• Structural Engineering and Mechanics
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• v.21 no.3
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• pp.351-367
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• 2005

Multi-span beams carrying multiple point masses are widely used in engineering applications, but the literature for free vibration analysis of such structural systems is much less than that of single-span beams. The complexity of analytical expressions should be one of the main reasons for the last phenomenon. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-span uniform beam carrying multiple point masses. First, the coefficient matrices for an intermediate pinned support, an intermediate point mass, left-end support and right-end support of a uniform beam are derived. Next, the overall coefficient matrix for the whole structural system is obtained using the numerical assembly technique of the finite element method. Finally, the natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the related eigenfunctions respectively. The effects of in-span pinned supports and point masses on the free vibration characteristics of the beam are also studied.

• Nuclear Engineering and Technology
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• v.44 no.2
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• pp.207-224
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• 2012

This article discusses selects of some outstanding problems in nuclear reactor analysis, with proposed approaches thereto and numerical test results, as follows: i) multi-group approximation in the transport equation, ii) homogenization based on isolated single-assembly calculation, and iii) critical spectrum in Monte Carlo depletion.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.531-550
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• 2008

This paper adopts the numerical assembly method (NAM) to determine the exact solutions of natural frequencies and mode shapes of a multi-span and multi-step beam carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and springmass systems. First, the coefficient matrix for an intermediate station with various concentrated elements, cross-section change and/or pinned support and the ones for the left-end and right-end supports of a beam are derived. Next, the overall coefficient matrix for the entire beam is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact solutions for the natural frequencies of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and the associated mode shapes are obtained by substituting the corresponding values of integration constants into the associated eigenfunctions.

• The KSFM Journal of Fluid Machinery
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• v.18 no.6
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• pp.5-11
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• 2015

In a pressurized water reactor (PWR), control rod assembly (CRA) falls into the guide tubes of a fuel assembly due to gravity for scram. Various theoretical approaches and numerical analyses have been performed because its shape is simple and its design was completely developed several decades ago. A control rod assembly for a sodium-cooled faster reactor (SFR) which is geometrically more complicated is being actively developed in Korea nowadays. Drop time and impact velocity of a CRA are important parameters with respect to reactivity insertion time and the mechanical robustness of a CRA and a guide duct. In this paper, computational method considering simultaneously the equation of motion for rigid body and the Navier-Stokes equations for fluid is suggested and verified by comparison with theoretical analysis results. Through this valuable CFD analysis method, drop time and impact velocity of initially designed SFR CRA are evaluated before performing scram tests with it.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.399-416
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• 2010

The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of a multi-step beam carrying multiple rigid bars, with each of the rigid bars possessing its own mass and rotary inertia, fixed to the beam at one point and supported by a translational spring and/or a rotational spring at another point. Where the fixed point of each rigid bar with the beam does not coincide with the center of gravity the rigid bar or the supporting point of the springs. The effects of the distance between the "fixed point" of each rigid bar and its center of gravity (i.e., eccentricity), and the distance between the "fixed point" and each linear spring (i.e., offset) are studied. For a beam carrying multiple various concentrated elements, the magnitude of each lumped mass and stiffness of each linear spring are the well-known key parameters affecting the free vibration characteristics of the (loaded) beam in the existing literature, however, the numerical results of this paper reveal that the eccentricity of each rigid bar and the offset of each linear spring are also the predominant parameters.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.701-717
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• 2006

In the existing reports regarding free transverse vibrations of the Euler-Bernoulli beams, most of them studied a uniform beam carrying various concentrated elements (such as point masses, rotary inertias, linear springs, rotational springs, spring-mass systems, ${\ldots}$, etc.) or a stepped beam with one to three step changes in cross-sections but without any attachments. The purpose of this paper is to utilize the numerical assembly method (NAM) to determine the exact natural frequencies and mode shapes of the multiple-step Euler-Bernoulli beams carrying a number of lumped masses and rotary inertias. First, the coefficient matrices for an intermediate lumped mass (and rotary inertia), left-end support and right-end support of a multiple-step beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact natural frequencies and the associated mode shapes of the vibrating system are determined by equating the determinant of the last overall coefficient matrix to zero and substituting the corresponding values of integration constants into the associated eigenfunctions, respectively. The effects of distribution of lumped masses and rotary inertias on the dynamic characteristics of the multiple-step beam are also studied.

• Nuclear Engineering and Technology
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• v.33 no.1
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• pp.93-101
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• 2001

The spacer grid is one of the main structural components in the fuel assembly, which supports the fuel rods, guides cooling water, and protects the system from an external impact load, such as earthquakes. Therefore, the mechanical and structural properties of the spacer grids must be extensively examined while designing them. In this paper, a numerical method for predicting the buckling strength of spacer grids is presented. Numerical analyses on the buckling behavior of the spacer grids are performed for a various array of sizes of the grids considering that the spacer grid is an assembled structure with thin-walled plates and imposing proper boundary conditions by nonlinear dynamic finite element method using ABAQUS/Explicit. Buckling tests on several numbers of specimens of the spacer grid were also carried out in order to compare the results between the test and the simulation result. The drop test is accomplished by dropping a carriage on the specimen at a pre-determined position. From this test, the specimens are buckled only at the uppermost and the lowermost layer among the multi-cells, which is similar to the local buckling at the weakest point of the grid structure. The simulated results also similarly predicted the local buckling phenomena and were found to give good correspondence with the experimental values for the thin-walled grid structures.

• Nuclear Engineering and Technology
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• v.48 no.1
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• pp.33-42
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• 2016

Spacer grids play an important role in maintaining the proper form of the fuel assembly structure and ensuring the safety of reactor core design. This study applies the Monte Carlo method to the analysis of the neutronics effects of spacer grids in a typical pressurized water reactor (PWR). The core problem used to analyze the neutronics effects of spacer grids is a modified version of Korea Advanced Institute of Science and Technology benchmark problem 1B, based on an Advanced Power Reactor 1400 (APR1400) core model. The spacer grids are modeled and added to this test problem in various ways. Then, by running MCNP5 for all cases of spacer grid modeling, some important numerical results, such as the effective multiplication factor, the spatial distributions of neutron flux, and its energy spectrum are obtained. The numerical results of each case of spacer grid modeling are analyzed and compared to assess which type has more advantages in accuracy of numerical results and effectiveness in terms of geometry building. The conclusion is that the most realistic modeling for Monte Carlo calculation is the "volume-preserving" streamlined heterogeneous spacer grids, but the "banded" dissolution spacer grids modeling is a more practical yet accurate model for routine (deterministic) analysis.

• Proceedings of the KWS Conference
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• 2006.05a
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• pp.92-93
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• 2006

In recent time there are vigorous requirement for the use of thick steel plate in various industrial fields including shipbuilding industry. Application of TMCP steel plates, especially, is increase progressively. As a welding process for thick steel plate assembly high heat input welding method is used. However, HAZ softening of TMCP steel plates has a possibility to reduce the strength of welded joint. In this study, therefore, tensile strength of TMCP welds had softened HAZ was examined using numerical calculation and experiment.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.153-176
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• 2003

From the equation of motion of a "bare" non-uniform beam (without any concentrated elements), an eigenfunction in term of four unknown integration constants can be obtained. When the last eigenfunction is substituted into the three compatible equations, one force-equilibrium equation, one governing equation for each attaching point of the concentrated element, and the boundary equations for the two ends of the beam, a matrix equation of the form [B]{C} = {0} is obtained. The solution of |B| = 0 (where ${\mid}{\cdot}{\mid}$ denotes a determinant) will give the "exact" natural frequencies of the "constrained" beam (carrying any number of point masses or/and concentrated springs) and the substitution of each corresponding values of {C} into the associated eigenfunction for each attaching point will determine the corresponding mode shapes. Since the order of [B] is 4n + 4, where n is the total number of point masses and concentrated springs, the "explicit" mathematical expression for the existing approach becomes lengthily intractable if n > 2. The "numerical assembly method"(NAM) introduced in this paper aims at improving the last drawback of the existing approach. The "exact"solutions in this paper refer to the numerical results obtained from the "continuum" models for the classical analytical approaches rather than from the "discretized" ones for the conventional finite element methods.