• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.12
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• pp.3991-4002
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• 1996

Thermally fully developed and thermally developing laminar flows of a Bingham plastic in a circular pipe have been studied analytically. For thermally fully developed flow, the Nusselt numbers and temperature profiles are presented in terms of the yield stress and Peclet number, proposing a correlation formula between the Nusselt number and the Peclet number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet and Brinkman numbers on the Nusselt number are discussed.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1326-1338
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• 2017

The continuous energy Monte Carlo neutron transport code, MC21, was coupled to the CTF subchannel thermal-hydraulics code using a combination of Consortium for Advanced Simulation of Light Water Reactors (CASL) tools and in-house Python scripts. An MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 6 demonstrated good agreement with MC21/COBRA-IE and VERA solutions. The MC21/CTF solution for VERA Core Physics Benchmark Progression Problem 7, Watts Bar Unit 1 at beginning of cycle hot full power equilibrium xenon conditions, is the first published coupled Monte Carlo neutronics/subchannel T-H solution for this problem. MC21/CTF predicted a critical boron concentration of 854.5 ppm, yielding a critical eigenvalue of $0.99994{\pm}6.8E-6$ (95% confidence interval). Excellent agreement with a VERA solution of Problem 7 was also demonstrated for integral and local power and temperature parameters.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.27-47
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• 2012

It has become apparent from the recent work by Choi et al. [3] on the nonlinear beam deflection problem, that analysis of the integral operator $\mathcal{K}$ arising from the beam deflection equation on linear elastic foundation is important. Motivated by this observation, we perform investigations on the eigenstructure of the linear integral operator $\mathcal{K}_l$ which is a restriction of $\mathcal{K}$ on the finite interval [$-l,l$]. We derive a linear fourth-order boundary value problem which is a necessary and sufficient condition for being an eigenfunction of $\mathcal{K}_l$. Using this equivalent condition, we show that all the nontrivial eigenvalues of $\mathcal{K}l$ are in the interval (0, 1/$k$), where $k$ is the spring constant of the given elastic foundation. This implies that, as a linear operator from $L^2[-l,l]$ to $L^2[-l,l]$, $\mathcal{K}_l$ is positive and contractive in dimension-free context.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• 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.

• Solar Energy
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• v.8 no.1
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• pp.82-94
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• 1988

The hydrodynamic stability equations for natural convection flows adjacent to a vertical isothermal surface in cold or warm water (Boussinesq or non-Boussinesq situation for density relation), constitute a two-point-boundary-value (eigenvalue) problem, which was solved numerically using the simple shooting and the orthogonal collocation method. This is the first instance in which these stability equations have been solved using a computer code COLSYS, that is based on the orthogonal collocation method, designed to solve accurately two-point-boundary-value problem. Use of the orthogonal collocation method significantly reduces the error propagation which occurs in solving the initial value problem and avoids the inaccuracy of superposition of asymptotic solutions using the conventional technique of simple shooting.

• Bulletin of the Society of Naval Architects of Korea
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• v.21 no.2
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• pp.19-27
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• 1984

An extension of the finite element method to the stability analysis of shells of revolution under static axisymmetric loading is presented in this paper. A systematic procedure for the formulation of the problem is based upon the principle of virtual work. This procedure results in an eigenvalue problem. For solution, the shell of revolution is discretized into a series of conical frusta. The buckling mode in the circumferential direction is assumed, this assumption makes the problem economical for the computing time. The present method is applied to a number of shells of revolution, under axial compression or lateral pressure, and comparision are made with other theoretical results. The results show good agreement each other. The effects of aspect ratio, boundary conditions and buckling modes on the buckling strength of shells of revolution are studied. Also the optimum shape of cylindrical shell under uniform axial compression is obtained from the view point of structural stability.

• Nuclear Engineering and Technology
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• v.15 no.2
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• pp.135-141
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• 1983

Computational accuracy of the modified Borresen's coarse-mesh diffusion theory scheme is investigated with the steady-state solutions of the two- and three-dimensional LRA-BWR bench-mark problem. By comparing the numerical results available for the critical eigenvalue and power distribution of the LRA-BWR, it is shown that the modified scheme is capable of predicting the power distribution of the multi-dimensional BWR problem with an improved accuracy.

• Steel and Composite Structures
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• v.48 no.6
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• pp.641-648
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• 2023

In this article, we explore the issue concerning semiconductors half-space comprised of materials with varying thermal conductivity. The problem is within the framework of the generalized thermoelastic model under one thermal relaxation time. The half-boundary space's plane is considered to be traction free and is subjected to a thermal shock. The material is supposed to have a temperature-dependent thermal conductivity. The numerical solutions to the problem are achieved using the finite element approach. To find the analytical solution to the linear problem, the eigenvalue approach is used with the Laplace transform. Neglecting the new parameter allows for comparisons between numerical findings and analytical solutions. This facilitates an examination of the physical quantities in the numerical solutions, ensuring the accuracy of the proposed approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.99-106
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• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.