can be globally and consistently identified. To update the level set function during the optimization process, the least-squares finite element method is employed. As demonstrative examples for the flexibility and usefulness of the proposed method, the level set based topology optimization considering lightweight design of 3D shell structure is carried out.