• 대한기계학회논문집
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• 제17권12호
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• pp.3007-3019
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• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.

• 한국전산구조공학회논문집
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• 제12권1호
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• pp.67-74
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• 1999

본 문에서는 선체 중앙부의 유한요소 모델링과 진동해석이 수행되었다. 횡부재와 종통부재가 만나 3차원적으로 연결되어 있는 선체구조는 복잡한 구조적 특성 때문에 모델링에 많은 노력이 필요하다. 선수, 선미부에 비해 비교적 부재간의 접속이 간단한 중앙평행부의 진동해석과 같은 경우에는 모델링 기법을 개발해 사용할 수도 있다. 중앙부 횡부재와 종통부재가 만나는 부분의 접속성과 형상표현을 위해 keypoint, super element(SE) 개념을 도입하였고 형성된 SE 들을 isoparametric mapping 기법을 접속된 3차원 부재용으로 개선하여 유한요소로 분할하였다. 진동해석용으로 형성된 선체중앙부 요소망을 ANSYS로 가시화하였고 자유진동해석을 수행하였다.

• 대한기계학회논문집
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• 제18권2호
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• pp.271-277
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• 1994

The fatigue crack opening behavior is analyzed using finite element method. Because extremely fine mesh subdivision is required when using constant stress constant strain triangular element, this study uses conventional two dimensional eight node isoparametric elements. Since plasitc zone size is similar to crack propagating length per each load cycle because of relatively large element size, a new analysis model that a crack propagates every two load cycle is suggested. the opening load and crack opening displacement can be obtained accurately by this method.

• 대한기계학회논문집A
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• 제22권1호
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• pp.206-214
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• 1998

When a crack meets bimaterial interface stress singularity depends on the elastic constants of the adjacent materials. In the present study we are going to describe the finite element formulation for problems with a crack to be embedded in the stiffer material$({\mu}_2/{\mu}_1)$. The cubic isoparametric singular element, represented by adequately shifting the mid-side nodes adjacent to the crack tip is constructed to enclose the crack tip. An alternative method to obtain the optimal position of the mid-side nodes of cubic isoparametric elements is presented. In addition, a proper definition for the stress intensity factors of a crack normal to bimaterial interface is provided. It is based upon near a tip displacement solutions. Models for numerical analysis are two dimensional elastic bodies with a through crack under plain strain. The results obtained are compared with the previous solutions.

• 대한기계학회논문집A
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• 제21권12호
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• pp.1973-1983
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• 1997

Higher order isoparametric elements are usually used in the finite element analysis because they can represent easily the geometric shape of a complex structure ad can improve the solution quality. When these elements are used, the position of internal nodes affects greatly on the solution accuracy. Decreasing of the accuracy related to the position of internal nodes is due to non-conformal mapping often results in an unstable Jacobian value. This paper, in order to remove this difficulty, suggests a modified shape function which can establish conformal mapping between two coordinate systems. Numerical experiments with the proposed shape function show that a stable solution can be obtained without respect to the position of internal nodes, and offer convenience that one can take arbitrarily the position of internal nodes considering only the geometric shape of element boundaries.

• Structural Engineering and Mechanics
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• 제57권3호
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• pp.473-506
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• 2016

The aim of this work is the development of a 2D quadrilateral isoparametric finite element model, based on a layerwise approach, for the bending analysis of sandwich plates. The face sheets and the core are modeled individually using, respectively, the first order shear deformation theory and the third-order plate theory. The displacement continuity condition at the interfaces 'face sheets-core' is satisfied. The assumed natural strains method is introduced to avoid an eventual shear locking phenomenon. The developed element is a four-nodded isoparametric element with fifty two degrees-of-freedom (52 DOF). Each face sheet has only two rotational DOF per node and the core has nine DOF per node: six rotational degrees and three translation components which are common for the all sandwich layers. The performance of the proposed element model is assessed by six examples, considering symmetric/unsymmetric composite sandwich plates with different aspect ratios, loadings and boundary conditions. The numerical results obtained are compared with the analytical solutions and the numerical results obtained by other authors. The results indicate that the proposed element model is promising in terms of the accuracy and the convergence speed for both thin and thick plates.

• 대한기계학회논문집
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• 제17권10호
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• pp.2398-2406
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• 1993

Abdi's numerical method(ref.13) for representing a stress singularity by shifting the mid-side nodes of isoparametric elements is reviewed. A simple technique to obtain the optimal position of the mid-side nodes in quadratic isoparametric finite element is presented. From this technique we can directly obtain the position of the side-nodes adjacent to the crack tip. It is also observed that the present technique provides good accuracy for the expression of the opening displacement and the determination of the mid-side nodes for more wide range of material properties than that obtained by Abdicant the finite element method is applied to determine stress intensity factors for pressurized crack perpendicular to and terminating at the interface of two bonded dissimilar materials. A proper definition for stress intensity factors of a crack perpendicular to bimaterial interface is provided. It is based upon a near-tip displacement solutions on the crack surface for interface crack between two dissimilar materials. Numerical testing is carried out with the eight-node and six-node elements. The results obtained are compared with the previous solutions.

• 한국산학기술학회논문지
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• 제19권11호
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• pp.205-212
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• 2018

본 연구에서는 상용 해석프로그램에서 구현하기에 어려움이 있는 지반공학적 문제를 해결하기 위한 쉽고 직관적인 해석 프로그램 개발의 일환으로 계산의 정확도가 상대적으로 높은 요소를 채택한 유한요소법을 정식화 하고 해석과정을 프로그램화 하였다. 개발된 프로그램의 계산과정에 있어서의 신뢰성 확인을 위해 두 가지 예에 대한 해석을 수행하고 결과분석을 해 보았는데 첫 번째 예는 등방구속압이 요소에 작용하는 경우이고 나머지 예는 전단응력이 요소의 측면에 작용하는 경우이다. 유한요소를 구성하는 요소로는 등매개변수 사변형 요소를 채택하였는데 요소내의 변위는 요소의 절점변위와 형상함수로 표현된다. 전체좌표(global coordinate)에 의한 미분계수로 표현되는 변형률을 얻기 위해 자코비언과 자연좌표(natural coordinate)를 이용하는 계산과정을 코딩하였다. 요소의 강성행렬을 정의하는 이중적분식을 수치적분으로 변환시키기 위해 4점 가우스 구적법을 적용하였다. 개발된 프로그램의 계산과정 검증을 위해 등방구속압이 작용하는 요소에 대한 해석을 수행한 결과 요소내의 네 개의 가우스점과 요소 중앙에 대해 계산된 응력값이 등방구속압과 일치됨을 알 수 있었다. 개발된 프로그램의 계산과정 검증을 위해 전단응력이 작용하는 요소에 대한 해석을 수행한 결과 요소내에 발생되는 횡방향응력 및 연직응력이 위치에 따라 변화됨을 알 수 있었으며 외력에 대한 발생응력의 크기 및 분포양상이 합리적임을 알 수 있었다.

• 대한토목학회논문집
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• 제13권2호
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• pp.41-49
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• 1993

2차원 곡선보요소를 이용하여 대변형효과 및 탄소성거동을 고려한 유한요소법을 제시한다. Total Lagrangian 방법을 적용하며, 보요소는 평면응력요소로부터 유도된다. 또한, 임의의 단면을 갖는 평면뼈대 구조의 탄소성 해석을 수행하기 위하여 layered approach를 사용한다. 비선형 유한요소해석은 하중증분 또는 변위증분법을 적용한다. 본 연구에서 제안한 보요소의 거동과 정확도를 검증하기 위하여, 다른 문헌의 결과와 본 연구의 결과를 비교 분석한 해석예제를 제시한다.

• Structural Engineering and Mechanics
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• 제14권3호
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• pp.245-262
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• 2002

The free vibration analysis of stiffened laminated composite plates has been performed using the layered (zigzag) finite element method based on the first order shear deformation theory. The layers of the laminated plate is modeled using nine-node isoparametric degenerated flat shell element. The stiffeners are modeled as three-node isoparametric beam elements based on Timoshenko beam theory. Bilinear in-plane displacement constraints are used to maintain the inter-layer continuity. A special lumping technique is used in deriving the lumped mass matrices. The natural frequencies are extracted using the subspace iteration method. Numerical results are presented for unstiffened laminated plates, stiffened isotropic plates, stiffened symmetric angle-ply laminates, stiffened skew-symmetric angle-ply laminates and stiffened skew-symmetric cross-ply laminates. The effects of fiber orientations (ply angles), number of layers, stiffener depths and degrees of orthotropy are examined.