• 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.

• 대한토목학회논문집
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• 제13권5호
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• pp.29-37
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• 1993

본 논문은 추계론적 유한요소해석의 한 방법인 가중적분법의 확장에 대해서 논하였다. 가중적분법의 사용은 Deodatis에 의해서 삼각형요소로 확장되었다. 이에 의해서 2차원 문제에 대한 응답변화도를 수치적인 해석에 의해서 얻을 수 있게 되었다. 본 논문에서는 가중적분법을 일반 평면요소를 사용할 수 있도록 확장한다. 제안된 방법에 의해서 확정론적 유한요소해석에서 사용된 요소망은 추계론적 유한요소해석에서도 그대로 사용할 수 있도록 되었다. 나아가서, CST요소는 상수만을 그 요소로 가지는 변위-변형률 행렬을 가지는 특수한 경우이므로 제안된 방법을 사용할 경우 CST요소와 일반 평면 사변형 요소를 혼용하여 사용할 수 있을 것이다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.351-356
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• 2000

Various transition elements are generally used for the effective analysis of a complicated mechanical structure. In this paper, a solid-to-beam transition finite element which connects a continuum element and a $c^1-continuity$ beam element each other is proposed. The shape functions of the transition finite elements, which a 8-noded hexahedral solid element fur 3D analysis and a 4-noded quadrilateral plane element fur 2D analysis are connected to a Euler's beam element, are explicitely formulated. In order to show the effectiveness and convergence characteristics of the proposed transition elements. numerical tests are performed for various examples and their results are compared with those obtained by other methods. As the result of this study. following conclusions are obtained: (1)The proposed transition finite elements show the monotonic convergence characteristics because of having used the compatible displacement folds. (2)As being used the transition element in the finite element analysis, the finite element modelings are more convenient and the analysis results are more accurate because of the formulation characteristies of the Euler's beam element.

• Structural Engineering and Mechanics
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• 제26권1호
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• pp.69-86
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• 2007

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

• 대한기계학회논문집A
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• 제24권9호
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• pp.2292-2301
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• 2000

We propose an accurate and efficient estimation method of transverse shear stresses for analysis and design of laminated composite structures by 4-node quadrilateral degenerated shell elements. To get proper distributions of transverse shear stresses in each layer, we use 3-dimensional equilibrium equations instead of constitutive equations with shear correction factors which vary diversely according to the shapes of shell sections. Three dimensional equilibrium equations are integrated through the thickness direction with complete polynomial membrane stress fields, which are recovered by REP (Recovery by Equilibrium in Patches) recovery method. The 4-node quadrilateral degenerated shell element used in this paper has drilling degrees of freedom and shear stresses derived from assumed strain fields that are set up at natural coordinate systems. The numerical results demonstrate that the proposed estimation method attains reasonable accuracy and efficiency compared with other methods and FE analysis using 4-node degenerated shell elements.

• Structural Engineering and Mechanics
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• 제25권2호
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• pp.269-273
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• 2007

• 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.

• 전산구조공학
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• 제8권4호
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• pp.189-198
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• 1995

비압축성 물체를 위한 일반적인 유한요소 공식화는 흔히 사용되는 사각형요소에서조차 압력해의 진동화(oscillations) 또는 pressure modes 현상을 나타낸다. 압력해의 안정화를 위한 규준은 소위 Babuska-Brezzi 안정조건이며, 위의 요소들은 이 조건을 만족시키지 못한다. 본 연구에서는 선형변위해와 상수값의 압력해를 갖는 사각형요소 사용시 압력해를 안정화시키기 위해 요소의 변에서 발생하는 불연속압에 근거한 압력연속여분치를 사용한다. 이 압력여분치를 비압축성 탄성론으로부터 유도되는 Q1P0요소에 적용하며 매개변수의 변화에 따른 수치해의 안정화의 정도를 연구한다. 압력해는 압력 여분치 사용시 안정화될 수 있으며, 해의 안정화는 매개변수에 민감성을 나타내었다.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.623-637
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• 1999

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

• 대한기계학회논문집A
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• 제35권9호
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• pp.1091-1097
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• 2011

SGBEM-FEM 교호법은 유한 물체 내에 존재하는 삼차원 균열을 해석하는 유용한 방법으로 알려져 있다. 이 방법으로 일반적인 평면 혹은 비평면 삼차원 균열에 대한 정확한 응력강도계수를 구할 수 있다. 기존의 방법에서는 균열을 모델화 하는데 8 절점 사각형 경계요소를 사용한다. 그러나 임의 형상의 균열의 경우는 3 절점 삼각형 요소를 사용하여 균열을 모델화 하는 것이 더 편리하다. 따라서 본 논문에서는 3 절점 삼각형 요소와 7 절점 사각형 요소를 사용하여 전진 프런트 법으로 균열을 모델링 하였다. 사용된 균열 모델의 정확성을 검토하기 위하여 몇 가지 형상의 균열에 대하여 응력강도계수를 구하여 기존의 해와 비교하였다.