• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.29-36
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• 2004

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

• 한국전산유체공학회지
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• 제4권2호
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• pp.67-73
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• 1999

In the present paper, three types of the flow solvers were used to investigate the influence on the airfoil shape optimization. The adopted equations, i.e., Euler, thin layer Navier-Stokes and full Navier-Stokes ones. are solved using implicit LU-ADI decomposition scheme. The gradient projection method with the sinusoidal function was used as an optimization algorithm. The present numerical method was applied to the drag minimization problems under the initial shape of NACA0012 airfoils.

• Structural Engineering and Mechanics
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• 제5권6호
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• pp.679-689
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• 1997

The damage of concrete subjected to multiaxial complex loading involves strong anisotropy due to its highly heterogeneous nature and the geometrically anisotropic characteristic of the microcracks. A comprehensive description of concrete damage is proposed by introducing a fourth-order anisotropic damage tenser. The evolution of damage is assumed to be related to the principal components of the current states of stress and damage. The unilateral effect of damage due to the closure and opening of microcracks is taken into account by introducing projection tensors that are also determined by the current state of stress. The proposed damage model considers the different kinds of damage mechanisms that result in different failure modes and different patterns of microdefects that cause different unilateral effects. This damage model is embedded in a thermomechanically consistent constitutive equation in which hardening and the triaxial compression caused shear-enhanced compaction can also be taken into account. The validity of the proposed model is verified by comparing theoretical and experimental results of plain and steel fiber reinforced concrete subjected to complex triaxial stress histories.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.25-37
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• 2001

We consider the finite element method applied to nonlinear Sobolev equation with smooth data and demonstrate for arbitrary order ($k{\geq}2$) finite element spaces the optimal rate of convergence in $L_{\infty}\;W^{1,{\infty}}({\Omega})$ and $L_{\infty}(L_{\infty}({\Omega}))$ (quasi-optimal for k = 1). In other words, the nonlinear Sobolev equation can be approximated equally well as its linear counterpart. Furthermore, we also obtain superconvergence results in $L_{\infty}(W^{1,{\infty}}({\Omega}))$ for the difference between the approximate solution and the generalized elliptic projection of the exact solution.

• 대한기계학회논문집
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• 제14권5호
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• pp.1059-1068
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• 1990

본 연구에서는 4변이 단순지지되고 보강재가 등간격으로 조밀하게 배치된 편 면직교보강평판에 조합하중이 작용하는 경우 최소중량화에 따른 최적설계변수들을 비 선형 최적화기법인 미분벡터유영법(gradient projection method)에 의하여 산정한다. 설계제한조건으로 전체좌굴응력, 평판및 보강재의 국부좌굴응력, 각부의 항복응력제한 그리고 설계변수들의 상, 하한치의 제한등을 설정하고 전체좌굴에 대한 지배방정식으 로 등가의 직교이방성 평판의 좌굴에 관한 평형방정식을 사용한다. 직교 보강의 경 우 기존연구결과와 비교, 분석하여 본 해석의 유용성을 입증하고 조합하중의 작용에 따른 대칭경사보강의 효율성도 검토한다.

• 소성∙가공
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• 제28권3호
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• pp.145-153
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• 2019

The objective of this study is to analyze the mechanical splicing characteristic of the threaded bar according to the contact conditions of the transverse rib. In order to consider the contact conditions of the rib, selection of the main variables including the gap of the core diameter ($l_c$), rib angle (${\theta}$), and the number of contacts ($C_N$) of transverse rib was done. So as to analyze the splicing characteristic of the D51 threaded bar, a finite element (FE) simulation of the tensile test was conducted using the designed D51 threaded bar and coupler. Through FE simulation results, it was verified that the mechanical slicing characteristics varied based on the main design variables ($l_c$, ${\theta}$, and $C_N$). It was further confirmed that it was important to determine the $C_N$ in consideration of $l_c$. Additionally, the tensile test results of the D25 and D51 threaded bar combined with the couplers were similar to FE simulation results. Furthermore, to quantitatively evaluate FE simulation and test results, the calculation equation for the contacted projection area ratio (R) of the transverse rib was proposed. To secure a mechanical splicing joint of the threaded bar, it was established that the R calculated using the proposed equation had to be greater or equal to 40%.

• Nuclear Engineering and Technology
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• 제56권8호
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• pp.2948-2957
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• 2024

High-order harmonic techniques can be used to recreate neutron flux distributions in reactor cores using the neutron diffusion equation. However, traditional source iteration and source correction iteration techniques have sluggish convergence rates and protracted calculation periods. The correctness of the implicitly restarted Arnoldi method (IRAM) in resolving the eigenvalue problems of the one-dimensional and two-dimensional neutron diffusion equations was confirmed by computing the benchmark problems SLAB_1D_1G and two-dimensional steady-state TWIGL using IRAM. By integrating Galerkin projection with Proper Orthogonal Decomposition (POD) techniques, a POD-Galerkin reduced-order model was developed and the IRAM model was used as the full-order model. For 14 macroscopic cross-section values, the TWIGL benchmark problem was perturbed within a 20% range. We extracted 100 sample points using the Latin hypercube sampling method, and 70% of the samples were used as the testing set to assess the performance of the reduced-order model The remaining 30% were utilized as the training set to develop the reduced-order model, which was employed to rebuild the TWIGL benchmark problem. The reduced-order model demonstrates good flexibility and can efficiently and accurately forecast the effective multiplication factor and neutron flux distribution in the core. The reduced-order model predicts k_eff and neutron flux distribution with a high degree of agreement compared to the full-order model. Additionally, the reduced-order model's computation time is only 10.18% of that required by the full-order model.The neutron flux distribution of the steady-state TWIGL benchmark was recreated using the reduced-order model. The obtained results indicate that the reduced-order model can accurately predict the k_eff and neutron flux distribution of the steady-state TWIGL benchmark.Overall, the proposed technique not only has the potential to accurately project neutron flux distributions in transient settings, but is also relevant for reconstructing neutron flux distributions in steady-state conditions; thus, its applicability is bound to increase in the future.

• 전기학회논문지P
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• 제66권3호
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• pp.129-134
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• 2017

We investigated theoretically the quantum optical transition properties of Si, in quasi 2-Dimensinal Landau splitting system, based on quantum transport theory. We apply the quantum transport theory (QTR) to the system in the confinement of electrons by square well confinement potential under linearly polarized oscillating field. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS). In order to analyze the quantum transition, we compare the temperature and the magnetic field dependencies of the QTLW and the QTLS on four transition processes, namely, the intra-leval transition process, the inter-leval transition process, the phonon emission transition process and the phonon absorption transition process.

• Wind and Structures
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• 제12권1호
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• pp.1-19
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• 2009

In this paper, the airflow around an ideal thin plate (hereafter referred to as ITP) with various ratios of central slot is simulated by using the finite-difference-method (FDM)-based Arbitrary-Lagrangian-Eulerian descriptions for the rigid oscillating body. The numerical procedure employs the second-order projection scheme to decouple the governing equations, and the multigrid algorithm with three levels to improve the computational efficiency in evaluating of the pressure equation. The present CFD method is validated through comparing the computed flutter derivatives of the ITP without slot to Theodorsen analytical solutions. Then, the unsteady aerodynamics of the ITP with and without central slot is investigated. It is found that even a smaller ratio of central slot of the ITP has notable effects on pressure distributions of the downstream section, and the pressure distributions on the downstream section will further be significantly affected by the slot ratio and the reduced wind speeds. Continuous increase of $A_2^*$ with the increase of central slot may be the key feature of the slotted ITP. Finally, flutter analyses based on the flutter derivatives of the slotted ITP are performed, and moreover, flutter instabilities of a scaled sectional model of a twin-deck bridge with various ratios of deck slot are investigated. The results confirm that the central slot is effective to improve bridge flutter stabilities, and that the flutter critical wind speeds increase with the increase of slot ratio.

• Journal of Electrical Engineering and Technology
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• 제13권1호
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• pp.352-361
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• 2018

This paper proposes a sensing system of the Halbach array permanent magnet spherical motor(PMSM). The rotor position can be obtained by solving three rotation angles, which revolves around 3 reference axes of the stator. With the development of 3-D hall sensor, the position identification problem of the Halbach array PMSM based on rotor magnetic field is studied in this paper. A nonlinear and serious coupling relationship between the rotation angles and the measured magnetic flux density is established on the basis of the rotation transformation theory and the magnetic field model. In order to get rid of the influence on position detection caused by the harmonics of rotor magnetic field and the stator coil magnetic field, a sensor location combination scheme is proposed. In order to solve the nonlinear equation fast and accurately, a new position solution algorithm which combines the merits of gradient projection and particle swarm optimization(PSO) is presented. Then the rotation angles are obtained and the rotor position is identified. The validity of the sensing system is verified through the simulation.