• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.2
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• pp.135-144
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• 2009

In this present work, spline FEA for the trimmed NURBS surface of the 2D linear elasticity problem is presented. The main benefit of the proposed method is that no additional efforts for modeling of trimmed NURBS surfaces are needed and the information of the trimming curves and trimmed surfaces exported from the CAD system can be directly used for analysis. For this, trimmed elements are searched by using NURBS projection scheme. The integration of the trimmed elements is performed by using the NURBS-enhanced integration scheme. The formulation of constructing stiffness matrix of trimmed elements is presented. In this formulation, the information of the trimming curve is used for calculating the Jacobian as well as for obtaining integration points. The robustness and effectiveness of the proposed method are investigated through various numerical examples.

• Journal of Mechanical Science and Technology
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• v.15 no.5
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• pp.592-601
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• 2001

An automatic mesh generation scheme with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed. In this paper NURBS surface geometries in the IGES format have been employed to represent geometric models. For unstructured mesh generation with quadrilateral elements, a domain decomposition algorithm employing loop operators has been modified. As for the surface meshing, an indirect 2D approach is proposed in which both quasi-expanded planes and projection planes are employed. Sampled meshes for complex models are presented to demonstrate the robustness of the algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.794-801
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• 2006

The linkage framework of geometric modeling and analysis based on the NURBS technology is developed in this study. The NURBS surfaces are generated by interpolating the given set of data points or by extracting the necessary information to construct the NURBS surface from the IGES format file which is generated by the commercial CAD systems in the present study. Numerical examples shows the rate of displacement convergence according to the paramterization methods of the NURBS surface. NURBS can generate quadric surfaces in an exact manner. It is the one of the advantages of the NURBS. A trimmed NURBS surface that is often encountered in the modeling process of the CAD systems is also presented in the present study. The performance of the developed geometrically exact shell element integrated with the exact geometric representations by the NURBS equation is compared to those of the previous reported FE shell elements in the selected benchmark problems.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.105-112
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• 2007

The linkage framework of geometric modeling based on NURBS(Non-Uniform Rational B-Spline) surface and shell finite analysis is developed in the present study. For this purpose, geometrically exact shell finite element is implemented. NURBS technology is employed to obtain the exact geometric quantities for the analysis. Especially, because NURBS is the most powerful and wide-spread method to represent general surfaces in the field of computer graphics and CAD(Computer Aided Design) industry, the direct computation of surface geometric quantities from the NURBS surface equation without approximation shows great potential for the integration between geometrically exact shell finite element and geometric modeling in the CAD systems. Some numerical examples are given to verify the performance and accuracy of the developed linkage framework. In additions, trimmed surfaces with some cutouts are considered for more practical applications.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.894-899
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• 2000

An automatic mesh generation system with unstructured quadrilateral elements on trimmed NURBS surfaces has been developed.. In this paper, NURBS surface geometries in the IGES format have been used to represent model shape. NURBS surface is represented as parametric surface. So each surface could be mapped to a 2D parametric plane through the parametric domain. And then meshes with quadrilateral elements are constructed in this plane. Finally, the constructed meshes are mapped back to the original 3D surface through the parametric domain. In this paper, projection plane, quasi-expanded plane and parametric Plane are used as 2D mesh generation plane. For mapping 3D surface to parametric domain, Newton-Rhapson Method is employed. For unstructured mesh generation with quadrilateral elements on 2D plane, a domain decomposition algorithm using loop operators has been employed. Sample meshes are represented to demonstrate the effectiveness of the proposed algorithm.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2009.04a
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• pp.63-66
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• 2009

본 논문에서는 트림영역이 있는 NURBS 평면을 등기하 해석할 수 있는 방법을 제시한다. 기존 등기하 해석법으로 트림 NURBS 곡면을 해석하기 위해서는 해석 도메인이 여러 개의 사각형 패치로 분할되어있어야 한다. 그러나 본 연구에서 제안한 방법은 CAD에서 제공하는 트림곡선의 정보를 해석에 직접 사용할 수 있기 때문에 CAD 모델을 별도로 재구성해야하는 번거로움이 없다. NURBS 곡선 투영법을 이용하여 트림되는 요소를 찾고, 트림된 요소는 쿼드트리 분할법과 NEFEM에서 사용된 적분방법을 동시에 고려하면 어떤 경우의 트림 요소라도 적분이 가능하다. 다양한 수치 예제를 통하여 제안한 해석 방법을 검증하고, 기존의 등기하해석법으로 해석하기 어려운 다수의 트림영역이 존재하는 NURBS 평면을 해석하여 본 방법의 유용성을 검토한다.

• Korean Journal of Computational Design and Engineering
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• v.2 no.3
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• pp.133-141
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• 1997

In the process of car body design, various surfaces are generated from the given boundary curves. Depending upon the method of the surface generation and the quality of the boundary curves provided, the resulting surfaces may have global or local irregularities in many cases. Thus it would be necessary for the designer to evaluate the surface quality and to modify the surface or to use the different generation method based on the evaluation results. This capability is very important because the defect of the surface quality detected in the production stage will require the rework of the dies and will cause a big loss in cost and time. A method of surface interrogation using reflection line is introduced. In this paper, We applied reflection mapping to generate reflection lines on the trimmed NURBS surface. Since reflection lines are obtained from reflection mapping that uses simple and physically acceptable mapping algorithm, they can be efficiently used to simulate the reflection test on the real part in the production line.

• Journal of Mechanical Science and Technology
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• v.15 no.2
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• pp.160-171
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• 2001

Depending upon the method of the surface generation and the quality of the designed boundary curves, the resulting surfaces may have global or local irregularities in many cases. Thus, it would be necessary for the designer to evaluate the surface quality and to modify the surface. This is very important because the defect of the surface causes the rework of the dies, increasing cost and delivery time significantly. To simulate the reflection line test in the actual production line, a faster algorithm for generating reflection lines is presented. In this paper, among various surface interrogation methods using reflection lines, Blinn-Newell type of reflection mapping is applied to generate the reflection lines on the trimmed NURBS surfaces. The derivation of reflection lines is formulated as a surface-plane intersection problem (Jung 1994) and is solved by surface-contouring techniques. Also, for eliminating the discontinuity of reflection lines due to the configuration of reflection map, a modified reflection map is proposed. An efficient traced contouring technique is utilized for the computational efficiency and proves to be well suited for the real-time quality-assessment task.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.1 s.173
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• pp.173-181
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• 2000

Depending upon the method of the surface generation and the quality of the boundary curves provided, the resulting surfaces may have global or local irregularities in many cases. Thus it would be necessary for the designer to evaluate the surface quality and to modify the surface. This capability is very important because the defect of the surface requires the rework of the dies that causes a big loss in cost and delivery time. To simulate the reflection line test in the actual production line, a faster generation algorithm is presented. Among., various surface interrogation methods using reflection lines, Blinn-Newell type of reflection mapping is applied to generate reflection lines on the trimmed NURBS surface. The generation of reflection lines is formulated as a surface-plane intersection problem, and solved by surface-contouring techniques. In addition, a modified reflection map is proposed to eliminate the discontinuity of reflection lines due to the configuration of the reflection map. A fast reflection line algorithm is developed utilizing an efficient traced contouring technique, and proved to be well suited for real-time quality-assessment task.