• Structural Engineering and Mechanics
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• 제74권4호
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• pp.547-557
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• 2020

In this paper, an automatic adaptive mesh refinement procedure is presented for two-dimensional problems on the basis of a new probabilistic error estimator. First-order perturbation theory is employed to determine the lower and upper bounds of the structural displacements and stresses considering uncertainties in geometric sizes, material properties and loading conditions. A new probabilistic error estimator is proposed to reduce the mesh dependency of the responses dispersion. The suggested error estimator neglects the refinement at the critical points with stress concentration. Therefore, the proposed strategy is combined with the classic adaptive mesh refinement to achieve an optimal mesh refined properly in regions with either high gradients or high dispersion of the responses. Several numerical examples are illustrated to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm and the results are compared with the classic adaptive mesh refinement strategy described in the literature.

• Structural Engineering and Mechanics
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• 제59권5호
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• pp.901-920
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• 2016

MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.

• Structural Engineering and Mechanics
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• 제17권3_4호
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• pp.379-391
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• 2004

This paper deals with the development of h-version adaptive mesh refinement and recovery strategy using variable-node elements and its application to various engineering field problems with 2D quadrilateral and 3D hexahedral models. The variable-node elements which have variable mid-side nodes on edges or faces are effectively used in overcoming some problems in connecting the different layer patterns of the transition zone between the refined and coarse mesh. A modified recovery technique of gradients adequate for variable-node elements and proper selection of error norms for each engineering field problems are proposed. In the region in which the error is greater than the permissible refinement error, the mesh is locally refined by subdivision. Reversely, in some parts of the domain having the error smaller than the permissible recovery error, the mesh is locally recovered (coarsened) by combination. Hierarchical structures (e.g. quadtrees and octrees) and element-based storage structures are composed to perform this adaptive process of refinement and recovery. Some numerical examples of a 3D heat conduction analysis of the concrete with hydration heat and a 2D flow analysis of vortex shedding show effectiveness and validity of the proposed scheme.

• 한국전산구조공학회논문집
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• 제23권3호
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• pp.331-340
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• 2010

적응적 hp-세분화 기법과 그 기법의 효과적인 구성방법을 포함한 새로운 적응적 유한요소 알고리즘의 기초이론 및 적용이 이 연구를 통해 제시되었다. 적응적 hp-세분화 기초의 유한요소기법은 적분형 르장드르 형상함수와 요소별로 불균등한차수의 분배 및 비정형적인 절점연결과 관련된 연속조건을 만족시킬 수 있는 제약조건을 필요로 한다. 따라서 요소간의 접합부분에서 적응적 hp-유한요소망의 연속성이 중요한 문제로 대두된다. 이러한 문제를 요소경계에 연속성 제약조건을 절점연결 사상행렬을 적용하여 해결하였다. 또한, 적분형 르장드르 형상함수의 계층성질을 이용하여 제시된 알고리즘의 효율적 정식화 방안을 제시하였다. 간단한 캔틸레버문제가 h-세분화, p-세분화 그리고 hp-세분화 방법에 의해 계산되었다. hp-세분화의 결과는 다른 방식의 세분화에 비해 보다 빠른 수렴성을 보여 주는 것이 확인되었다. 그러므로 제시된 hp-세분화 알고리즘은 실제문제에 효율적으로 적용될 수 있을 것으로 생각된다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.481-486
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• 2007

The Zienkiewicz-Zhu(Z/Z) error estimate is slightly modified for the hierarchical p-refinement, and is then applied to L-shaped plates subjected to bending to demonstrate its effectiveness. An adaptive procedure in finite element analysis is presented by p-refinement of meshes in conjunction with a posteriori error estimator that is based on the superconvergent patch recovery(SPR) technique. The modified Z/Z error estimate p-refinement is different from the conventional approach because the high order shape functions based on integrals of Legendre polynomials are used to interpolate displacements within an element, on the other hand, the same order of basis function based on Pascal's triangle tree is also used to interpolate recovered stresses. The least-square method is used to fit a polynomial to the stresses computed at the sampling points. The strategy of finding a nearly optimal distribution of polynomial degrees on a fixed finite element mesh is discussed such that a particular element has to be refined automatically to obtain an acceptable level of accuracy by increasing p-levels non-uniformly or selectively. It is noted that the error decreases rapidly with an increase in the number of degrees of freedom and the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• 한국정보과학회논문지:데이타베이스
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• 제30권3호
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• pp.286-295
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• 2003

공간 선택 질의에 사용되는 질의 윈도우로는 직사각형이 주로 사용된다. 하지만, 공간 선택 질의의 윈도우로는 직사각형이 아닌 일반적인 다각형 모양도 가능하며, 최근에는 GIS 등과 같은 응용 프로그램들이 성능 향상으로 인해 보다 많은 공간 데이터를 다룰 수 있게 됨에 따라, 여러 다양한 종류의 응용도 많이 등장하고 있다. 따라서, 직사각형뿐만 아니라 임의의 다각형 형태의 질의 윈도우에도 적합한 정제 단계 수행 전략에 대해 고려해 볼 필요가 있다. 이러한 전략으로는 기존의 공간 조인에서와 같이 plane-sweep 알고리즘을 이용하는 방법이 일반적이다. 하지만, 공간 데이터와 질의 윈도우의 특성을 관찰해보면, 일반적으로 질의 윈도우가 공간 데이터보다 훨씬 간단한 모양으로 구성되어 있음을 알 수 있으므로, 본 논문에서는 이러한 상황에 보다 적합한 정제 단계 수행 방법을 제시하고 있다. 실험을 통해 알 수 있듯이, 질의 윈도우를 구성하는 점의 개수가 약 20개 이하인 일반적인 경우에는, 본 논문에서 제시하는 새로운 방법이 기존의 방법보다 20% 정도 향상된 성능을 보이고 있다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년도 학술대회
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• pp.334-336
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• 2008

A novel adaptive mesh refinement (AMR) strategy based on the Moment-of-Fluid (MOF) method for volume-tracking dynamic interface computation is presented. The Moment-of-Fluid method is a new interface reconstruction and volume advection method using volume fraction as well as material centroid. The mesh refinement is performed based on the error indicator, the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process. Using the AMR-MOF method, the accuracy of volume-tracking computation with evolving interfaces is improved significantly compared to other published results.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2008년 추계학술대회논문집
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• pp.334-336
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• 2008

A novel adaptive mesh refinement (AMR) strategy based on the Moment-of-Fluid (MOF) method for volume-tracking dynamic interface computation is presented. The Moment-of-Fluid method is a new interface reconstruction and volume advection method using volume fraction as well as material centroid. The mesh refinement is performed based on the error indicator, the deviation of the actual centroid obtained by interface reconstruction from the reference centroid given by moment advection process. Using the AMR-MOF method, the accuracy of volume-tracking computation with evolving interfaces is improved significantly compared to other published results.

• 한국전산유체공학회지
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• 제14권1호
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• pp.18-23
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• 2009

A novel adaptive mesh refinement(AMR) strategy based on the Moment-of-Fluid(MOF) method for volume-tracking dynamic interface computation is presented. The Moment-of-Fluid method is a new interface reconstruction and volume advection method using volume fraction as well as material centroid. The adaptive mesh refinement is performed based on the error indicator, the deviation of the actual centroid obtained by interface reconstruction from the reference centroids given by moment advection process. Using the AMR-MOF method, the accuracy of volume-tracking computation with evolving interfaces is improved significantly compared to other published results.

• 대한기계학회논문집A
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• 제34권8호
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• pp.1007-1013
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• 2010

본 연구에서는 NURBS 의 국부 세분화 방법 중 하나인 계층적 B-스플라인을 이용해 스플라인 유한요소법의 국부 세분화를 수행하는 방법을 제안한다. 세분화가 필요한 영역에 전역 격자로부터 계층적으로 생성된 국소 격자를 중첩시켜 국부 세분화를 수행한다. 국소 격자의 매듭 벡터와 제어점은 전역 격자로부터 추출된 후 세분화 되는 과정을 거친다. 생성된 국소 격자에 적절한 연속성 조건을 부여 함으로써 전역 격자와 국소 격자의 연속성을 유지 한다. 제안된 방법을 이용해 수치 예제의 해석을 수행하였다. 이를 통해 기존 NURBS 기반 스플라인 유한요소법에 비해 제안된 방법의 효율성을 검증하였다.