• 대한기계학회논문집
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• 제18권11호
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• pp.2932-2943
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• 1994

An efficient approach to the automatic construction of effective quadrilateral finite element meshes for two-dimensional analysis is presented. The procedure is composed of, firstly, an initial mesh generation and, secondly, an h-version of adaptive refinement based on error analysis. As for an initial mesh generation scheme, a modified looping algorithm has been employed. For the adaptive refinement process, an error indicator obtained by computing the residual error of the equilibrium equations in the energy norm with a relaxation factor has been employed. Examples of mesh generation and self-adaptive mesh improvements are given. These example solutions demonstrate that an effective mesh for a given error tolerance can be obtained in a few steps of the analysis processes.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1990년도 가을 학술발표회 논문집
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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.

• 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.

• Structural Engineering and Mechanics
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• 제75권6호
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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.

• Structural Engineering and Mechanics
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• 제11권4호
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• pp.443-460
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• 2001

This paper presents an effective application of a variable-node axisymmetric solid element designated as AQV (Axisymmetric Quadrilateral Variable-node element). The variable-node element with physical midside nodes helps to overcome some problems in connecting the different layer patterns on a quadrilateral mesh in the adaptive h-refinement. This element alleviates the necessity of imposing displacement constraints on irregular (hanging) nodes in order to enforce the inter-element compatibility. Therefore, the elements with variable mid-side nodes can be used effectively in the local mesh refinement for the axisymmetric structures which have stress concentrations. A modified Gaussian quadrature should be adopted to evaluate the stiffness matrices of the variable-node elements mainly because of the slope discontinuity of assumed displacement within the elements. Some numerical examples show the usefulness of variable-node axisymmetric elements in the practical application.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회A
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• pp.632-635
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• 2007

Automobile tire has very complicated shape and is composed of rubber, steel cord and ply cord, Tread pattern of tire is very essential for the basic characteristics of tire, such as braking, acceleration and comfortableness. Tire components such as tread, sidewall, and spex are prepared by forcing uncured rubber compound through an extruder to shape during curing process. Because of its complexity of shape, adaptive mesh refinement was used for the analysis of tire tread. Effects of forming variables were evaluated.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2010년 춘계학술대회논문집
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• pp.534-541
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• 2010

A high-order accurate Euler flow solver based on a discontinuous Galerkin method has been developed for the numerical simulation of unsteady flows on unstructured meshes. A multi-level solution-adaptive mesh refinement/coarsening technique was adopted to enhance the resolution of numerical solutions efficiently by increasing mesh density in the high-gradient region. An acoustic wave scattering problem was investigated to assess the accuracy of the present discontinuous Galerkin solver, and a supersonic flow in a wind tunnel with a forward facing step was simulated by using the adaptive mesh refinement technique. It was shown that the present discontinuous Galerkin flow solver can capture unsteady flows including the propagation and scattering of the acoustic waves as well as the strong shock waves.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.271-274
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• 2007

The finite element linear buckling analysis of folded plate structures using adaptive h-refinement methods is presented in this paper. The variable-node flat shell element used in this study possesses the drilling D.O.F. which, in addition to improvement of the element behavior, permits an easy connection to other elements with six degrees of freedom per node. The Box-typed structures can be analyzed using these developed flat shell elements. By introducing the variable node elements some difficulties associated with connecting the different layer patterns, which are common in the adaptive h-refinement on quadrilateral mesh, can be overcome. To obtain better stress field for the error estimation, the super-convergent patch recovery is used. The convergent buckling modes and the critical loads associated with these modes can be obtained.