• 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.

• Transactions of Materials Processing
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• v.15 no.7 s.88
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• pp.512-517
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• 2006

In this paper, the cold extrusion process for internal spline forming using a thin and long tube has been analyzed by using a rigid plastic finite element code. The internal spline consists of 10 tooths. The cold extrusion process has been focused on the comparisions of load-stroke relation and filling states of the teeth according to design parameters. The design parameters involve extrusion ratio, extrusion angle and friction factor. The internal spline forming can cause the buckling and folding during the cold extrusion process because of using a thin and long tube. The optimum design parameters have been obtained through rigid-plastic finite elements analysis. The extrusion ratio and extrusion angle have great effects on the deformation characteristics of the cold extrusion process.

• Journal of Ocean Engineering and Technology
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• v.16 no.4
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• pp.19-24
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• 2002

항만공사같은 대규모의 매립공사에서 토공작업은 총공사비의 상당한 비중을 차지하므로 경제적인 시공을 위하여 절.성토량은 정확하게 계산되어야 한다. 따라서 본 연구는 주어진 3차원 표고데이터를 지나는 스플라인 곡면을 구하는 알고리즘을 제시함으로써 좀더 정확한 토공량 계산식의 결정을 목표로 한다. 스플라인에 대한 흥미로운 수학적 결과는 무척 많지만 본 연구에서는 스플라인 곡면을 기술하고 또, 그것을 이용하여 토공량 계산을 위한 알고리즘개발을 목표로 하기 때문에 알고리즘과 프로그래밍에 필요한 수학적 내용을 기술하며 그 수치적 계산결과는 Maple 프로그램을 이용하였다. 그리고 정확도를 비교하기 위하여 기존의 방법인 선형점고법, Chamber법, Chen과 Lin의 이론을 컴퓨터프로그램하여 본 연구에서 제시된 방법과 정확도를 비교, 분석한다. 아울러 각 이론식의 결과에 대한 보다 정확한 검사를 위하여 x, y 함수식을 이용한 실험지형을 인위적으로 만들었으며 그 때의 값을 기준값으로 하였다. 따라서 실험수치지형에 대한 기준값이 절대값에 가까우므로 각 토공량식들의 오차규명을 보다 명확하고 확실하게 비교할 수 있도록 하였다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.866-871
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• 1994

B-spline curves and surfaces are effective solutions for design and modelling of the freeform models. The control methods of these are using with control points, knot vectors and weight of NURBS. Using control point is easy and resonable for representation of general models. But the movement of control points bring out the reformation of original convex hull. The B-splines with nonuniform knot vector provide good result of the shape modification without convex hull reforming. B-splines are constructed with control points and basis functions. Nonuniform knot vectors effect on the basis functions. And the blending curves describe the prorities of knot vectors. Applying of these, users will forecast of the reformed curves after modifying controllabler primitives.

• The Journal of the Korea Contents Association
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• v.5 no.6
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• pp.97-108
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• 2005

In this paper a method of reconstructing a desired image through the geometrical transformation and the interpolation techniques is presented by comparing different interpolation schemes. Several different interpolation schemes are compared with respect to the amount of error that is the difference between the original and the reverse-projective transformed images. Higher ordered B-spline interpolation turned to be superior to other techniques in reconstructing the image which is desired to be close to the unskewed image as much as possible. In the results, this paper demonstrates that the reverse projection using the higher ordered B-spline interpolation is superior to those conventional interpolation methods, linear, cubic spline for reconstructing image. In experiments, the error decreases as the order of B-spline increases. The proposed technique is useful for various practical and theoretical applications in the area of satellite, medical, and commercial image processing.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.435-438
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• 1997

This paper presents the process generating a SAC(Sectional Area Cure) by using ASMOD(Adaptive Spline Modeling of Observation Data). That is, we define SACs of real ships as B-spline curves by a hybrid cure approximation(which is the combination method of a B-spline fitting method and a genetic algorithm) and accumulate a database of control points. Then we let ASMOD learn from the correlation principal dimensions with control points.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.1-10
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• 2001

In the reverse engineering, surfaces are modeled for new products by interpolating the digitized data points obtained by measuring the existing shapes. However, many measuring or deviation errors are happened during the measuring process. If these errors are ignored, designers could get undesirable results. Therefore, it is important to handle such errors and fairing procedure with the esthetics criteria is needed during surface modeling process. This paper presents algorithms for the fairing of B-spline surfaces. The algorithms are based on automatic repositioning of control points for B-spline surfaces. New positions of the control points are determined by solving a non-linear programming of which the objective functions are derived variously using derived surfaces and constraints are established by distance measures between the original and the modified control points. Changes in surface shapes are analyzed by illustrations of their shapes and continuous plotting of gaussian and mean curvatures.

• Journal of Ship and Ocean Technology
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• v.10 no.1
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• pp.10-26
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• 2006

The radiation problem for oscillating bodies on the free surface has been formulated by the over-determined Green integral equation, where the boundary condition on the free surface is satisfied by adopting the Kelvin-type Green function and the irregular frequencies are removed by placing additional control points on the free surface surrounded by the body. The B-Spline based higher order panel method is then applied to solve the problem numerically. Because both the body geometry and the potential on the body surface are represented by the B-Splines, that is in polynomials of space parameters, the unknown potential can be determined accurately to the order desired above the constant value. In addition, the potential expressed in B-Spline can be differentiated analytically to get the velocity on the surface without introducing any numerical error. Sample computations are performed for a semispherical body and a rectangular box floating on the free surface for six-degrees of freedom motions. The added mass and damping coefficients are compared with those by the already-validated constant panel method of the same formulation showing strikingly good agreements.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.31-45
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• 2006

Recently advanced device and sophisticated manufacture process by high-density, high-integration require critical inspection criteria in SMT(surface mounting technologies). Especially for solder paste which come out over 60% of inferior goods of all product, 3-dimensional inspection replaces 2-D inspection as a effectiveness substitute of this trend. Therefore this paper proposes a fast 3-D inspection system and measurement algorithm automatically inspecting 3-D solder paste of PCB in SMT assembly line. The proposed method generates 3-D surface of data using B-spline algorithm and then extracts to inspect the pad.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.2
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• pp.185-199
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• 1999

본 연구에서는 새로운 spline 유한대판 요소를 제안하였다. 제안된 정식화는 등매개 개념에 의해 기하학적 형상과 변위장을 가정함에 있어 길이방향은 3차의 B-spline 곡선으로, 횡방향에 대해서는 Lagrange 다항식에 의해 표현된다. 이 논문은 평판과 쉘해석에 있어서의 등매개 spline 유한대판 요소의 개선에 목적을 두고 있다. 이 새로운 요소는 스트립의 내부 절점에서 6개의 자유도를 갖는 합-응력 감절점 쉘 요소로부터 유도하였다. 스트립의 기하학적 형상은 강체 회전에 대한 정의에 위배되지 않고도 두께 방향을 따라 Jacobian이 일정하다는 가정을 따랐으며 고체역학에서 정의되는 면내 회전을 penalty 함수에 의한 구속조건으로 간주하여 면내 회전에 관계된 자유도를 생성하였다. 제안된 요소에 대하여 쉘의 전형적인 문제에 대한 수치예제를 보였으며 이 스트립 요소의 성능을 평가하였다.