• 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.

• 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.

• 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.

• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.125-150
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• 2013

This paper intends to present an application of isogeometric analysis in crack problems. An isogeometric formula is developed based on NURBS basis functions - enriched and adopted via X-FEM enrichment functions. The proposed method which is represented by the combination of the two above-mentioned methods, first by using NURBS functions models the geometry exactly and then by defining level set function on domain, identifies available discontinuity in elements. Additional DOFs are allocated to elements containing the crack and X-FEM enrichment functions enrich approximate solution. Moreover, a subelement refinement technique is used to improve the accuracy of integration by the Gauss quadrature rule. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of the proposed method during calculation of crack parameters.

• 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.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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• pp.339-342
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• 2003

This paper newly proposes a mesh regularization method for the enhancement of the efficiency in sheet metal forming analysis. The regularization method searches for distorted elements with appropriate searching criteria and constructs patches including the elements to be modified. Each patch is then extended to a three-dimensional surface in order to obtain the information of the continuous coordinates. In constructing the surface enclosing each patch, NURBS(Non-Uniform Rational B-Spline) surface is employed to describe a three-dimensional free surface. On the basis of the constructed surface, each node is properly arranged to form unit elements as close as to a square. The analysis results with the proposed method are compared to the results from the direct forming analysis without mesh regularization in order to confirm the validity of the method.

• Transactions of Materials Processing
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• v.12 no.4
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• pp.401-407
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• 2003

This paper newly proposes a mesh regularization method for the enhancement of the efficiency in sheet metal forming analysis. The regularization method searches for distorted elements with appropriate searching criteria and constructs patches including the elements to be modified. Each patch is then extended to a three-dimensional surface in order to obtain the information of the continuous coordinates. In constructing the surface enclosing each patch, NURBS(Non-Uniform Rational B-Spline) surface is employed to describe a three-dimensional free surface. On the basis of the constructed surface, each node is properly arranged to form unit elements as close as to a square. The state variables calculated from its original mesh geometry are mapped into the new mesh geometry for the next stage or incremental step of a forming analysis. The analysis results with the proposed method are compared to the results from the direct forming analysis without mesh regularization in order to confirm the validity of the method.

• Journal of Korea Game Society
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• v.2 no.1
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• pp.62-68
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• 2002

This paper presents a method for tessellating trimmed NURBS surface with preserving sharp shape Although several existing approaches need a large number of triangular meshes to represent sharp shape of surface, resulting triangular meshes may not reflect sharp edges properly. In this study, we flit detect the sharp shape of NURBS surface automatically using C1 continuous condition and then use constraint Delaunay triangulation method to present exact sharp shape with the minimum triangular meshes. And we also use approximated developed surface domain as triangulation domain of rimmed NURBS surface. In this way, the shape of triangular elements on the triangular domains is approximately preserved and can avoid distortion when mapped into three-dimensional space. finally, we show examples that demonstrate the effectiveness of the proposed scheme in terms of reducing the number of triangular meshes and preserving sharp shape of surface more exactly.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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• pp.451-460
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• 2007

The surface of 3D shell structure is created by using NURBS and nodes for generating finite element mesh on the surface are created by using external node offset method. In so doing the shortest distance between nodes on the top and bottom surface is searched and then the coordinates of nodes are determined by calculating the mid point of them in the middle of top and bottom surface. Triangular elements are formed on mid surface, and the average aspect ratio of the generated triangular elements are over 0.9.