• 한국공간구조학회논문집
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• 제24권1호
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• pp.65-72
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• 2024

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

• 동력기계공학회지
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• 제15권6호
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• pp.95-100
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• 2011

In this study, an evaluation equation of energy efficiency of pneumatic driving apparatus is proposed. The evaluation equation is derived from state equation and energy equation of air in a control volume, and, the equation of motion of a moving part of a pneumatic cylinder. As a result, distribution of consumption energy and energy efficiency of pneumatic driving apparatus can be analyzed quantitatively. The effectiveness of the proposed method is proved by a pneumatic cylinder driving apparatus using a meter-out driving method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제23권1호
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• pp.1-18
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• 2019

In contrast to the well-developed convex splitting schemes for gradient flows of two-component system, there were few efforts on applying the convex splitting idea to gradient flows of multi-component system, such as the vector-valued Cahn-Hilliard (vCH) equation. In the case of the vCH equation, one need to consider not only the convex splitting idea but also a specific method to manage the partition of unity constraint to design an unconditionally energy stable scheme. In this paper, we propose a constrained Convex Splitting (cCS) scheme for the vCH equation, which is based on a convex splitting of the energy functional for the vCH equation under the constraint. We show analytically that the cCS scheme is mass conserving and unconditionally uniquely solvable. And it satisfies the constraint at the next time level for any time step thus is unconditionally energy stable. Numerical experiments are presented demonstrating the accuracy, energy stability, and efficiency of the proposed cCS scheme.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 춘계학술대회논문집
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• pp.277-282
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• 2009

A temperature equation which is derived from an enthalpy transport equation by using an assumption of a constant specific heat is very attractive for analyses of heat and fluid flows. It can be used for an analysis of a solid-fluid conjugate heat transfer, and it does not need a numerical method to find temperature from a temperature-enthalpy relation. But its application is limited because of the assumption. A new method is derived in this study, which is a temperature-explicit formulation of the energy equation. The enthalpy form of the energy equation is used in the method. But the final discrete form of the equation is expressed with temperature. It can be used for a solid-fluid conjugate heat transfer and multiphase flows. It is found by numerical tests that it is very efficient and as accurate as the standard enthalpy formulation.

• 한국토양비료학회지
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• 제44권3호
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• pp.337-343
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• 2011

A particular empirical equation for rainfall kinetic energy is needed to compute rainfall erosivity, calculated by the annual sum of the product of total rainfall energy and maximum 30-min rainfall intensity. If rainfall kinetic energy equation was different, rainfall erosivity will be produced differently. However, the previous studies in Korea had little concern about rainfall kinetic energy equation and it was not clear which rainfall kinetic energy is suitable for Korea. The purpose of this study is to analyze and evaluate the difference of the rainfall erosivity based on different rainfall kinetic energy equations obtained from previous studies. This study introduced new rainfall erosivity factors based on rainfall kinetic energy equation of Noe and Kwon (1984) that is only regression model developed in Korea. Data of annual rainfall erosivity for 21 weather stations in 1980~1999 were used in this study. The result showed that rainfall erosivity factors by the previous equations had been about 10~20% overestimated than rainfall erosivity by Noe and Kwon (1984)'s equation in Korea.

• East Asian mathematical journal
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• 제19권2호
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• pp.173-187
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• 2003

We study decay estimates of the energy for the nonlinear wave equation in the whole space. We note that the method of proof is based on the multiplier technique and on the unique continuation, and no geometrical condition is imposed on the boundary.

• 대한수학회보
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• 제56권1호
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• pp.265-276
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• 2019

For a simple implementation, a linear convex splitting scheme was coupled with the Fourier spectral method for the Cahn-Hilliard equation with a logarithmic free energy. However, an inappropriate value of the splitting parameter of the linear scheme may lead to incorrect morphologies in the phase separation process. In order to overcome this problem, we present a nonlinear convex splitting Fourier spectral scheme for the Cahn-Hilliard equation with a logarithmic free energy, which is an appropriate extension of Eyre's idea of convex-concave decomposition of the energy functional. Using the nonlinear scheme, we derive a useful formula for the relation between the gradient energy coefficient and the thickness of the interfacial layer. And we present numerical simulations showing the different evolution of the solution using the linear and nonlinear schemes. The numerical results demonstrate that the nonlinear scheme is more accurate than the linear one.

• 대한기계학회논문집
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• 제17권9호
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• pp.2172-2180
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• 1993

Under general loadings, including body forces, crack-face tractions and thermal loading, the energy release rate equation for a two-dimensional cracked body is presented. Defining the virtual crack extension as the variation of the geometry, the equation is directly derived by a shape design sensitivity of the potential energy. Although the form of the derived energy release rate equation is different from other researchers's results, the three example show that the former is exactly the same as the latter. However, the final integral equation do not involve the derivative of the displacement on the crack surface and crack tip region, thereby improving the numerical accuracy in the computation of the energy relase rate. Moreover, as it was derived from the governing equation including non-linear elasticity without special assumptions, the energy release rate of a elasto-plastic fracture can be obtained and any numerical stress analysis method can be applied.

• 대한기계학회논문집
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• 제11권1호
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• pp.1-18
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• 1987

본 연구에서는 입자가 부상된 이상난류제트유동에 Einstein의 확산모형, Pes- kin모형, 3-방정식 모형, 4-방정식 모형, 대수응력모형 등을 적용하여 해석하고 각 모 형들의 결과를 비교 분석하였다. 이상난류유동의 수치해석에서 공기는 제1유체유동 으로 하고 첨가되는 고체분말의 흐름은 밀도(.rho.$_{p}$), 층류동점성계수(.nu.$_{p}$), 과점성계수(.nu.$_{pt}$ )를 갖는 제2유체유동의 흐름으로 간주하였다.

• 에너지공학
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• 제14권2호
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• pp.147-152
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• 2005

본 논문에서는 화력발전소 보일러 연료소비량을 측정에 의하지 않고 계산으로 구하는 방법을 세부 항목 별로 유도하고 그 결과를 검증하였다. 보일러 경계를 출입하는 Energy in Energy out의 정량적 관계를 분석하여 Energy in에 해당하는 투입열량과 Energy out에 해당하는 흡수열량 및 손실열량으로부터 에너지 출입의 유기적인 관계식을 수립하여 연료소비량 계산식을 유도, 정립하고 실제 운전중인 석탄 및 중 유연소 발전소에 적응하여 계산식의 정확성을 검증하였다.