• Steel and Composite Structures
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• v.28 no.6
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• International Journal of Advanced Culture Technology
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• v.3 no.1
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• pp.68-77
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• 2015

This study was the use of the finite element method in the deep drawing process of a rectangular shell cup. The aim was to analyse the equivalent strain in the workpiece and to find out what happened to the disc blank sheet before the forming by stamping. The rectangular shell cup was $24{\times}30{\times}20$ mm. and made of 2mm.thick SUS 403 and SUS 304 stainless steel. There were 3 types of blank sheets: 1) square sheet 2) 45 degree angled edge cutting sheet 3) circular sheet. It was found out that the drawing up with the use of 3 types of blank sheet made of SUS 304 stainless steel had no risk in the workpiece. For the stamping of the rectangular shell that used a square sheet made of SUS 403 stainless steel, it was found out that there was no risk in the work piece, but with the use of 45 degree angled edge cutting sheet or round sheet, the work piece had a risk to be damaged.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.3
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• pp.24-29
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• 1981

This paper is studied an efficient temperature distribution and heat transfer of two-dimensional rectangular cross-section by the higher-order triangular finite dynamic element and finite difference. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and convection matrices. Numerical solution results of temperature distribution presented herein clearly optimum element and show that FEM10 is the most accurate temperature distribution, but heat transfer and computational effort is the most acquired.

• Korean Journal of Computational Design and Engineering
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• v.10 no.3
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• pp.162-167
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• 2005

A 3D solid element mesh generation algorithm was newly developed. 3D surface points of global rectangular coordinates were supplied by a 3D laser scanner. The algorithm is strait forward and simple but it generates hexahedral solid elements. Then, the surface rectangular elements were generated from the solid elements. The key of the algorithm is elimination of unnecessary elements and 3D boundary surface fitting using given 3D surface point data.

• Proceeding of KASS Symposium
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• 2006.05a
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• pp.256-264
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• 2006

This paper describes the formulation of rectangular flat shell element that is modeled with the six degree of freedoms including a rotational degree of freedom. The rectangular finite element matrix with a rotational degree of freedom is developed using a beam stiffness matrix and compared with other methods. The outputs of the quantity of vertical deflection of cantilever beam show us the improving evidence of the Frame-Shell finite element matrix in a calculation of vertical deflections of cantilever beam.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.51 no.8
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• pp.449-456
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• 2002

3D Equivalent magnetic Circuit Network Method (EMCNM) is comparatively the easy way that analyzes 3D models of Electric Machine by using permeance as a distributive magnetic circuit parameter under the existing magnetic equivalent circuit method and Numerical Method. The existing 3D EMCNM could not correctly describe the shape of an analysis target when using rectangular shape element or fan shape element, so it made errors when calculating permeance. Therefore, this paper proposes the trapezoidal element contained rectangular element, fan-shape element, and quadrilateral element to express a shape. The proposed method in this research was confirmed as a useful and an accurate method through comparing with the analysis result of SRM model that is sufficiently guaranteed by 2D-Analysis.

• Computers and Concrete
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• v.3 no.4
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• pp.235-248
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• 2006

This investigation presents an analysis procedure for simulating the compressive behavior of a rectangular concrete column confined by fiber-reinforced plastic (FRP) under uniaxial load. That is, the entire stress-strain curve can be drawn through the present analysis procedure. The modified Mander's stress-strain model (Mander, et al. 1988) and finite element method are adopted in this analysis procedure. The numerical analysis results are compared with the experimental results to verify the accuracy of the analysis procedure. This study offers a useful analysis procedure of researching the compressive behavior of rectangular concrete columns confined by FRP. Two main parameters, the number of FRP layers and the radius of the round corners of a rectangular column, are investigated. The numerical results show that non-uniform stresses occur and reduce the sectional effective area owing to the geometry of the confined rectangular column. The stresses are concentrated at the corners of the rectangular column. Compressive strength of a rectangular column increases greatly because the number of FRP layers increase. The maximum predicted compressive stress of the rectangular column has approximately 10% error as compared to the experimental results. Comparing the numerical and experimental results demonstrates that the accuracy of this analysis procedure is credible. Besides, the stress-strain curves of the R30 models, which are rectangular concrete column with large radius of round corners, are almost bilinear. This calculated results conform to the expectation and show the present analysis procedure are more suitable than Mander's model (1988) to analyze the compressive behavior of the rectangular concrete column confined by FRP.

• Steel and Composite Structures
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• v.5 no.2_3
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• pp.203-233
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• 2005

This paper presents the findings of a design development project for perforated beams fully integrated with building services. A unified design approach for both steel and composite beams with large rectangular web openings is proposed which is based on plastic design methods and formulated in accordance with analytical structural design principles. Moreover, finite element models are established after careful calibration against test data, and comparison on the predicted ultimate loads of two composite beams with rectangular web openings from the finite element models and the proposed design method is also presented. It is demonstrated that the proposed design method is able to predict the ultimate loads of composite beams with rectangular web openings against 'Vierendeel' mechanism satisfactorily.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.583-603
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• 2015

There are so many applications of perforated pates with various penetration patterns. If they are penetrated regularly, it can be represented by solid plate with equivalent material properties, which has a benefit of finite element modelling and reducing computation time for the analysis. Because the equivalent material properties suggested already are not proper to be applicable for the dynamic analysis, it is necessary to extract the equivalent material properties for the dynamic analysis. Therefore, in this study, the equivalent modulus of elasticity are obtained for the perforated plate with a triangular penetration pattern by comparing the natural frequencies of the perforated plate with those of solid plate, which are represented with respect to the ligament efficacy. Using the equivalent material properties suggested, the modal analyses of the partially perforated rectangular plate with a triangular penetration pattern are performed and its applicability is shown by comparing natural frequencies of perforated and homogeneous solid plates from finite element method and analytical method.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2001.05a
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• pp.85-88
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• 2001

Examination of the die design is carried out for a multi-stage rectangular cup drawing process with the large aspect ratio with the aid of the finite element analysis. The analysis considers the deep drawing process with the ironing process for the thickness control in the cup wall. Simulation is performed to investigate the deformation mechanism in the initial design and the modified design. The analysis clarifies that the irregular cross section and the irregular contact condition produces unfavorable deformation. The analysis results show that the modified design improves the quality of a deep-drawn product with the low possibility of failure. The analysis result also shows good agreement with the experimental one.