• 한국CDE학회논문집
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• 제4권1호
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• pp.32-42
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• 1999

Approximate lofting or skinning is one of practical surface modeling techniques well used in CAD and reverse engineering applications. Presented in this paper is a method for approximately lofting a given set of curves wihin a specified tolereance. It is based on refitting input curves simultaneously on a common knot vector and interpolating them to get a resultant NURBS surface. A concept of reducing the number of interior knots of the common knot vector is well adopted to acquire more compact representation for the resultant surface. Energy minimization is newly introduced in curve refitting process to stabilize the solution of the fitting problem and get more fair curve. The proposed approximate lofting provides more smooth surface models and realizes more efficient data reduction expecially when the parameterization and compatibility of input curves are not good enough. The method has been successfully implemented in a new CAD/CAM product VX Vision? of Varimetrix Corporation.

• 한국자동차공학회논문집
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• 제6권4호
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• pp.141-150
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• 1998

The measurement of strains in stamped sheet metal is essential to the design and manufacture of sound sheet metal products. The measured strains can also be used in verifying the reliability of the computer analysis such as finite element analysis. In most engineering applications, strains are measured from the deformed square grids or deformed circular grids in comparison with the initial undeformed grids. In such a case, however, strains are averaged in each grid and the localized strain in a region smaller than a grid size can not be measured. In the present study, the B-spline surface interpolation technique is introduced in order to measure the strains more exactly and effectively. The strains calculated by using the surface interpolation technique are compared with the strains calculated from the three-noded grids as well as with the finite element analysis.

• 대한기계학회논문집A
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• 제33권2호
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• pp.127-134
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• 2009

T-splines are recently proposed geometric modeling tools. A T-spline surface is a NURBS surface with T-junctions and is defined by a control grid called T-mesh. Local refinement can be performed very easily for T-splines while it is limited for B-splines or NURBS. Using T-splines, patches with unmatched boundaries can be combined easily without special technique. In this study, the analysis methodology using T-splines is proposed. In this methodology, T-splines are used both for description of geometries and for approximation of solution spaces. Two-dimensional linear elastic and dynamic problems will be solved by employing the proposed T-spline finite element method, and the effectiveness of the current analysis methodology will be verified.

• 대한산업공학회지
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• 제26권2호
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• pp.95-100
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• 2000

Presented in this paper is a scheme for constructing ball rolling blends of a non-uniform B-spline surface(NUBS) patches. Ball rolling blending is a popular technique for blending between parametric surfaces. Along the "common edge" of a pair of "base surfaces" to be blended, a sequence of "ball positions" is sampled. The radius of the ball may vary along the line. At each sampling point, a ball center point and a pair of ball contact points are computed by applying a Jacobian inversion method. Using ball contact points, the constructing scheme of blend NUBS patches consists three steps; 1) determination of intermediate control vertices; 2) determination of boundary vectors; 3) determination of B-spline control vertices. The proposed blending scheme has been tested in a Omega CAM system and found to be working satisfactorily.

• 한국CDE학회논문집
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• 제9권1호
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• pp.1-10
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• 2004

In the process of finite element analysis, mesh generation is tedious job which consumes tremendous time. Therefore, the automation of well shaped mesh generation from the minimal boundary input data is desirable to improve reliability and accuracy of the analysis and also to reduce the process time of the entire design process. The automation of triangular mesh generation has been relatively well treated due to its robustness and ease of handling when compared to rectangular element mesh generation. In this study, the offset method developed previously for generating plane rectangular element mesh has been corrected and modified to generate triangular element mesh on the B-spline surface having arbitrary holes. The result shows that the generated triangular mesh has the average aspect ratio over 0.9. The designed arbitrary surface shape has been interactively constructed by non-uniform B-spline theory for triangular mesh generation.

• 한국정밀공학회지
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• 제13권1호
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• pp.108-115
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• 1996

Forging of trapezoidal spline, serration and square spline with solid cylindrical billets and hollow one has been investigated by means of upper bound method. Kinematically admissible velocity fields for forging of splines have been proposed in this study. The half pitch of spline has been divided into several deformation regions. The neutral surface is introduced into forging of splines with flat punch and, for each step, it is assumed as a circle with its radius $r_n$. Upper bound solutions obtained by proposed kinematically admissible velocity fields are useful to predict the loads for forging of splines.

• Journal of Advanced Marine Engineering and Technology
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• 제21권4호
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• pp.381-386
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• 1997

The offsetting method using geometric properties of B-spline control polygon is more faster than using of general normal vector in offset processing. But this method itself does not solve the prob¬lems of loop removal in normal offsetting. Generally the distance between neighborhood spans of B-spline control polygon is greater than the offset distance, the loops are occurred in offsetting. For generating of the more precision tool-path in NC machining, the loops of offset must be removed. In this paper, two methods for loop removal are introduced in offsetting of B-spline curve. One is using the intersection of B-spline control span which being occurred of the loop. The other is using two B-spline curve divisions divided from original B-spline curve or its offset curve. After the inter¬section point of loop was searched, the loop being removed to cusp. Also the method for filleting of cusp is inspected to more precision cutting. It is shown that the offsetting using B-spline control polygon is more effective in the sculptured surface machining.

• 한국해양공학회지
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• 제22권5호
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• pp.25-30
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• 2008

A B-spline based high order panel method was developed for the motion of bodies in an ideal fluid, either of infinite extent or with a free boundarysurface. In this method, both the geometry and the potential are represented by the B-spline, which guarantees more accurate results than most potential based low order methods. In the present work, we applied this B-spline based high order method to the radiation problem of floating bodies. The boundary condition on the free surface was satisfied by adopting a Kelvin-type Green function and irregular frequencies were removed by placing additional control points on the free surface surrounding the body. The numerical results were validated by comparison with existing numerical and experimental results.

• 한국정밀공학회지
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• 제15권12호
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• pp.81-88
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• 1998

Measurement and inspection of freeform surfaces are required in reverse design processes. In the case of surface measurement using a touch probe, probe radius compensation affects measuring accuracy. But current industrial practice depends upon an operator's experience to compensate for probe radius. In this paper, an on-the-machine measuring and inspection system for freeform surfaces is studied. Probe radius compensation methodology is investigated by modeling of B-spline surfaces based on digitized data. The accuracy and reliability of the developed system is verified through various kinds of numerical simulations and on-the-machine experiments.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.303-310
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• 2001

We propose the framework which directly links shell finite element to the free form surface geometric modeling. For the development of a robust shell element, a first order shear deformable shell theory and partial mixed variational functional are provided. Bubble functions are included in the shape function of displacement to improve the performance of the developed element. The Spline/NURBS is used to generate the general free form of parameterized shell surfaces. The proposed shell finite element model linked with NURBS surface representation provides efficiency for design and analysis. Numerical examples are given in order to assess the accuracy of the performances of the proposed element.