• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.37-49
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• 1999

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, We also have a good approximations of the largest eigenvalue of a Symmetric matrix from Lanczos algorithm. We apply it for the largest eigenproblem of a very large symmetric matrix with a good initial points.

• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.561-573
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• 2011

For efficient calculation of natural modes of structures, a numerical scheme which accelerates convergence of the subspace iteration method by employing accelerated starting Lanczos vectors was proposed in 2005. This paper is an extension of the study. The previous study simply showed feasibility of the proposed method by analyzing structures with smaller degrees of freedom. While, the present study verifies efficiency of the proposed method more rigorously by comparing closeness of conventional and accelerated starting vectors to genuine eigenvectors. This study also analyzes an example structure with larger degrees of freedom and more complex constraints in order to investigate applicability of the proposed method.

• Journal of Korea Society of Industrial Information Systems
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• v.4 no.4
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• pp.88-93
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• 1999

Several Iterative methods are considered, Gram-Schmidt algerian for thin orthogonalization and Lanczos methodfor a few extreme eigenvalues. For these methods, a variants of method is derived for which only one synchronization point per on iteration is required; that is one global communication in a message passing distributed-memory machine per one iteration is required The variant is called restructured method, and restructured method has better parallel properties to the conventional method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.1 s.94
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• pp.112-117
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• 2005

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in order to accelerate the convergence of the subspace iteration method. Proposed methods are divided into two forms according to the number of starting vectors. The first method composes 2p starting vectors when the number of required modes is p and the second method uses 1.5p starting vectors. To investigate the efficiency of proposed methods, two numerical examples are presented.

• Steel and Composite Structures
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• v.44 no.2
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• pp.171-181
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• 2022

Functionally graded material (FGM) has been spotlighted as an advanced composite material due to its excellent thermo-mechanical performance. And the buckling of FGM resting on elastic foundations has been a challenging subject because its behavior is directly connected to the structural safety. In this context, this paper is concerned with a numerical buckling analysis of metal-ceramic FG plates resting on a two-parameter (Pasternak-type) elastic foundation. The buckling problem is formulated based on the neutral surface and the (1,1,0) hierarchical model, and it is numerically approximated by 2-D natural element method (NEM) which provides a high accuracy even for coarse grid. The derived eigenvalue equations are solved by employing Lanczos and Jacobi algorithms. The numerical results are compared with the reference solutions through the benchmark test, from which the reliability of present numerical method has been verified. Using the developed numerical method, the critical buckling loads of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1852-1861
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• 1997

An enhanced subspace iteration algorithm has been developed to solve eigenvalue problems reliably and efficiently. Basic subspace iteration algorithm has been improved by eliminating recalculation of converged eigenvectors, using Krylov sequence as initial vectors and incorporating with shifting techniques. The number of iterations and computational time have been considerably reduced when compared with the original one, and reliability for catching copies of the multiple roots has been retained successfully. Further research would be required for mathematical justification of the present method.

• 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.

• Proceedings of the KAIS Fall Conference
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• 2012.05b
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• pp.631-633
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• 2012

본 논문은 구조용 후판 강재로 절곡되었을 때, 절곡부재의 구조연성 변화에 대한 해석 방안과 이에 따른 해석적 평가 사례를 제시하고 있다. 절곡 방법에 의한 제작과정에서 재료는 변형경화 현상이 발생한다. 이로 인해 구조연성 저하가 불가피하기 때문에 절곡부재의 휨연성 검토가 필요하다. 해석 방안은 유한요소해석 프로그램인 ABAQUS를 이용하였다. Lanczos 알고리즘을 적용한 고유치해석과 재료 비탄성-기하비선형을 고려한 비선형 해석을 하였다. 비선형해석 절곡에 의한 재료특성을 고려하였다. 극한 하중과 파괴모드를 평가하기 위해 Newton-Raphson method, modified Riks method를 적용한 단계별 하중재하 해석을 실시하였다. 본 연구를 통해 휨연성을 평가하는데 활용 될 것으로 판단된다.

• Journal of KSNVE
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• v.8 no.4
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• pp.690-699
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• 1998

This paper discusses the techniques, procedures and the results of the ground vibration test(GVT) performed on the development aircraft and the simple procedure of FE model updating technique from the GVT results. The GVT was carried out using random excitation technique with MIMO(Multi-Input-Multi-Output) data acquistion method, and taking full advantage of poly-reference global parameter estimation technique to identify the vibration modes. In dynamic FE modeling, the aircraft was represented by beam elements and all dynamic analysis was performed using MSC/NASTRAN for this model. In updating procedure, the stiffness of the beam model was adjusted iteratively so as to get the natural frequencies and mode shapes close to the GVT results.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.743-749
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• 2007

Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large size problems, but, originally, it was designed to calculate only the smallest eigenvalues. In this paper, an updated version of AS is proposed to calculate the interior eigenvalues over a specified range by using a shift value, which is referred to as the shifted AS. Numerical experiments demonstrate that the proposed method has better efficiency to compute numerous interior eigenvalues for the finite element models of structural problems than a Lanczos-type method.