• Structural Engineering and Mechanics
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• 제15권5호
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• pp.579-608
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• 2003

This paper deals with adaptive finite element analysis of linearly elastic structures using different error estimators based on flux projection (or best guess stress values) and residual methods. Presentations are given on a typical h-type adaptive analysis, a mesh refinement scheme and the coupling of adaptive finite element analysis with automatic mesh generation. Details about different error estimators are provided and their performance, reliability and convergence are studied using six node quadratic triangular elements. Several examples are presented to demonstrate the reliability of different error estimators.

• Structural Engineering and Mechanics
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• 제39권6호
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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.

• 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.

• 한국게임학회 논문지
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• 제9권4호
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• pp.97-106
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• 2009

본 논문은 적응적 메쉬 구조를 이용하여 가상 종이 객체를 실시간에 시뮬레이션 하는 방법을 제안한다. 제안된 기법은 임의의 삼각 메쉬에 적용될 수 있으며, 안정적인 수치 적분과 변형 기반 메쉬 세분화를 이용하여 효율적으로 종이 표면의 주름과 구김을 생성한다. 종이 객체의 구겨짐을 사실적으로 표현하기 위하여 부러지는 스프링을 가진 적응적 메쉬 구조를 사용한다. 적응적 구조가 지속적으로 질점을 삽입 혹은 삭제하기 때문에, 질량과 운동량의 보존이 고려되어야만 사실적인 종이 시뮬레이션이 가능하다. 제안된 기법은 실시간 환경에서 종이와 같이 얇은 쉘 구조의 사실적인 애니메이션을 생성한다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.288-295
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• 2003

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 recovery technique. In case of the recovery technique, the SPR(superconvergent patch recovery) approach has been modified for p-adaptive mesh refinement. 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. To verify the proposed algorithm, the limit value approach is proposed which utilizes the exact strain energy computed from the extrapolation equation. A new pre-processor is developed for the p-version finite element program in which the vector graphic editor is used for the automatic generation of node connection and coordinate by halfedge solid data structure according to uniform or nonuniform p-distribution. The general 2-D algorithm is also developed to generate face modes and internal modes in accordance with different mesh types. The quality of the error estimator is investigated with the help of two mumerical examples. The results show that the sequences of p-distributions obtained by the proposed error indicator closely follow the optimal trajectory.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 2000년도 춘계학술발표대회 논문집
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• pp.80-84
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• 2000

A mesh superposition technique is presented for an efficient analysis of structural behavior. Refined child mesh is superimposed over parent elements for the region of interest. It is a kind of adaptive mesh refinement, which allows locally refined mesh without introducing transition region or multipoint constraints. Proper boundary condition is necessary to avoid redundant rigid body motion and kinematic compatibility between neighbor elements. Delamination buckling analysis is conducted to demonstrate accuracy and efficiency of the present method.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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• pp.87-90
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• 1988

This paper reports a simple posteriori error estimate method for adaptive finite element mesh generation using quadratic shape function especially for the magnetic field problems. The elements of quadratic shape function have more precise solution than those of linear shape function. Therefore, the difference of two solutions gives error quantity. The method uses the magnetic flux density error as a basis for refinement. This estimator is tested on two dimensional problem which has singular points. The estimated error is always under estimated but in same order as exact error, and this method is much simpler and more convenient than other methods. The result shows that the adaptive mesh gives even better rate of convergence in global error than the uniform mesh.

• 대한전기학회논문지
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• 제37권3호
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• pp.141-145
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• 1988

This paper reports a new and simple posteriori error estimate method for adaptive finite element mesh genration especially for the magnetic field problems. To estimate local errors, we consider the interelement boundary conditions. Elements which violate much the conditions are considered to have great errors. Magnetic flux density errors are considered as a basis for refinement. This estimator is tested on two dimensional proplems with singular points. The estimated errors are always under estimated but in same order as exact errors, and this algorithm is much simpler and more convenient than other methods. The adaptive mesh gives much better rate of convergence in global errors than the uniform mesh.

• 한국지진공학회논문집
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• 제23권1호
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• pp.83-88
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• 2019

Structural analysis remains as an essential part of any integrated civil engineering system in today's rapidly changing computing environment. Even with enormous advancements in capabilities of computers and mobile tools, enhancing computational efficiency of algorithms is necessary to meet the changing demands for quick real time response systems. The finite element method is still the most widely used method of computational structural analysis; a robust, reliable and automated finite element structural analysis module is essential in a modern integrated structural engineering system. To be a part of an automated finite element structural analysis, an efficient adaptive mesh generation scheme based on R-H refinement for the mesh and error estimates from representative strain values at Gauss points is described. A coefficient that depends on the shape of element is used to correct overly distorted elements. Two simple case studies show the validity and computational efficiency. The scheme is appropriate for nonlinear and dynamic problems in earthquake engineering which generally require a huge number of iterative computations.

• 한국수자원학회논문집
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• 제44권7호
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• pp.511-522
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• 2011

적응적 메쉬세분화기법과 분할격자기법을 적용한 2차원 천수방정식모형을 활용하여 구조물을 고려한 극한 홍수 실험을 모의하였다. 본 연구에 사용된모형은 두 격자생성 기법을함께 사용함으로서 복잡한 경계를보다 적은 격자로 효율적으로 표현하는 것이 가능하며, 동적 적응 메쉬세분화기법을 사용하여 흐름이 빠르게 변하는 영역에서 정확도를 유지하면서도 효율적으로 계산하는 것이 가능하다. HLLC 리만근사해법과 MUSCL 기법을 적용하여 시공간상에서 2차정도를 유지하며, 댐붕괴파와 같은 불연속적인 흐름을 정확하게 모의할 수 있다. 모형의 검증을 위해 IMPACT 프로젝트에서 수행한 도시지역 극한홍수실험을 모의하였다. 실험결과와 모의결과가 양호하게 일치하는 것을 확인하였으며, 천이류 현상과 함께 구조물에 의한 홍수파 전달 양상이 의미있는 수준으로 모의된 것을 확인하였다. 또한 분할격자기법의 사용으로 모델의 격자 민감도가 향상되었다. 본 모델은 댐붕괴와 같이 내수침수현상이 지배적이지 않은 도시범람을 모의하는데 활용할 수 있을 것으로 기대된다.