• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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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.

• Journal of the Korea Society of Computer and Information
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• v.8 no.1
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• pp.7-12
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• 2003

Because some systems limit the supported maximal degree, the degree reduction of NURBS is necessary in Parametric curves and surfaces of the different geometric modeling systems. Therefore an approximate degree reduction method of NURBS curves was introduced in this research. Also the existing Eck's B$\'{e}$zier degree reduction method and knot removal algorithm were used to reduce data in the degree reduction process. Finally we found that this method was stable, efficient for implementations, and easy to use algorithms.

• Journal of the Korea Computer Graphics Society
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• v.4 no.2
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• pp.47-55
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• 1998

본 논문은 일반화된 원통(generalized cylinder)의 모양을 상호작용을 통해 조절할 수 있도록 하는 직접 제어 방법을 제시한다. 이 연구에서는 일반화된 원통을 단면을 이루는 B-스플라인 곡선이 B-스플라인 동작에 의해서 움직여 지나간 스윕(sweep) 곡면으로 해석한다. 만들어진 곡면은 주어진 단연 곡선들을 골격 곡선을 따라서 보간하는 NURBS 곡면으로 나타내어진다. 사용자가 일반화된 원통 곡면 위의한 점을 움직일 때, 단면의 모양과 해당하는 동작을 수정하여 일반화된 원통의 곡면이 사용자에 의해 움직여진 위치를 지나도록 변형시킨다. 곡면의 변형은 목표 추적 과정을 거쳐 이루어진다. 이 방법에 의해 구현된 시스템을 이용하여 실시간으로 일반화된 원통을 직접 제어를 통해 디자인 할 수 있다.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.3
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• pp.111-122
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• 2000

It is difficult to make shape library for featrue-based modeling because free-form surface is various shaped complicated To make modeling using similar shape feature-based model is easy and fast. Recently RE(Reverse Engineering) technolo-gy is very convenient method to get free-form surface. This study develops surface editor which makes surface modeling to manipulate control points and this study We study on the effective model data management using database system.

• Journal of Ocean Engineering and Technology
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• v.20 no.3 s.70
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• pp.82-87
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• 2006

An approach to model a high-speed monohull vessel is introduced. The high-speed monohull form belonging to the category of multihull is drawing new attention, due to the rapidly growing trend of fast passenger ships and military purpose. Multihull forms are much thinner in their overall shape, compared to those of the conventional commercial vessels. Moreover, the parent hull forms are not readily obtainable when a new design is intended, which makes it hard to perform various technical calculations in terms of hull optimization, hydrodynamic computation, structural design, and so forth. In this paper, a parametric technique is used to design a high-speed hull form. To model a hull form, NURBS (Non Uniform Rational B-Spline) representation is used. The goal of research is to provide a fast and convenient tool to design an initial hull form with fewer parameters available in the early design stage. The technique employed in this paper will be applied to the design of multihull forms, such as catamaran, trimaran, and semi-swath.

• Journal of the Korean Society for Precision Engineering
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• v.15 no.10
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• pp.148-155
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• 1998

For products of various shapes, compound surfaces are used. Blending surfaces are essential to the products of the compound surfaces. In this paper a method of making shape of blending surface flexible with parameter control is discussed. The parameter has quantitative control of shape of the blend. The blending surface is applied to NURBS and simple primitives in solid model. Intersection curves of surfaces is used to provide the blend with generality. Rail curve are found with the intersection curves. The blend is generated by rail curves and parameter control. Also, In strict constraint condition, blending surface with flexible shapes is discussed, keeping ;${GC}^1$ and ;${GC}^2$ continuity between free-formed surfaces and solids. Joining blending ,bridge blending and blending surface at corner are generated.

• Journal of Korean Association for Spatial Structures
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• v.12 no.1
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• pp.77-85
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• 2012

The membrane structure maintains stable form by giving initial tension to ductile membrane and increasing the stiffness of exterior that is much adopted in the large span spatial structure by making its thickness thin. This kind of membrane structure has characteristic that can express free-form curve, so the selection of structural form is very important. So, this paper proposes the expression of free-form surface based on NURBS basis function and the finite element method considering geometrical nonlinearity for the deduction of large deformation result. Also, for minimizing the approximation of the surface that is derived from the form-finding result, the interface method that change finite element mesh to NURBS is proposed. So, the optimum surface of free-form membrane is derived.

• Korean Journal of Computational Design and Engineering
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• v.6 no.2
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• pp.89-100
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• 2001

Swept volume is the sweeping region of moving objects. It is used in various applications such as interference detection in assembly design, visualization of manipulator motions in robotics, simulation of the volume removal by a cutter in NC machining. The shape of swept volume is defined by the envelope, which is determined by the boundary of moving objects and its direction of motion. In order to implement the generation of swept volume, researchers have taken much effort to develop the techniques how to generate the envelope. However, their results are confined to envelope generated only in simple shape objects, such as polyhedra or quadric surfaces. This study provided the envelope generation algorithm of NURBS objects. Characteristic points were obtained by applying the geometric conditions of envelope to NURBS equations, and then characteristic curves were created by means of interpolating those points. Silhouette edges were determined in the following procedures. First, two adjacent surfaces which have the same edge were found from B-Rep data. Then, by taking the scalar product of velocity vector of a point on that edge with each normal vector on two surfaces, silhouette edges were discriminated. Finally, envelope was generated along moving direction in the form of ruled surfaces by using both the partial information between initial and final position of objects affecting envelope along with characteristic curves and silhouette edge. Since this developed algorithm can be applied not only to NURBS objects but also to their Boolean objects, it can be used effectively in various applications.

• Korean Journal of Computational Design and Engineering
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• v.5 no.2
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• pp.144-154
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• 2000

We propose an algorithm for obtaining a triangular approximation of a trimmed NLRBS surface. Triangular approximation is used in the pre-processing step of many applications such as RP(Rapid Prototyping), NC(Numerical Control) and FEA(Finite Element Analysis), etc. The algorithm minimizes the number of triangular elements within tolerance and generates a valid triangular mesh for STL file and NC tool path generation. In the algorithm, a subdivision method is used. Since a patch is a basic element of triangular mesh creation, boundary curves of a patch are divided into line segments and the division of curves is applied for the interior of the surface. That is, boundary curves are subdivided into line segments and two end points of each line segment are propagated to the interior of the surface. For the case of a trimmed surface, triangulation is carried out using a model space information. The algorithm is superior because the number of elements can be controlled as the curvature of the surface varies and it generates the triangular mesh in a trimmed region efficiently. To verify the efficiency, the algorithm was implemented and tested for several 3D objects bounded by NURBS surfaces.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.55-60
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• 2011

In the present work, isogeometric analysis in linear elasticity problem is conducted using the basis functions from NURBS. The objectives of isogeometric analysis introduced is to integrate both geometric modeling(CAD) and computational analysis(CAE), and this can be accomplished from direct usage of geometric modeling by NURBS as the computational mesh. The merit of the isogeometry analysis is that NURBS surface are able to represent exact geometry from the control points and knot vectors, and also subsequent refinement is relatively simple relatively. In order to verify the computer codes developed in this study, it has been applied to two structural models of which geometry are simple ; 1) circular cylinder subjected to the constant internal pressure loading, 2) square plate with circular hole at center subjected to uniform tension. The exact solutions of these two models are available. Convergence of the approximate solutions by the present code for the isogeometry analysis are investigated by mesh refinement with inserting knots (h-refinement) and by mesh refinement with order elevation of the basis functions (p-refinement).