• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.323-332
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• 2022

This paper presents a numerical study on multigrid algorithms of V-cycle type for problems posed in the Hilbert space H(curl) in three dimensions. The multigrid methods are designed for discrete problems originated from the discretization using the hexahedral Nédélec edge element of the lowest-order. Our suggested methods are associated with smoothers constructed by substructuring based on domain decomposition methods of nonoverlapping type. Numerical experiments to demonstrate the robustness and the effectiveness of the suggested algorithms are also provided.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1133-1145
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• 2000

It is necessary to develop an efficient analysis method to identify the dynamic characteristics of a large mechanical structure and update its finite element model. That is because these processes need the huge computation of a large structure and iterative estimation due to the use of the first- order sensitivity. To efficiently carry out these processes, a new method, called the generalized free-interface mode sensitivity method, has been proposed in the authors' preceeding paper. This method is based on substructuring approach such as a free-interface method and a generalized synthesis algorithm. In this paper, the proposed method is applied to the model updating of a car body structure to verify its accuracy and reliability for a large mechanical structure.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.16-22
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• 2001

In this study for reduction degree of freedom of dynamic model, a mixed method to combined finite element method and transfer matrix method is presented. This offers the advantages of an automatic reduction in the size of the eigenvalues problem and of a straightforward means of dynamic substructuring. The analytical procedure in this method for dynamic analysis of 3-dimensional cantilevered box beam are described. the result of numerical example is shown to demonstate the efficiency and accuracy of this method. The result form this example agree well those obtained by ANSYS, By using this technique, the number of nodes required in the regular finite element method is reduced and therefore a smaller com-puter can be used.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.201-206
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• 2000

In this work transfer function synthesis method based on FRF data of each substructure is investigated for a complex structure composed of many substructures. Though the transfer function synthesis method has superiority to analyze the characteristics of interfaces among substructures effectively, many problems arise in the computation process, especially matrix inversion process. Due to computational problems, the error between the data obtained by test and the predictions through computations is inevitable. So in this paper, computational aspects in the transfer function synthesis method are examined through a steering system problem of passenger car. For the FBS method, frequency response functions of 3 substructures are measured experimentally. Effects of several parameters such as matrix inversion method, connection conditions between substructures and off-diagonal terms on system response are studied numerically.

• Structural Engineering and Mechanics
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• v.7 no.6
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• pp.575-588
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• 1999

A boundary element method is applied to the analysis of crack trajectory in materials with complex microstructure, such as discontinuously reinforced composite materials, and systems subjected to complex loading, such as indentation. The path followed by the crack(s) has non-trivial geometry. A study of the stress intensity factors and fracture toughness of such systems must therefore be accompanied by an analysis of crack trajectory. The simulation is achieved using a dual boundary integral method in planar problems, and a single boundary integral method coupled with substructuring in axisymmetric problems. The direction of crack propagation is determined using the maximum mechanical energy release rate criterion. The method is demonstrated by application to (i) a composite material composed of components having the elastic properties of aluminium (matrix) and silicon carbide (reinforcement), and (ii) analysis of contact damage induced by the action of an indenter on brittle materials. The chief advantage of the method is the ease with which problems having complex geometry or loading (giving rise to complex crack trajectories) can be treated.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.359-368
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• 2018

Dynamic analysis of complex and large structures may be costly from a numerical point of view. For coupled vibroacoustic finite element models, the importance of reducing the size becomes obvious because the fluid degrees of freedom must be added to the structural ones. In this paper, a component mode synthesis method is proposed for large vibroacoustic interaction problems. This method couples fluid subdomains and dynamical substructuring of Craig and Bampton type. The acoustic formulation is written in terms of the velocity potential, which implies several advantages: coupled algebraic systems remain symmetric, and a potential formulation allows a direct extension of Craig and Bampton's method to acoustics. Those properties make the proposed method easy to implement in an existing finite element code because the local numerical treatment of substructures and fluid subdomains is undifferentiated. Test cases are then presented for axisymmetric geometries. Numerical results tend to prove the validity and the efficiency of the proposed method.

• Journal of KSNVE
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• v.8 no.1
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• pp.139-145
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• 1998

A great deal of effort has been invested in upgrading the performance and the efficiency of dynamic analysis of mechanical structures. Using experimental modal analysis(EMA) or finite element analysis(FEA) data of mechanical structures, the performance and efficiency can be effectively evaluated. In order to analyze complex structures such as automobiles and aircrafts, for the sake of computing efficiency, the dynamic substructuring techniques that allow to predict the dynamic behavior of a structure are widely used. Through linking a modal model obtained from EMA and an analytical model obtained from FEA, the best conditioned strucutres can be proposed. In this study, a new algorithm of substructre synthesis method, Multi-FRF synthesis method, is proposed to analyze a structure composed of many substructures.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.356-361
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• 2008

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the previous study, we proposed a two-level condensation scheme (TLCS) for the construction of a reduced system. And we have improved previous TLCS with combination of the iterated improved reduced system method (IIRS) to increase accuracy of the higher modes intermediate range. In this study, we apply previous improved TLCS to multi-level sub-structuring scheme. In the first step, the global system is recursively partitioned into a hierarchy of sub-domain. In second step, each uncoupled sub-domain is condensed by the improved TLCS. After assembly process of each reduced sub-eigenvalue problem, eigen-solution is calculated by Lanczos method (ARPACK). Finally, Numerical examples demonstrate performance of proposed method.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1529-1536
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• 2004

A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3782-3791
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• 1996

A great deal of effert has been invested in upgrading the performance and the efficiency of mechanical structures. Using experimental modal analysis(EMA) or finite element analysis(FEA) data of mechanical structures, this performance and efficiency can be effectively evaluated. In order to analyze complex structures such as automobiles and aircraft, for the sake of computing efficiency, the dynamic substructuring techniques that allow to predict the dynamic behavior of a structure based on that of the composing structures, are widely used. By llinking a modal model obtained from EMA and an analytical model obtained from FEA, the best conditioned structures can be desinged. In this paper, a new algorithm for structural dynamic modification-SRFSM (substructure response function sensitivity method) is proposed by linking frequency responce function synthesis and response function sensitivity. A mehtod to obtain response function sensitivity using direct derivative of mechanical impedance, is also used.