• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.2 s.257
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• pp.211-220
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• 2007

This work presents an iterated improved reduced system (IIRS) procedure combined with sub-structuring scheme for large structures. Iterated IRS methods are usually more efficient than others because the dynamic condensation matrix is updated repeatedly until the desired convergent values are obtained. However, using these methods simply for large structures causes expensive computational cost and even makes analyses intractable because of the limited computer storage. Therefore, the application of sub-structuring scheme is necessary. Because the large structures are subdivided into several (or more) sub-domains, the construction of dynamic condensation matrix does not require much computation cost in every iteration. This makes the present method much more efficient to compute the eigenpairs both in lower and intermediate modes. In Part I, iterated IRS method combined with sub-structuring scheme for undamped structures is presented. The validation of the proposed method and the evaluation of computational efficiency are demonstrated through the numerical examples.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.1
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• pp.33-42
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• 1987

Grid structures are extensively used in bridge and slab strucures. When the elements are assembled for the entire structure the number of degree of freedom may be very large and thus, the stiffness, mass, and damping matrices become of large dimension. Undoubtedly, determining natural frequencies and mode shapes of such structures are complicated and require large computer costs. For these reasons various eigenvalue economizer procedures have been developed, which serve to reduce the number of degree of freedom. This paper proposes an economic method of dynamic analysis of grid stuctures using static and dynamic condensation techniques. The accuracy and economy of this method are investigated by comparing some results of model analysis of N-degree of freedom. It has been shown that the method achieves remarkable economy at only a little cost of accuracy.

• Architectural research
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• v.10 no.2
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• pp.21-26
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• 2008

The number of measured degrees of freedom for detecting the damage of any structures is usually less than the number of model degrees of freedom. It is necessary to expand the measured data to full set of model degrees of freedom for updating modal data. This study presents the expansion methods to estimate all static displacements and dynamic modal data of finite element model from the measured data. The static and dynamic methods are derived by minimizing the variation of the potential energy and the Gauss's function, respectively. The applications illustrate the validity of the proposed methods. It is observed that the numerical results obtained by the static approach correspond with the Guyan condensation method and the derived static and dynamic approaches provide the fundamental idea for damage detection.

• 한국연소학회:학술대회논문집
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• 2005.10a
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• pp.20-27
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• 2005

I consider the structure of steady wave system which is admitted by the continuum equations for materials that undergo phase transformations with exothermic chemical reaction. In particular, the dynamic phase front structures between liquid and gas phases, and solid and liquid phases are computationally investigated. Based on the one-dimensional continuum shock structure analysis, the present approach can estimate the nano-width of waves that are present in combustion. For illustration purpose, n-heptane is used in the evaporation and condensation analysis and HMX is used in the melting and freezing analysis of energetic materials of interest. On-going effort includes extension of this idea to include broad range of liquid and solid fuels, such as rocket propellants.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.10a
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• pp.19-26
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• 2004

This study constructs the reduced system by two-level condensation scheme. This scheme consists of two steps. First step selects the candidate area for the primary degrees of freedom by energy estimation in element level. In the second step, the primary degrees of freedom are selected by the sequential elimination scheme. The efficiency and reliability of this scheme is shown through the prediction of eigenvalues of a few numerical examples. Time integration in the reduced system can save the computing time effectively. The well-constructed reduced system can present the accurate behavior of the structure under arbitrary dynamic loads so much as the global system. Through the numerical example, the efficiency and reliability of the proposed scheme will be demonstrated.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.873-880
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• 2006

Since the mega frame structure has significant numbers of elements and nodes, it takes tremendous times and computer memories to analyze and design the structures. Therefore, the exclusive structural analysis program for mega frame system is developed to reduce the efforts and time required for the analysis and design of mega frame structure. To this end, an efficient modelling technique using the characteristics of mega frame structures and an efficient analytical model, which uses a few DOFs selected by the user using the matrix condensation method. are developed in tins study. Static and dynamic analyses are conducted using an example structure.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.347-352
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• 2007

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. In the first step, the selection of candidate elements by energy estimation, Rayleigh quotient, through Ritz vector calculation. In the second step, the primary degrees of freedom are selected by the sequential elimination method from the degrees of freedom connected to the candidate elements in the first step. In the present study, we propose TLCS combined with iterative improved reduced system (IIRS) to increase accuracy of the higher modes in the intermediate range. Also, it is possible to control the accuracy of the eigenvalues and eigenmodes of the reduced system. Finally, numerical examples demonstrate the performance of the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.57-63
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• 2007

The systematic method to construct equivalent static load from a given dynamic load is proposed in the present study. Previously reported works to construct equivalent static load were based on ad hoc methods. Due to improper selection of loading position, they may results in unreliable structural design. The present study proposes the employment of primary degrees of freedom for imposing the equivalent static loads. The degrees of freedom are selected by two-level condensation scheme with reliability and efficiency. In several numerical examples, the efficiency and reliability of the proposed scheme is verified by comparison displacement for equivalent static loading and dynamic loading at the critical time.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1996.10a
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• pp.78-85
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• 1996

The effect of vertical vibration of a beam is significantly influenced by higher modes of vibration. Therefore, a beam can be modeled using several elements must De used to represent a vibrating beam. As a result, analysis of a space framed structure for vertical vibration requires increase number of elements leading to more complicated model with many degree of freedom which requires large amount of computing resources for dynamic analysis. An efficient analysis method for vertical vibration of space framed structures are proposed in this paper which is presented in three method. The first method is to determine minimum nodes that shall be used to obtain dynamic response with the vertical vibration. Secondly, matrix condensation methods are introduced to reduce the computation efforts used to perform dynamic analysis and the selection of primary degree-of-freedom is proposed. The third method is of using the mass participation factor for the selection of primary degree-of-freedom.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.691-711
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• 2006

This paper uses the finite element method to simultaneously consider the coupled cable-deck vibrations and the parametric vibrations of stay cables in dynamic analysis of a cable-stayed bridge. The stay cables are represented by some cable finite elements, which can consider the parametric vibration of the cables. In addition to modeling stay cables using multiple link cable elements, a procedure for removing the self-weight term of cable element is proposed. A eigenvalue analysis process using dynamic condensation method for sorting out the natural modes of the girder-tower vibrations and the Rayleigh damping considering element damping for damping matrix are also proposed for dynamic analyses of cable-stayed bridges. The possibilities of using cable elements and of using global and local vibrations to evaluate the parametric vibrations of stay cables in a cable-stayed bridge are confirmed, respectively.