• Journal of Applied and Pure Mathematics
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• v.5 no.3_4
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.9
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• pp.881-887
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple rectangular holes. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a rectangular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• International Journal of Air-Conditioning and Refrigeration
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• v.10 no.4
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• pp.192-200
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• 2002

A modified asymmetric rectangular fin is analysed using the two-dimensional separation of variables method. This modified rectangular fin is made by attaching the wing on the top side of a rectangular fin. Heat loss from each side of this modified rectangular fin is calculated. The relative increasing ratio of heat loss between a modified rectangular fin and a rectangular fin is presented as a function of dimensionless fin volume, wing height and the location of the wing. Especially, to show the remarkable effect of the wing on the heat loss, the relative increasing ratios of heat loss between two different volume increasing methods are listed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.3
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• pp.304-314
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• 2004

An experimental study has been conducted to measure the temperature fields and the local film cooling effectiveness for two and three staggered rows of the rectangular shaped-holes with various blowing rates. The hydraulic diameter of rectangular-shaped hole is 10mm. To compare with the film cooling performance of rectangular-shaped hole, two kinds of circular holes are tested. One has the same hydraulic diameter as the rectangular hole and the other has the same cross sectional area. Also, rectangular holes with expanded exit with same inlet area as rectangular ones are tested. Temperature fields are measured using a thermocouple rake attached on three-axis traversing system. Adiabatic film cooling effectiveness on the surface are obtained based on experimental results of thermochromic liquid crystals. The film cooling effectiveness is measured for various blowing rates and compared with the results for the cylindrical holes. In case of 2 rows, the rectangular holes has better performance than circular holes due to its slot-like geometry. In case of 3 rows, the effecta of hole shape is not clear.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1177-1182
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have be en many methods developed for the free vibration of the rectangular plate with a rectangular cutout., very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian co ordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• Steel and Composite Structures
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• v.20 no.3
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• pp.599-621
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• 2016

In order to study the working mechanism of rectangular steel-concrete composite columns subjected to compression-bending load and further determine the seismic performance index, a bottom strengthened rectangular steel reinforced concrete (SRC) column with concealed steel plates and a bottom strengthened rectangular concrete filled steel tube (CFST) columns were proposed. Six column models with different configurations were tested under horizontal low cyclic loading. Based on the experiments, the load-bearing capacity, stiffness and degradation process, ductility, hysteretic energy dissipation capacity, and failure characteristics of the models were analyzed. The load-bearing capacity calculation formulas for a normal section and an oblique section of bottom strengthened rectangular steel-concrete composite columns were pesented and a finite element (FE) numerical simulation of the classical specimens was performed. The study shows that the load-bearing capacity, ductility, and seismic energy dissipation capacity of the bottom strengthened rectangular steel-concrete composite columns are significantly improved compared to the conventional rectangular steel-concrete composite columns and the results obtained from the calculation and the FE numerical simulation are in good agreement with those from the experiments. The rectangular steel-concrete composite column with bottom strengthened shows better seismic behavior and higher energy dissipation capacity under suitable constructional requirements and it can be applied to the structure design of high-rise buildings.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.6 s.111
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• pp.643-650
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• 2006

This paper is concerned with the vibration analysis of a simply-supported rectangular plate with a circular cutout. Even though there have been many methods developed for the free vibration of the rectangular plate with a rectangular cutout, very few research has been carried out for the rectangular plate with a circular cutout. In this paper, a new methodology called independent coordinate coupling method, which was developed to save the computational effort for the free vibration analysis of rectangular plate with a rectangular cutout, is applied to the case of circular cutout. The independent coordinate coupling method employs the global coordinate system for the plate and the local coordinate system for the cutout. In the case of the rectangular plate with a circular cutout, the global coordinate system is the Cartesian coordinate system and the local coordinate system is the polar coordinate system. By imposing the compatibility condition, the relationship between the global coordinates and the local coordinates is derived. This equation is then used for the calculation of the mass and stiffness matrices resulting in eigenvalue problem. The numerical results show the efficacy of the proposed method.

• 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.

• Journal of the Korean Society of Safety
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• v.18 no.1
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• pp.101-107
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• 2003

Dynamic behavior of flexible rectangular liquid storage structures is analysed by the developed method. The rectangular liquid storage structures are assumed to be fixed to the ground and a moving coordinate system is used. The irrotational motion of invicid and incompressible ideal fluid is represented by two analytic solutions. One is the solution of the fluid motion in the rigid rectangular liquid storage structure due to ground motions and the other is the solution of the fluid motion by the motion of the wall in the flexible rectangular liquid storage structure. The motion of structure is modeled by finite elements. The fluid-structure interaction effect is reflected into the coupled equation of motion as added fluid mass matrix. The free surface sloshing motion and hydrodynamic pressure acting on the wall in the flexible rectangular liquid storage structure due to the horizontal ground motion are obtained by the developed method and verified.

• Transactions of Materials Processing
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• v.13 no.4
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• pp.307-318
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• 2004

Rectangular drawn case with extreme aspect ratio is widely used for electrical parts such as a lithium-ion battery container, semi-conductor case and so on. Additionally, from the recent trend towards miniaturization of the multi-functional mobile device, demands for rectangular case with the narrow width are increased. In this study, numerical and experimental approaches for the multi-stage deep drawing process have been carried out. Based on the research results of the width of 5.95mm model, finite element analysis for storage case of rectangular cup type was verified to the width of 4.95mm. Also, a series of manufacturing experiments for rectangular case is conducted and the deformed configuration of the rectangular drawn case are investigated by comparing with the results of the numerical analysis. And the modification of the initial blank is performed to minimize the trimmed material amount. By the application of the modified blank, the sound shape of the deformed parts is improved.