• 전산구조공학
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• 제8권3호
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• pp.79-89
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• 1995

본 논문에서는 평판 두께 방향의 선형 및 비선형 응력 분포를 일정한 크기의 단순응력 상태로 가정하는 분할판(Two-element plate) 개념을 이용하여 비선형 특성을 나타내는 평판의 강도해석을 할 수 있는 Reissner 범함수와, 재질 특성은 선형이면서 기하학적 비선형 특성만을 갖는 평판의 강도해석을 할 수 있는 변형 Reissner 범함수를 모델링하였다. 두 종류의 Reissner 범함수들을 근거로 하여 축방향 하중을 받는 평판의 선형 좌굴과 좌굴후의 비선형 특성 및 최대강도들을 계산할 수 있는 유한요소 방정식과 프로그램 개발을 시도하였다. 개발한 프로그램을 이용한 수치해석 결과, 분할판 이론을 사용한 선형좌굴해석 결과가 기존의 평판이론을 사용한 선형좌굴해석 결과와 유사항 경향을 나타냄으로써 분할판 이론에 근거한 유한요소법을 하중과 경계조건 및 구성재질이 다양한 일반적인 평판의 강도해석에 확대 적용함은 물론 좌굴후 비선형재질 특성으로 인한 평판의 최대강도도 예측 가능하다고 생각한다.

• 대한토목학회논문집
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• 제8권2호
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• pp.25-32
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• 1988

본 연구에서는 8절점 28자유도를 갖는 사각형 고차 판 유한 요소를 면내고차 변위를 고려하여 3차원 연속체로부터 유도하였다. 요소매트릭스들은 판의 운동방정식으로부터 Galerkin 가중잔차법으로 유도하고 감차적분을 수행하여 구하였다. 고차 판 유한요소를 이용하여 판의 처짐해석과 자유진동해석을 수행한 결과 판의 두께와 경게조건에 관계없이 매우 정확한 결과를 나타내었다.

• 한국공간구조학회논문집
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• 제14권2호
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• pp.59-68
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• 2014

A study on the vibration and buckling analyses of laminated composite plates is described in this paper. In order to carry out the analyses of laminated composite plates, a NURBS-based isogeometric general plate element based on Reissner-Mindlin (RM) theory is developed. The non-uniform rational B-spline (NURBS) is used to represent the geometry of plate and the unknown displacement field and therefore, all terms required in this element formulation are consistently derived by using NURBS basis function. Numerical examples are conducted to investigate the accuracy and reliability of the present plate element. From numerical results, the present plate element can produce the isogeometric solutions with sufficient accuracy. Finally, the present isogeometric solutions are provided as future reference solutions.

• Structural Engineering and Mechanics
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• 제68권4호
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• pp.385-398
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• 2018

In the present paper, we offer a new flat shell finite element. It is the result of the combination of a membrane element and a bending element, both based on the strain-based formulation. It is known that $C^{\circ}$ plane membrane elements provide poor deflection and stress for problems where bending is dominant. In addition, they encounter continuity and compliance problems when they connect to C1 class plate elements. The reach of the present work is to surmount these problems when a membrane element is coupled with a thin plate element in order to construct a shell element. The membrane element used is a triangular element with four nodes, three nodes at the vertices of the triangle and the fourth one at its barycenter. Each node has three degrees of freedom, two translations and one rotation around the normal. The coefficients related to the degrees of freedom at the internal node are subsequently removed from the element stiffness matrix by using the static condensation technique. The interpolation functions of strain, displacements and stresses fields are developed from equilibrium conditions. The plate element used for the construction of the present shell element is a triangular four-node thin plate element based on Kirchhoff plate theory, the strain approach, the four fictitious node, the static condensation and the analytic integration. The shell element result of this combination is robust, competitive and efficient.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.37-44
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• 2003

In this proposed work, computational, finite element model far multi-delaminated plates will be developed. In the current analysis procedures of multi-delaminated plates, different elements are used at delaminated and undelaminated region separately. In the undelaminated region, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. Element mass and stiffness matrices of each region (delaminated, undelaminated and transition region) will be assembled for global matrix.

• Structural Engineering and Mechanics
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• 제19권2호
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• pp.199-215
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• 2005

An assumed stress quadrilateral thin/moderately thick plate element HQP4 based on the Mindlin/Reissner plate theory is proposed. The formulation is based on Hellinger-Reissner variational principle. Static and free vibration analyses of plates are carried out. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis of plates. Satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis.

• 한국전산구조공학회논문집
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• 제22권5호
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• pp.421-428
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• 2009

본 연구에서는 2방향 중공슬래브의 효율적인 진동해석을 위하여 등가의 플레이트 모델을 개발하였다. 이를 위하여 3차원 입체요소 중공슬래브 모델에 대응하는 플레이트 슬래브 모델의 등가 질량과 강성을 산출하였다. 개발된 등가 플레이트 모델의 정확성과 효율성을 검증하기 위하여 예제해석을 수행하였다. 해석결과 등가 플레이트모델의 고유진동수는 3차원 입체요소모델과 비교하여 매우 정확한 것을 확인하였다. 또한 보행하중이 가해지는 2방향 중공슬래브에 대해 등가플레이트 모델과 3차원 입체요소 모델을 사용하여 시간이력해석을 수행한 후 그 결과를 비교하였다. 해석결과 등가의 플레이트 모델이 해석시간을 상당히 줄이면서도 3차원 입체요소 모델과 거의 일치하는 결과를 나타내는 것을 확인하였다.

• Steel and Composite Structures
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• 제11권5호
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• pp.359-374
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• 2011

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

• Structural Engineering and Mechanics
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• 제41권2호
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• pp.205-229
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• 2012

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations ${\theta}_x$ and ${\theta}_y$ are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

• 대한기계학회논문집A
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• 제22권3호
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• pp.635-643
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• 1998

A spectral element method(SEM) is introduced for the vibration analysis of a rectangular plate subject to dynamic concentrated loads. First, the spectral plate element is derived from the relations between the forces and displacements along the two opposite edges of plate element. The global spectral matrix equation is then formulated by assembling two spectral plate elements so that the dynamic concentrated load is located at the connection nodal line between two plate elements. the concentrated load is then spatially Fourier transformed in the direction of the connection nodal line to transform the two-dimensional plate problem into a simplified equivalent one-dimensional beam-like problem. We may benefit from these procedures in that the spectral results from the present SEM is compared with the exact analytical solutions to prove the remarkable accuracy of the present SEM, while this is not true for conventional finite element solutions, especially at high frequency.