• The Pure and Applied Mathematics
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• v.29 no.3
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• pp.245-254
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• 2022

In this paper, we use some theta-function identities involving certain parameters to show how to evaluate Rogers-Ramanujan continued fraction R($e^{-2{\pi}\sqrt{n}}$) and S($e^{-{\pi}\sqrt{n}}$) for $n=\frac{1}{5.4^m}$ and $\frac{1}{4^m}$, where m is any positive integer. We give some explicit evaluations of them.

• Transactions of Materials Processing
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• v.13 no.2
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• pp.168-173
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• 2004

Microforming can be a good application for bulk metallic glasses. It is important to simulate the deformation behaviour of the bulk metallic glasses in a supercooled liquid region for manufacturing micromachine parts. For these purposes, a correct constitutive model which can reproduce viscosity results is essential for good predicting capability. In this paper, we studied deformation behaviour of the bulk metallic glasses using the finite element method in conjunction with the fictive stress constitutive model which can describe non-Newtonian as well as Newtonian behaviour. A combination of kinetic equation which describes the mechanical response of the bulk metallic glasses at a given temperature and evolution equations fur internal variables provide the constitutive equation of the fictive stress model. The internal variables are associated with fictive stress and relation time. The model has a modular structure and can be adjusted to describe a particular type of microforming process. Implementation of the model into the MARC software has shown its versatility and good predictive capability.

• Transactions of Materials Processing
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• v.13 no.2
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• pp.160-167
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• 2004

In order to theoretically analyze the creep behavior of high Cr steel at $600^{\circ}C$, a unified elasto-viscoplastic constitutive model based on the consideration of dislocation density is proposed. A combination of a kinetic equation describing the mechanical response of a material at a given microstructure in terms of dislocation glide and evolution equations for internal variables characterizing the microstructure provides the constitutive equations of the model. Microstructural features of the material such as the grain size and spacing between second phase particles are directly implemented in the constitutive equations. The internal variables are associated with the total dislocation density in a simple model. The model has a modular structure and can be adjusted to describe a creep behavior using the material parameters obtained from uniaxial tensile tests.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.10
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• pp.691-699
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• 2022

Large aperture antennas with long focal lengths in space have important application for telecommunications, Earth observation and science missions. This paper aims to understand the dynamics of deployment of large mesh antennas and to provide a multibody model for determining the driving forces for the design of reflectors and booms. The modular deployable reflector and boom are designed based on the deployment unit cell. A multibody dynamic model is formulated with Kane's equation and simulated using the pseudo upper triangular decomposition (PUTD) method for solving the constrained problem. Based on the multibody dynamic model, the kinetics of the deployment, the motor driving forces, and the structural dynamic deformation are investigated.

• Journal of the Korean Geotechnical Society
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• v.33 no.3
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• pp.49-62
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• 2017

In order to understand response of geo-structures to the freezing-thawing process in the ground, it is necessary to consider phase change of the pore water of the ground and also to understand soil interaction with structures. In this study, numerical analysis was carried out for freezing and thawing effect on the modular road system. Neumann's theoretical equation for freezing-thawing processes in porous media can be used to estimate frozen depth and heaving from basic soil properties and ground and surface temperature, but its application is limited to the case for the sediment with fully saturated condition and zero unfrozen water content. Numerical analysis of the modular road system was performed on various soil types and different ground water table as the varying freezing index. The amount of heaving in the silty soil was much larger than those in granite weathered soil or sandy soil, and lowering groundwater level reduced ground heaving induced by freezing. Numerical analysis for temperature history of the ground surface predicted residual heaving near the surface by the freeze-thaw process in silty soil. It ought to reduce stiffness and bearing capacity of the ground so that it will impair stability and serviceability of new road system. However, the amount of residual heaving was insignificant for the road system installed in weathered soil granite and sandy soil. Since modular road system is a pavement structure mounted on the supporting substructure unlike the prevalent road pavement system, strict criteria should be applied for uniform and differential settlement of the pavement system.

• Journal of the Earthquake Engineering Society of Korea
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• v.1 no.3
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• pp.29-35
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• 1997

The megastructure combined with the modular concept is an effcient structural system adequate for ultra-tail buildings for the future. An ingeneous structural control system can be developed by separating the internal subframe in one or many modules from the external megaframe, thus taking advantage of the effect of tuned mass dampers without adding any aditional mass. This so called mega-subcontrol system is generally modeled by a 20DF system for parametric study and for finding optimal values of the parameters. In this study the equation of motion for the system is obtained frist and the preconditions for the simplified modeling are investigated. Finally the optimal value for the subsreucture strffness is fomputed with given mass and damping ratios and transfer functions for responses are abtained for white noise ground exitation to verify the effectiveness of the mega-subcontrol system.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.11a
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• pp.35-38
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• 2007

Aiming at time-dependent performance prediction of Liquid Rocket Engine(LRE) system, Modular Program for Conceptual Design of LRE is reviewed, and a modeling and dynamic analysis of rocket engine system with reference to Rocket Engine Dynamic Simulator(REDS) is outlined. Component modeling is based on classical thermodynamic and inviscid theories, and were formulated mathematically in terms of essential parameters. Essential design parameters are addressed. The rocket engine is modeled as a system of pipes with various hydraulic elements, and then the operate characteristic of that elements are simulated by solving conservation equation sequentially.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1467-1474
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• 2014

In this paper, we consider the two computer intensive methods for extended Euclidean algdrithm. Two methods we propose are C-programming based approach and Microsoft excel based method, respectively. Thses methods are applied to the derivation of greatest commnon devisor, multiplicative inverse for modular operation and the solution of diophantine equation. Concrete investigation for extended Euclidean algorithm with the computer intensive process is given. For the application of extended Euclidean algorithm, we consider the RSA encrytion method which is still popular recently.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.10
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• pp.155-162
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• 2019

Hybrid precast concrete panel is a wall element that is able to quickly construct the core wall structure for moderate-rise modular buildings. Hybrid precast concrete panel has unique characteristics which is a pair of C-shaped steel beams combined at the top and bottom of a concrete wall, In this study, an improved anchorage detail for vertical rebar is proposed to ensure the lateral force resistance performance of hybrid precast concrete panel emulating monolithic concrete wall. Also, the structural performance of horizontal connection is investigated experimentally with the bolt spacing parameter. And the behavior of hybrid precast concrete panel with the improved detail is compared with the monolithic concrete wall tested in a previous study. Finally, the required thickness of C-shaped steel beam to eliminate or minimize the deformation in horizontal connection is calculated by prying action equation.

• Journal of the Korean Geotechnical Society
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• v.38 no.7
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• pp.49-62
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• 2022

The hollow modular concrete block reinforced foundation method is one of the ground reinforcement foundation methods that uses hexagonal honeycomb-shaped concrete blocks with mixed crushed rock to reinforce soft grounds. It then forms an artificial layered ground that increases bearing capacity and reduces settlement. The hollow modular honeycomb-shaped concrete block is a geometrically economical, stable structure that distributes forces in a balanced way. However, the behavioral characteristics of hollow modular concrete block reinforced foundations are not yet fully understood. In this study, a bearing capacity test is performed to analyze the reinforcement effectiveness of the hollow modular concrete block through the laboratory model tests. From the load-settlement curve, punching shear failure occurs under the unfilled sand condition (A-1-N). However, the filled sand condition (A-1-F) shows a linear curve without yielding, confirming the reinforcement effect is three times higher than that of unreinforced ground. The bearing capacity equation is proposed for the parts that have contact pressure under concrete, vertical stress of hollow blocks, and the inner skin friction force from horizontal stress by confining effect based on the schematic diagram of confining effect inside a hollow modular concrete block. As a result of calculating the bearing capacity, the percentage of load distribution for contact force on the area of concrete is about 65%, vertical force on the area of hollow is 16.5% and inner skin friction force of area of the inner wall is about 18.5%. When the surcharge load is applied to the concrete part, the vertical stress occurs on the area of the hollow part by confining effect first. Then, in the filled sand in the hollow where the horizontal direction is constrained, the inner skin friction force occurs by the horizontal stress on the inner wall of the hollow modular concrete block. The inner skin friction force suppresses the punching of the concrete part and reduces contact pressure.