• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.1
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• pp.49-66
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• 2022

The G-Euler process has been proposed to overcome the difficulties of the calculation of the exponential function of the Jacobian. It is an explicit method that uses the exponential function of the scalar skew-symmetric matrix. We define the moving shapes of true solutions and the moving shapes of numerical solutions. It is discussed whether the moving shape of the numerical solution matches the moving shape of the true solution. The match rates of these two kinds of moving shapes are sequentially calculated by the G-Euler process without using the true solution. It is shown that the closer the minimum match rate is to 100%, the more closely the numerical solutions follow the true solutions to the end. The minimum match rate indicates the reliability of the numerical solution calculated by the G-Euler process. The graphs of the Lorenz system in Perko [1] are different from those drawn by the G-Euler process. By the way, there is no basis for claiming that the Perko's graphs are reliable.

• Structural Engineering and Mechanics
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• v.32 no.4
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• pp.501-516
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• 2009

This paper aims to study the large deflections of variable-arc-length elastica subjected to the terminal forces (e.g., axial force and torque). Based on Kirchhoff's rod theory and with help of Euler parameters, the set of nonlinear governing differential equations which free from the effect of singularity are established together with boundary conditions. The system of nonlinear differential equations is solved by using the shooting method with high accuracy integrator, seventh-eighth order Runge-Kutta with adaptive step-size scheme. The error norm of end conditions is minimized within the prescribed tolerance ($10^{-5}$). The behavior of VAL elastica is studied by two processes. One is obtained by applying slackening first. After that keeping the slackening as a constant and then the twist angle is varied in subsequent order. The other process is performed by reversing the sequence of loading in the first process. The results are interpreted by observing the load-deflection diagram and the stability properties are predicted via fold rule. From the results, there are many interesting aspects such as snap-through phenomenon, secondary bifurcation point, loop formation, equilibrium configurations and effect of variable-arc-length to behavior of elastica.

• Transactions of Materials Processing
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• v.16 no.4 s.94
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• pp.276-281
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• 2007

The hardening and the constitutive equation based on the crystal plasticity are introduced for the numerical simulation of hemispherical sheet metal forming. For calculating the deformation and the stress of the crystal, Taylor's model of the crystalline aggregate is employed. The hardening is evaluated by using the Taylor factor, the critical resolved shear stress of the slip system, and the sum of the crystallographic shears. During the hemispherical forming process, the texture of the sheet metal is evolved by the plastic deformation of the crystal. By calculating the Euler angles of the BCC sheet, the texture evolution of the sheet is traced during the forming process. Deformation texture of the BCC sheet is represented by using the pole figure. The comparison of the strain distribution and punch force in the hemispherical forming process between the prediction using crystal plasticity and experiment shows the verification of the crystal plasticity-based formulation and the accuracy of the hardening and constitutive equation obtained from the crystal plasticity.

• ETRI Journal
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• v.37 no.5
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• pp.929-939
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• 2015

Ultra-high-frequency radio-frequency identification (UHF RFID) is widely applied in different industries. The Frame Slotted ALOHA in EPC C1G2 suffers severe collisions that limit the efficiency of tag recognition. An efficient full-duplex anti-collision scheme is proposed to reduce the rate of collision by coordinating the transmitting process of CDMA UWB uplink and UHF downlink. The relevant mathematical models are built to analyze the performance of the proposed scheme. Through simulation, some important findings are gained. The maximum number of identified tags in one slot is g/e (g is the number of PN codes and e is Euler's constant) when the number of tags is equal to mg (m is the number of slots). Unlike the Frame Slotted ALOHA, even if the frame size is small and the number of tags is large, there aren't too many collisions if the number of PN codes is large enough. Our approach with 7-bit Gold codes, 15-bit Gold codes, or 31-bit Gold codes operates 1.4 times, 1.7 times, or 3 times faster than the CDMA Slotted ALOHA, respectively, and 14.5 times, 16.2 times, or 18.5 times faster than the EPC C1 G2 system, respectively. More than 2,000 tags can be processed within 300 ms in our approach.

• Structural Monitoring and Maintenance
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• v.4 no.2
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• pp.115-131
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• 2017

Classical flutter of wind turbine blades indicates a type of aeroelastic instability with fully attached boundary layer where a torsional blade mode couples to a flapwise bending mode, resulting in a mutual rapid growth of the amplitudes. In this paper the monitoring problem of onset of flutter is investigated from a detection point of view. The criterion is stated in terms of the exceeding of a defined envelope process of a specific maximum torsional vibration threshold. At a certain instant of time, a limited part of the previously measured torsional vibration signal at the tip of blade is decomposed through the Empirical Mode Decomposition (EMD) method, and the 1st Intrinsic Mode Function (IMF) is assumed to represent the response in the flutter mode. Next, an envelope time series of the indicated modal response is obtained in terms of a Hilbert transform. Finally, a flutter onset criterion is proposed, based on the indicated envelope process. The proposed online flutter monitoring method provided a practical and direct way to detect onset of flutter during operation. The algorithm has been illustrated by a 907-DOFs aeroelastic model for wind turbines, where the tower and the drive train is modelled by 7 DOFs, and each blade by means of 50 3-D Bernoulli-Euler beam elements.

• Nuclear Engineering and Technology
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• v.54 no.10
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• pp.3909-3918
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• 2022

In the event of a severe accident, the reactor core may melt due to insufficient cooling. the high-temperature core melt will have a strong interaction (FCI) with the coolant, which may lead to steam explosion. Steam explosion would pose a serious threat to the safety of the reactors. Therefore, the study of steam explosion is of great significance to the assessment of severe accidents in nuclear reactors. This research focuses on the development of a two-dimensional steam explosion integrated analysis code called SEINA. Based on the semi-implicit Euler scheme, the three-phase field was considered in this code. Besides, the influence of evaporation drag of melt and the influence of solidified shell during the process of melt droplet fragmentation were also considered. The code was simulated and validated by FARO L-14 and KROTOS KS-2 experiments. The calculation results of SEINA code are in good agreement with the experimental results, and the results show that if the effects of evaporation drag and melt solidification shell are considered, the FCI process can be described more accurately. Therefore, it is proved that SEINA has the potential to be a powerful and effective tool for the analysis of steam explosions in nuclear reactors.