• Structural Engineering and Mechanics
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• 제4권5호
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• pp.569-586
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• 1996

A new three-dimensional 8-node solid element with rotational degrees of freedom is presented. The proposed element is established by adding rotational degrees of freedom to the basic 8-node solid element. Thus the element has three translations and three rotational degrees of freedom per node. The corner rotations are introduced by transforming the hierarchical mid-edge displacements which are parabolic shape along an edge. The derivation of the element is based on the mixed variational principles in which the rotations are introduced as independent variables. Several types of non-conforming modes are selectively added to the displacement fields to obtain a series of improved elements. The resulting elements do not have the spurious zero energy modes and Poisson's ratio locking and pass patch test. Numerical examples show that presented non-conforming solid elements with rotational degrees of freedom show good performance even in the highly distorted meshes.

• Structural Engineering and Mechanics
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• 제29권6호
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• pp.643-658
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• 2008

In this paper, we present a quadratic element model based on non-conforming displacement modes and modified shape functions. This new and refined 8-node hybrid stress plane element consists of two additional non-conforming modes that are added to the translational degree of freedom to improve the behavior of a membrane component. Further, the modification of the shape functions through quadratic polynomials in x-y coordinates enables retaining reasonable accuracy even when the element becomes considerably distorted. To establish its accuracy and efficiency, the element is compared with existing elements and - over a wide range of mesh distortions - it is demonstrated to be exceptionally accurate in predicting displacements and stresses.

• Structural Engineering and Mechanics
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• 제14권6호
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• pp.699-712
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• 2002

In this paper, a new quadrilateral 5-node non-conforming membrane element with drilling degrees of freedom is presented. The main advantage of these elements is the relatively small number of integration points to evaluate a stiffness matrix comparing to the existing transition membrane elements (CLM elements). Moreover, the presented elements pass the patch test by virtue of the Direct Modification Method incorporated into the element formulation. The presented 5-node elements are proved to be very efficient when used in the local mesh refinement for the in-plane structures which have stress concentrations. And some numerical studies also show the good performance of the new element developed in this study.

• Structural Engineering and Mechanics
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• 제10권2호
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• pp.93-110
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• 2000

An alternative interpretation of the completeness requirements for the higher order elements is presented. Apart from the familiar condition, $\sum_iN_i=1$, some additional conditions to be satisfied by the shape functions of higher order elements are identified. Elements with their geometry in the natural form, i.e., without any geometrical distortion, satisfy most of these additional conditions inherently. However, the geometrically distorted elements satisfy only fewer conditions. The practical implications of the satisfaction or non-satisfaction of these additional conditions are investigated with respect to a 3-node bar element, and 8- and 9-node quadrilateral elements. The results suggest that non-satisfaction of these additional conditions results in poorer performance of the element when the element is geometrically distorted. Based on the new interpretation of completeness requirements, a 3-node element and an 8-node rectangular element that are insensitive to mid-node distortion under a quadratic displacement field have been developed.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1998년도 가을 학술발표회 논문집
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• pp.27-34
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• 1998

A versatile flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. This element is formulated by the enhanced displacement field with the additional non-conforming displacement modes. Thus the element possesses six degrees-of-freedom (DOF) per node which permits an easy connection to other six DOF elements as well as the improvement of the element behavior. In plate bending part, this element is established by the combined use of the addition of non-conforming modes, the reduced (or selective) integration scheme, and the construction of the substitute shear strain fields. The achieved improvement may be attributable to the fact that the merits of these individual techniques are merged into the new element in a complementary manner. In membrane part, this element shows better membrane behavior as the nonconforming displacement mode is added to drilling mode.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1995년도 봄 학술발표회 논문집
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• pp.9-16
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• 1995

A new three-dimensional transition solid element with drilling degrees of freedom is presented. The proposed transition element is established by adding variable nodes to a basic 8-node element for an effective connection between the refined region and the coarse. The derivation of the element in this paper is based on the variational principles in which the drilling rotations are introduced as independent variables. This element was also improved through the addition of modified non-conforming modes. Numerical examples show that performance of the element and the applicability to 3D adaptations are satisfactory.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
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• pp.409-416
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• 2001

The present work is concerned with the development of new variable-node Mindlin plate bending elements. The proposed variable-node elements pass the patch tests, do not show spurious zero-energy modes, and do not produce shear locking phenomena. It is also shown that the elements produce reliable solutions through numerical tests for standard benchmark problems.

• 한국강구조학회 논문집
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• 제22권1호
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• pp.33-42
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• 2010

막구조의 설계에서 막재료의 효율적인 사용을 위해서는 측지선에 의한 재단도 해석을 수행해야 한다. 막구조의 측지선 결정방법은 크게 측지요소(geodesic element)를 이용한 비선형 형상해석에 의한 방법과 임의의 곡면 형상에 대한 측지선 탐색에 의한 방법으로 나눌 수 있는데, 현재까지 이 두 가지 해석법은 모두 3절점요소에 대한 적용알고리즘 만이 제시되었고, 4절점 요소에 대한 해석법은 제시되지 않았다. 이는 막구조의 설계에서 4절점 요소의 적용을 어렵게 하는 가장 큰 요인이라고 할 수 있다. 본 연구에서는 3절점, 4절점 평면요소에 동시에 적용 가능한 측지선 결정알고리즘을 제시한다. 이를 위해 저자의 이전 연구를 발전시켜 명시적 비선형 해석법인 동적이완법을 비선형 측지선 형상해석에 적용하였다. 또한 3절점요소 뿐만 아니라 4절점요소에 대해서도 측지요소의 도입에 의한 형상해석이 가능하도록 하였으며, 4절점요소와 측지선요소에 의한 비선형 형상해석 및 재단도 해석예제를 통하여 본 연구에서 제시한 알고리즘의 정확성 및 효율성을 검증하였다. 따라서 본 연구에서 제안한 측지선 형상해석알고리즘은 형상해석, 응력해석, 재단도 해석과 관련된 일련의 해석과정에 대한 4절점요소의 적용성을 높일 수 있을 것으로 사료된다.

• Structural Engineering and Mechanics
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• 제16권4호
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• pp.479-492
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• 2003

Non-conforming membrane elements which have variable number of mid-side nodes with drilling degrees of freedom and which is designated as NMDx have been presented in this paper. The non-conforming elements with variable number of mid-side nodes can be efficiently used in the local mesh refinement for the in-plane structures. To guarantee the developed elements always pass the patch test, the direct modification method is incorporated into the element formulation. Detailed numerical tests in this study show the validity of the variable node NC elements developed in this study and a wide applicability of these elements to practical problems.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.304-308
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• 2006

The focus of this study is modeling technique for a bellows in vehicle exhaust system. Bellows was developed using tile finite element model by replacing with the equivalent beam. The equivalent beam model were studied in detail. Non-structural node in the cross section of original model is given to expressing their motion. Equivalent mass matrix and stiffness matrix calculated using Guyan reduction method. Material Properties of beam was obtained from the direct comparison between equivalent model and that of Timoshenko beam model. The calculated natural frequencies and mode shape are compared with the reference results and coincided well. The results were compared with the confirmed results, which were in good agreement.