• Title/Summary/Keyword: local refinement

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Near-tip grid refinement for the effective and reliable natural element crack analysis

  • Cho, J.R.
    • Structural Engineering and Mechanics
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    • v.70 no.3
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    • pp.279-287
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    • 2019
  • This paper intends to introduce a near-tip grid refinement and to explore its usefulness in the crack analysis by the natural element method (NEM). As a sort of local h-refinement in FEM, a NEM grid is locally refined around the crack tip showing the high stress singularity. This local grid refinement is completed in two steps in which grid points are added and Delaunay triangles sharing the crack tip node are divided. A plane-state plate with symmetric edge cracks is simulated to validate the proposed local grid refinement and to examine its usefulness in the crack analysis. The crack analysis is also simulated using a uniform NEM grid for the sake of comparison. The near-tip stress distributions and SIFs that are obtained using a near-tip refined NEM grid are compared with the exact values and those obtained using uniform NEM grid. The convergence rates of global relative error to the total number of grid points between the refined and non-refined NEM grids are also compared.

Spline-Based Finite Element Analysis with T-Spline Local Refinement (T-스플라인 국부세분화를 고려한 스플라인 기반 유한요소해석)

  • Seo, Yu-Deok;Kim, Ki-Seung;Youn, Sung-Kie
    • Proceedings of the KSME Conference
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    • 2007.05a
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    • pp.366-371
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    • 2007
  • In many CAD systems, NURBS has been employed to construct exact geometries. Recently, NURBS finite element analysis methods were proposed by some authors for convenient connection between CAD and finite element analysis. Additional advantages of NURBS FEA, such as exact geometry and no mesh generation, are obtained. However, NURBS is inefficient in local refinement and merging patches. For refinement of local region in interest, additional control points should be inserted into the entire row or column which contains the local region. There is another inefficiency of NURBS during merging patches into a large structure due to propagation of control points. In order to overcome these inefficiencies of NURBS, T-spline was proposed by Sederberg. In this work, T-spline based finite element method is proposed for efficient local refinement and merging patches. At first, accuracy and efficiency of NURBS FEA is verified and efficiency of T-spline FEA is verified by comparing with NURBS FEA.

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Study on the Local Refinement in Spline Finite Element Method by Using Hierarchical B-spline (계층적 B-스플라인을 이용한 스플라인 유한요소법의 국부 세분화에 관한 연구)

  • Hah, Zoo-Hwan;Kim, Hyun-Jung;Youn, Sung-Kie
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.8
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    • pp.1007-1013
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    • 2010
  • A new local refinement scheme for spline finite element method has been proposed; this scheme involves the use of hierarchical B-spline. NURBS has been widely used in CAD; however, the local refinement of NURBS is difficult due to its tensor-product property. In this study, we attempted to use hierarchical B-splines as local refinement strategy in spline FEM. The regions of high gradients are overlapped by hierarchically-created local meshes. Knot vectors and control points in local meshes are extracted from global meshes, and they are refined using specific schemes. Proper compatibility conditions are imposed between global and local meshes. The effectiveness of the proposed method is verified on the basis of numerical results. Further, it is shown that by using a proposed local refinement scheme, the accuracy of the solution can be improved and it could be higher than that of the solution of a conventional spline FEM with relatively lower degrees of freedom.

An edge-based smoothed finite element method for adaptive analysis

  • Chen, L.;Zhang, J.;Zeng, K.Y.;Jiao, P.G.
    • Structural Engineering and Mechanics
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    • v.39 no.6
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    • pp.767-793
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    • 2011
  • An efficient edge-based smoothed finite element method (ES-FEM) has been recently developed for solving solid mechanics problems. The ES-FEM uses triangular elements that can be generated easily for complicated domains. In this paper, the complexity study of the ES-FEM based on triangular elements is conducted in detail, which confirms the ES-FEM produces higher computational efficiency compared to the FEM. Therefore, the ES-FEM offers an excellent platform for adaptive analysis, and this paper presents an efficient adaptive procedure based on the ES-FEM. A smoothing domain based energy (SDE) error estimate is first devised making use of the features of the ES-FEM. The present error estimate differs from the conventional approaches and evaluates error based on smoothing domains used in the ES-FEM. A local refinement technique based on the Delaunay algorithm is then implemented to achieve high efficiency in the mesh refinement. In this refinement technique, each node is assigned a scaling factor to control the local nodal density, and refinement of the neighborhood of a node is accomplished simply by adjusting its scaling factor. Intensive numerical studies, including an actual engineering problem of an automobile part, show that the proposed adaptive procedure is effective and efficient in producing solutions of desired accuracy.

Local Modification of a Surface and Multiple Knot Insertion by Using the Chebyshev Polynormial (Chebyshev 다항식에 기초한 다수개의 절점 삽입과 곡면의 국부 수정)

  • 최성일;김태규;변문현
    • Korean Journal of Computational Design and Engineering
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    • v.3 no.2
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    • pp.103-112
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    • 1998
  • In this paper insertion of numerous control points to be performed by using the Chebyshev polynomial root at the selection of knot vector. This method introduces a simple method of knot refinement and it is applied in a developed program. The Chebyshev roots exist densely in broth ends of the range and are proposed more effective knot refinement to modify a surface. Therefore, generated control points are relatively uniform in specified knot interval. In the surface generation, a local insertion of numerous control points are easily inserted by using the characteristic of Chebyshev polynomial roots at knot refinement. It is possible to create a complex surface with a single surface. The number of control point can be reduced by using the local insertion of control points in a required shape

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A Near-tip Grid Refinement for the Effective and Reliable Crack Analysis by Natural Element Method (효율적이고 신뢰성있는 자연요소 균열해석을 위한 균열선단 그리드 세분화기법)

  • Cho, Jin-Rae
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.32 no.3
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    • pp.183-190
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    • 2019
  • This paper introduces a near-tip grid refinement and explores its usefulness in the crack analysis by the natural element method(NEM). As a sort of local h-refinement in finite element method(FEM), a NEM grid is locally refined around the crack tip showing high stress singularity. This local grid refinement is completed in two steps in which grid points are added and Delaunay triangles sharing the crack tip node are divided. A plane strain rectangular plate with symmetric edge cracks is simulated to validate the proposed local grid refinement and to examine its usefulness in the crack analysis. The crack analysis is also simulated using a uniform NEM grid for comparison. Unlike the uniform grid, the refined grid provides near-tip stress distributions similar to the analytic solutions and the fine grid. In addition, the refined grid shows higher convergence than the uniform grid, the global relative error to the total number of grid points.

Polygonal finite element modeling of crack propagation via automatic adaptive mesh refinement

  • Shahrezaei, M.;Moslemi, H.
    • Structural Engineering and Mechanics
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    • v.75 no.6
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    • pp.685-699
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    • 2020
  • Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz-Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.

Image Retrieval Using Histogram Refinement Based on Local Color Difference (지역 색차 기반의 히스토그램 정교화에 의한 영상 검색)

  • Kim, Min-KI
    • Journal of Korea Multimedia Society
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    • v.18 no.12
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    • pp.1453-1461
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    • 2015
  • Since digital images and videos are rapidly increasing in the internet with the spread of mobile computers and smartphones, research on image retrieval has gained tremendous momentum. Color, shape, and texture are major features used in image retrieval. Especially, color information has been widely used in image retrieval, because it is robust in translation, rotation, and a small change of camera view. This paper proposes a new method for histogram refinement based on local color difference. Firstly, the proposed method converts a RGB color image into a HSV color image. Secondly, it reduces the size of color space from 2563 to 32. It classifies pixels in the 32-color image into three groups according to the color difference between a central pixel and its neighbors in a 3x3 local region. Finally, it makes a color difference vector(CDV) representing three refined color histograms, then image retrieval is performed by the CDV matching. The experimental results using public image database show that the proposed method has higher retrieval accuracy than other conventional ones. They also show that the proposed method can be effectively applied to search low resolution images such as thumbnail images.

Adaptive nodal generation with the element-free Galerkin method

  • Chung, Heung-Jin;Lee, Gye-Hee;Choi, Chang-Koon
    • Structural Engineering and Mechanics
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    • v.10 no.6
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    • pp.635-650
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    • 2000
  • In this paper, the adaptive nodal generation procedure based on the estimated local and global error in the element-free Galerkin (EFG) method is proposed. To investigate the possibility of h-type adaptivity of EFG method, a simple nodal refinement scheme is used. By adding new node along the background cell that is used in numerical integration, both of the local and global errors can be controlled adaptively. These errors are estimated by calculating the difference between the values of the projected stresses and original EFG stresses. The ultimate goal of this study is to develop the reliable nodal generator based on the local and global errors that is estimated posteriori. To evaluate the performance of proposed adaptive procedure, the convergence behavior is investigated for several examples.

Adaptive Mesh h-Refinement using Compatible Transition Elements in Plate Bending Problems (평판휨 문제에서 적합변이요소를 이용한 적응적 체눈 h-세분화)

  • 최창근;박용명
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1990.10a
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    • pp.9-15
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    • 1990
  • In this study, an adaptive mesh h-refinement procedure was presented in plate bending problems. By introducing the transition elements for the procedure, same drawbacks due to the irregular nodes are eliminated which are generated in the consequence of local mesh refinement in common adaptive h-version performed by single type of quadrilateral elements. For the above objective, compatible 5-node through 7-node transition plate bending elements are developed by including variable number of midside nodes. Using the Zienkiewicn-Zhu error estimator, some numerical examples are presented to show the effectiveness of the adaptive h-refinement using the transition elements.

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