• Structural Engineering and Mechanics
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• 제5권4호
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• pp.471-490
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• 1997

In this paper, the classical Irons' patch tests which have been generally accepted for the convergence proof of a finite element are performed for Mindlin plate bending elements with a special emphasis on the nonconforming elements. The elements considered are 4-node and 8-node quadrilateral isoparametric elements which have been dominantly used for the analyses of plate bending problems. It was recognized from the patch tests that some nonconforming Mindlin plate elements pass all the cases of patch tests even though nonconforming elements do not preserve conformity. Then, the clues for the Mindlin plate element to pass the Irons' patch tests are investigated. Also, the convergent characteristics of some nonconforming Mindlin plate elements that do not pass the Irons' patch tests are examined by weak patch tests. The convergence tests are performed on the benchmark numerical problems for both nonconforming elements which pass the patch tests and which do not. Some conclusions on the relationship between the patch test and convergence of nonconforming Mindlin plate elements are drawn.

• Structural Engineering and Mechanics
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• 제5권1호
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• pp.69-83
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• 1997

A new efficient hybrid/mixed thin~moderately thick plate bending element with 6-node (HM6-14) is formulated based on the Reissner-Mindlin plate bending theory. The convergence of this element is proved by error estimate theories and verified by patch test respectively. Numerical studies on such an element as HM6-14 demonstrate that it has remarkable convergence, invariability to geometric distorted mesh situations, to axial rotations, and to node positions, and no "locking" phenomenon in thin plate limit. The present element is suitable to many kinds of shape and thin~moderately thick plate bending problems. Further, in comparison with original hybrid/mixed plate bending element HP4, the present element yields an improvement of solutions. Therefore, it is an efficient element and suitable for the development of adaptive multi-field finite element method (FEM).

• 전산구조공학
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• 제10권2호
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• pp.179-188
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• 1997

본 논문에서는 평판 구조물의 효율적인 해석을 위한 4절점 평판휨 요소를 개발하였다. 이 요소는 전단변형을 고려하기 위해 Mindlin평판이론에 의하여 유도하였다. 평판휨 문제에서 4절점요소와 같은 저차의 등매개변수 Mindlin평판요소는 전단강성을 실제보다 강하게 평가하기 때문에 얇은 평판에서는 요소의 기능을 발휘하지 못한다. 이러한 문제점을 극복하기 위해 4절점 요소에 5개의 비적합변위모드를 추가함으로써 개선된 결과를 얻을 수 있었으며, 개발된 요소는 유사영에너지모드를 발생시키지 않는다. 아주 얇은 평판에서도 요소의 형상과 무관하게 전단구속현상을 극복하였으며, 예제 해석으로부터 변위의 신속한 수렴성과 단면력의 분포가 양호한 결과를 얻을 수 있었다. 또한 요소형상비가 매우 큰 경우에도 좋은 결과를 얻을 수 있었다.

• Structural Engineering and Mechanics
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• 제33권4호
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• pp.485-502
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• 2009

A new 8-node serendipity quadrilateral plate bending element (MQP8) based on the Mindlin-Reissner theory for the analysis of thin and moderately thick plate bending problems using Integrated Force Method is presented in this paper. The performance of this new element (MQP8) is studied for accuracy and convergence by analyzing many standard benchmark plate bending problems. This new element MQP8 performs excellent in both thin and moderately thick plate bending situations. And also this element is free from spurious/zero energy modes and free from shear locking problem.

• Structural Engineering and Mechanics
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• 제26권1호
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• pp.43-68
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• 2007

Using the Mindlin-Reissner plate theory, many quadrilateral plate bending elements have been developed so far to analyze thin and moderately thick plate problems via displacement based finite element method. Here new formulation has been made to analyze thin and moderately thick plate problems using force based finite element method called Integrated Force Method (IFM). The IFM is a novel matrix formulation developed in recent years for analyzing civil, mechanical and aerospace engineering structures. In this method all independent/internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper the force based new bilinear quadrilateral plate bending element (MQP4) is proposed to analyze the thin and moderately thick plate bending problems using Integrated Force Method. The Mindlin-Reissner plate theory has been used in the formulation of this element which accounts the effect of shear deformation. Standard plate bending benchmark problems are analyzed using the proposed element MQP4 via Integrated Force Method to study its performance with respect to accuracy and convergence, and results are compared with those of displacement based 4-node quadrilateral plate bending finite elements available in the literature. The results are also compared with the exact solutions. The proposed element MQP4 is free from shear locking and works satisfactorily in both thin and moderately thick plate bending situations.

• Structural Engineering and Mechanics
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• 제30권4호
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• pp.387-402
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• 2008

The Integrated Force Method (IFM) has been developed in recent years for the analysis of civil, mechanical and aerospace engineering structures. In this method all independent or internal forces are treated as unknown variables which are calculated by simultaneously imposing equations of equilibrium and compatibility conditions. The solution by IFM needs the computation of element equilibrium and flexibility matrices from the assumed displacement, stress-resultant fields and material properties. This paper presents a general purpose code for the automatic generation of element equilibrium and flexibility matrices for plate bending elements using the Integrated Force Method. Kirchhoff and the Mindlin-Reissner plate theories have been employed in the code. Paper illustrates development of element equilibrium and flexibility matrices for the Mindlin-Reissner theory based four node quadrilateral plate bending element using the Integrated Force Method.

• 한국강구조학회 논문집
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• 제16권3호통권70호
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• pp.295-303
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• 2004

본 연구에서는 등방성 및 복합적층판 해석을 위해 추가변형률을 갖는 개선된 4절점 Reissner-Mindlin 평판휨요소를 제안하였다. 전단잠김현상과 가상적인 제로에너지모드를 제거하기 위해 비적합 변위모드와 Bubble 함수식에 근거한 새로운 형태의 전단변형률을 추가함으로써 횡방향 전단거동을 개선하였다. Andelfinger와 Ramm(1993)이 제시한 기본적인 추가변형률은 면내거동을 개선시키고자 그대로 적용하였다. 1차전단변형이론에 근거한 새로 개발된 4절점 평판요소를 '14EASP'라 명하였다. 14EASP 유한요소의 특징과 성능을 평가하고자 몇가지의 수치해석예제를 적용하였으며, 다른 유한요소 및 해석적인 해와 비교하였다. 그 결과 본 연구에서 제안한 14EASP는 보다 안정적이고, 수렴성이 빠르며, 특히 요소형상이 왜곡된 경우에도 정확한 결과를 도출하였다.

• Structural Engineering and Mechanics
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• 제8권2호
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• pp.207-231
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• 1999

A versatile 4-node shell element which is useful for the analysis of arbitrary shell structures is presented. The element is developed by flat shell approach, i.e., by combining a membrane element with a Mindlin plate element. The proposed element has six degrees of freedom per node and permits an easy connection to other types of finite elements. In the plate bending part, an improved Mindlin plate has been established by the combined use of the addition of non-conforming displacement modes (N) and the substitute shear strain fields (S). In the membrane part, the nonconforming displacement modes are also added to the displacement fields to improve the behavior of membrane element with drilling degrees of freedom and the modified numerical integration (M) is used to overcome the membrane locking problem. Thus the element is designated as NMS-4F. The rigid link correction technique is adopted to consider the effect of out-of-plane warping. The shell element proposed herein passes the patch tests, does not show any spurious mechanism and does not produce shear and membrane locking phenomena. It is shown that the element produces reliable solutions even for the distorted meshes through the analysis of benchmark problems.

• Structural Engineering and Mechanics
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• 제59권6호
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• pp.1071-1094
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• 2016

We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral plate finite elements with 12 external degrees of freedom that pass the constant bending patch test for arbitrary node positions of which the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form. The new elements are compared to the existing linked-interpolation quadratic and nine-node cubic elements presented by the author earlier and to the other elements from literature that use the cubic linked interpolation by testing them on several benchmark examples.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.855-859
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• 2004

We develop a new four-node flat shell element which is accurate, efficient, and suitable to be used on general purpose. The new element has a hybrid Trefftz element with drilling degrees of freedom as a membrane part. We define the two independent displacement field: the internal displacement field that satisfies governing equations in the domain a priori and the boundary displacement field that is usually used as a conventional finite element method. The hybrid Trefftz variational formulation connects these two displacement fields on the boundary of the domain. To add drilling degrees of freedom, we introduce the Allman's quadratic displacement field to the boundary displacement field. As a result, our flat shell element has 6 degrees of freedom per a node. We also use the well-known DKMQ plate bending element for the plate part of the proposed element. The DKMQ element satisfies Mindlin-Reissner‘s plate theory along the edge of the element and gives proper behavior regardless of the thickness. A series of numerical experiments shows that the performance of the new element such as accuracy, rate of convergence, robustness to mesh quality, and so on.