• Structural Engineering and Mechanics
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• 제4권4호
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• pp.415-424
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• 1996

This paper presents a newly suggested calculation method in which an arbitrary quadrilateral element with curved sides is transformed to a normal rectangular one by mapping of coordinates, then the two-dimensional spline is adopted to approach the displacement function of this element. Finally the solution can be obtained by the least-energy principle. Thereby, the application field of Spline Finite Element Method will be extended.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1995년도 가을 학술발표회 논문집
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• pp.153-160
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• 1995

Mixed finite element formulations for incompressible materials show pressure oscillations or pressure modes in four-node quadrilateral elements. The criterion for the stability in the pressure solution is the so-called Babufka-Brezzi stability condition, and the four-node elements based on mixed variational principles do not appear to satisfy this condition. In this study, a pressure continuity residual based on the pressure discontinuity at element edges is used to study the stabilization of pressure solutions in bilinear displacement-constant pressure four-node quadrilateral elements. It is shown that the pressure solutions, although stable, exhibit sensitivity to the stabilization parameters.

• 충청수학회지
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• 제33권4호
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• pp.429-444
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• 2020

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

• 한국정밀공학회지
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• 제11권1호
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• pp.157-165
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• 1994

A general-purpose program for automatic two-dimensional finite-element modelling with quadrilateral elements was developed in this research. The conventional looping method employed in the program was introduced with emphasis on a new splitting criterion and a splitting scheme developed for improving the method. Some application examples were given, which show versatility and applicability of the developed program.

• 대한수학교육학회지:수학교육학연구
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• 제25권2호
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• pp.225-240
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• 2015

본 연구에서는 중점연결정리의 사각형으로의 확장을 소재로 학교수학에서 다루어지는 증명의 대표성에 대해 고찰하였다. 다양한 사각형을 생각하고, 그에 맞는 중점연결정리의 확장을 증명하였으며, 이들 증명 간의 관계를 파악하여 학교수학에서의 증명이 대표성을 가짐을 보였다. 한편, 이러한 내용에 기초한 실태조사에서 학생들은 사각형 종류의 일부만을 찾았으며, 찾은 사각형 각각에 대한 증명은 쉽게 완성하였으나, 같은 수학적 사실을 증명하고 있음에도 대상 도형이 바뀌면 다른 증명 방법이나 수학적 개념을 사용하는 경향을 보였다. 따라서 증명들 간의 관계를 파악하는 것을 어려워하였다. 이러한 사실들은 구체적 도형에 대한 증명은 할 수 있으나, 증명들 간의 관계를 이해하여 일반화하는 증명의 대표성에 대한 이해는 부족함을 보여준다. 따라서 증명활동이 유기적이고 의미론적으로 이루어질 필요가 있음을 알 수 있다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 추계학술대회논문집
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• pp.65-70
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• 2009

In this paper a hybrid grid generation program for general 2-D region is introduced. The program is developed by using JAVA programming language, and it can be used either as an application program on a local computer or as an applet in the network environment. The hybrid grid system for a 2-D problem means a combination of triangular cells and quadrilateral cells, and it can offer both of the high flexibility of triangular cells and the high accuracy and efficiency of structured-type quadrilateral cells. To accommodate a quadrilateral-cell region and a triangular-cell region into one computational domain, it is importance to take good care of the interface between two different regions so that overall good grid quality can be maintained. In this research advancing layer method(ALM) augmented by elliptic smoothing method is used for the quadrilateral-cell region and advancing front method(AFM) is used for the triangular-cell region. A special treatment technique for the interface between those two regions is also developed. The interface treatment technique is basically to prevent the propagation of small cell size due to ALM method into the triangular region and maintain the smooth transition of cell-size scale between two different regions. By applying current technique high-quality hybrid grids for general 2-D regions can be easily generated, and typical grid generation results and flow solutions are demonstrated.

• Structural Engineering and Mechanics
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• 제16권3호
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• pp.259-274
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• 2003

In this paper, a novel numerical solution technique, the differential cubature method is employed to study the buckling problems of thick plates with arbitrary quadrilateral planforms and non-uniform boundary constraints based on the first order shear deformation theory. By using this method, the governing differential equations at each discrete point are transformed into sets of linear homogeneous algebraic equations. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Detailed formulation and implementation of this method are presented. The buckling parameters are calculated through solving a standard eigenvalue problem by subspace iterative method. Convergence and comparison studies are carried out to verify the reliability and accuracy of the numerical solutions. The applicability, efficiency, and simplicity of the present method are demonstrated through solving several sample plate buckling problems with various mixed boundary constraints. It is shown that the differential cubature method yields comparable numerical solutions with 2.77-times less degrees of freedom than the differential quadrature element method and 2-times less degrees of freedom than the energy method. Due to the lack of published solutions for buckling of thick rectangular plates with mixed edge conditions, the present solutions may serve as benchmark values for further studies in the future.

• 한국CDE학회논문집
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• 제1권1호
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• pp.56-64
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• 1996

A quadrilateral-triangular mixed grid method for the solution of incompressible viscous flow is presented. The solution domain near the body surface is meshed using elliptic grid geneator to acculately simulate the viscous flow. On the other hand, we used unstructured triangular grid system generated by advancing front technique of a simple automatic grid generation algorithm in the rest of the computational domain. The present method thus is capable of not only handling complex geometries but providing accurate solutions near body surface. The numerical technique adopted here is PISO type finite element method which was developed by the present author. Investigations have been made of two-dimensional unsteady flow of Re=550 past a circular cylinder. In the case of use of the unstructured grid only, there exists a considerable amount of difference with the existing results in drag coefficient and vorticity at the cylinder surface; this may be because of the lack of the grid clustering to the surface that is a inevitable requirement to resolve the viscous flow. However, numerical results on the mixed grid show good agreements with the earlier computations and experimental data.

• 한국생산제조학회지
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• 제26권1호
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• pp.74-81
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• 2017

A crane is typically used as a means to lift and load equipment or materials. A surface vessel uses a towed object for underwater activity. Such a mechanism for dropping and lifting of equipment is necessary, and is called an overboarding unit. The present study is focused on the overboarding unit used for a crane structure. This paper deals with new overboarding mechanism design and GA-based $MATLAB^{(R)}$ optimization. By using a quadrilateral link mechanism, it is possible to set the constraint function for optimizing the GA method. The optimization with $MATLAB^{(R)}$ is followed by the $SolidWorks^{(R)}$ simulation and verification. When applying the proposed mechanism, the operator is expected to have a big advantage in safety and efficiency of operations. Furthermore, the technology developed in this study will be helpful in similar circumstances and in the proposed mechanism.

• 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.