• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.445-454
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• 1991

In this thesis, Mindlin plate element with nine nodes and three degrees-of-freedom at each node is formulated and is employed in eigen-analysis of a rectangular plates in order to alleviate locking phenomenon of eigenvalues. Eigenvalues and their modes may be locked if conventional $C_{0}$-isoparametric element is used. In order to reduce stiffness locking phenomenon, two methods (1, the general reduced and selective integration, 2, the new element that use of modified shape function) are studied. Additionally in order to reduce the error due to mass matrix, two mass matrixes (1, Gauss-Legendre mass matrix, 2, Gauss-Lobatto mass matrix) are considered. The results of eigen-analysis for two models (the square plate with all edges simply-supported and all edges built-in), computed by two methods for stiffness matrix and by two mass matrixes are compared with theoretical solutions and conventional numerical solutions. These comparisons show that the performance of the two methods with Gauss-Lobatto mass matrix is better than that of the conventional plate element. But, by considering the spurious rigid body motions, the element which employs modified shape function with full integration and Gauss-Lobatto mass matrix can elevate the accuracy and convergence of numerical solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.3
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• pp.419-429
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• 1992

본 연구에서는 면외 변형이 가능한 평면 곡선보에 수정 형상함수를 적용하여 탈락성 및 지속성 에너지에 포함된 가성구속에 의한 수치해의 거동을 고찰함과 동시에, 가성구속에 의한 오차 발생 요인이 제거된, 면외 변형이 가능한 평면 곡선보의 선형 요소를 제안하고자 한다.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.405-410
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• 2000

Generally, it is known that the reduced integration, modified shape function anisoparametric and non-conforming element can minimize the error induced by stiffness locking phenomenon in the finite element analysis. In this study, new anisoparametric curved beam elements are introduced by using different shape functions in each displacement field. When these shape functions are substitute for functional, we can expect that the undulate stress patterns are not appeared or minimized because there is no unmatched coefficient in the constrained energy equation. As a result of numerical test, the undulate stress patterns are disappeared, and displacement and stress are coincide with the exact solutions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.10
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• pp.2640-2652
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• 1994

The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.365-371
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• 1998

In the present study, we attempted to add the incompatible functions as additional variable terms to the conventional u-p formulation. It is derived from the four-field generalized variational principle that encompasses velocity, pressure, velocity strains and stress fields as independent interpolated variables. As a severe test of the present formulation, we have investigated the driven cavity with the corner velocity singularity like leaky lid. Through the test, the present element performs very well without unstable oscillation of pressure distribution.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.11
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• pp.2922-2931
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• 1994

We propose a modified 6-node element, where the sampling point of Gauss quadrature moved in the thickness direction. The modified 6-node element has been applied to static problems and forced motion analyses. In this study, this method is extended to the finite element analysis of the natural frequencies of two dimensional problems. We also propose a modified 16-node element for three dimensional problems, which behaves much like a 20-node element with smaller degree of freedom. The modified 6-node and 16-node elements have been applied to the modal analyses of beams and plates, respectively. The results agree well with the results of the 8-node or 20-node element models.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2078-2086
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• 1996

This paper introduces two three-dimensional eight-node hexagonal elements obtained by using multivariable variational mehtod. Both of them are based on the modified hellinger-reissner principle to employ incompatible displacements and assumed stresses of assumed strains. The internal functions of element are introduced to as element formulation through two different methods : the first one uses the functions determined directly from the element boundary condition of the incompatible displacements ; while the second, being a kind of B-bar mehtod, employs the modification technique of strain-displacement matrix to pass the patch test. The elements are evaluated on the selective problems of bending and material incompressibility with regular and distorted meshes. The results show that the new elements perform with good accuracy in both of deformation and stress calculation and they are insensitive to distorted geometry of element.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.486-494
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• 1995

This paper introduces two kinds of new four-node quadrilateral axisymmetric elements with independently-assumed strains. They are formulated by the modified Hellinger-Reissner principle so as to employ incompatible displacements and assumed strains. In one of the present elements, the strains from incompatible displacements are corrected to pass the constant strain patch test. The other contains incompatible functions that are obtained from the element boundary condition. The elements are evaluated on the several problems of bending and material incompressibility with regular and distorted meshes. The results show that the new element performs excellently in deformation and stress calculation.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3020-3027
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• 1993

Curved beam element has received attention because of its own usefulness and its bearing on general curved elements like shells. In conventional curved beam elements stiffness matrix is overestimated and eigensolutions are poor. To avoid this phenomenon it is necessary to use a large number of elements and, as a result, the total number of degrees of freedom is increased. In this paper the two-noded, with three degrees of freedom at each node, in-plane curvature-based curbed beam element is employed in eigen-analysis of curved beam. It is shown that the curvature-based beam element is very efficient in vibration analysis and also that it is applicable to both thin and thick curved beams.