• Journal of Ocean Engineering and Technology
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• v.13 no.1 s.31
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• pp.39-50
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• 1999

특이 가중함수로 표현된 shepard interpolant와 일관조건을 사용하여 무요소법 형성함수를 도출하였다. 따라서 통상의 EFGM(Element Free Galerkin Method)과는 달리 변위로 주어지는 경계조건을 자연스럽게 부과할 수 있다. 수치계산 예로서 외팔보 문제를 다루었는데 보이론과 비교하여 매우 잘 맞는 결과를 보여주고, 유한요소법과의 결합도 자연스럽게 이루어짐을 보인다. 또 penny-shaped 균열을 다루는데, 응력확대계수는 균열 표면의 변위로부처 직접 계산하여 해석해와 비교한다.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.697-700
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• 2011

본 논문에서는 X-FEM을 사용하여 혼합모드 하중 상태에서의 이차원 선형탄성체의 균열문제에 대한 형상 설계민감도 해석을 수행하였다. X-FEM이란 균열과 같은 특수한 해를 근사하는 방법으로써, 확장함수를 도입하여 FEM의 한계를 극복하는 방법론이다. X-FEM 하에서 해를 근사하는 데 쓰이는 확장함수들은 불연속성과 특이성을 포함하고 있어 물리적 영역에 의존한다. 이는 설계민감도 해석을 수행하는 과정에서 그러한 의존성을 고려해주는 것이 필요하다. 따라서 본 논문에서는 X-FEM 기반의 형상 설계민감도 해석해를 제안하고자 한다. 식의 유도는 전 미분 공식에 기초하고 있으며, 형상함수의 설계변분에 대한 의존성에 관한 항을 추가시켰다. 또한, 균열 주위의 국부적인 공간에서의 확장된 자유도에 설계속도를 가한다. 이에 대한 몇 가지 수치 예제를 통하여 개발된 방법론의 타당성을 확인하였다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.3
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• pp.295-300
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• 1985

본 논문에서는 Dhir의 이론에 따라서 Mapping함수로 고차다항식을 사용하여 여러가지 하중상태에 따른 최적형상을 연구하고 Mapping함수에 포함되어 있는 계수가 응력집중 및 형상변화에 미치는 영향을 검토하며 광탄성 실험을 통하여 이론의 타당성 을 입증하고자 하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.223-231
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• 2019

A continuum-based design sensitivity analysis(DSA) method is developed for electrostatic problems. To consider high order objective functions, we use 9-node finite element basis functions for analysis and DSA methods. As the design variables are parameterized with B-spline functions, smooth boundary variations are naturally obtained. To solve mesh entanglement problems during the optimization process, a mesh regularization scheme is employed. By minimizing the Dirichlet energy functional, mesh uniformity can be automatically achieved. In numerical examples for maximizing dielectrophoresis forces, the numerical results are compared with well-known electrode geometries and the obtained characteristics are discussed.

• Journal of Korean Ophthalmic Optics Society
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• v.16 no.4
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• pp.439-444
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• 2011

Purpose: To represent the shape of toric corea in the elliptical function for the determination of curvature distribution and lacrimal thickness between cornea and contact lens when the lens is fitted. Methods: Topography measurements of corneal curvature and curvature equation derived from the assumed elliptical function were evaluated using the Excel program which included the necessary equation derived. Results: Mathematical expressions for the cornea whose ribbon shaped-topography image, in which the center does not coincide with the corneal apex, can be determined. Conclusions: For the application where the higher accuracy on the cornea is not required, such as higher order aberration, the cornea cal be expressed in the simple elliptical function.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.04a
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• pp.573-578
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfies the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfies the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beam.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.591-598
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• 2009

Starting from the rotating beam finite element in which the interpolating shape functions satisfy the governing static homogeneous differential equation of Euler-Bernoulli rotating beams, we derived new shape functions that satisfy the governing differential equation which contains the terms of hub radius and setting angle. The shape functions are rational functions which depend on hub radius, setting angle, rotational speed and element position. Numerical results for uniform and tapered cantilever beams with and without hub radius and setting angle are compared with the available results. It is shown that the present element offers an accurate method for solving the free vibration problems of rotating beams.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.18 no.2
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• pp.103-111
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• 2005

In this paper, a new meshfree technique which improves the numerical integration accuracy is introduced. This new method called thc Petrov-Galerkin natural clement method(PG-NEM) by authors is based on the Voronoi diagram and the Delaunay triangulation which is based on the same concept used lot conventional natural clement method called the Bubnov-Galerkin natural element method(BG-NEM). But, unlike the BG-NEM, the test basis function is differently chosen, based on the concept of Petrov-Galerkin, such that its support coincides exactly with a regular integration region in background mesh. Therefore, it is expected that the proposed technique ensures the remarkably improved numerical integration accuracy in comparison with the BG-NEM.

• 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.20 no.3
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• pp.311-319
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate, hollow cylinder and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.