• Structural Engineering and Mechanics
• /
• v.38 no.4
• /
• pp.429-441
• /
• 2011

In large-scale problem, a huge size of computational resources is needed for a reliable solution which represents the detailed description of dynamic behavior. Recently, eigenvalue reduction schemes have been considered as important technique to resolve computational resource problems. In addition, the efforts to advance an efficiency of reduction scheme leads to the development of the multi-level system condensation (MLSC) which is initially based on the two-level condensation scheme (TLCS). This scheme was proposed for approximating the lower eigenmodes which represent the global behavior of the structures through the element-level energy estimation. The MLSC combines the multi-level sub-structuring scheme with the previous TLCS for enhancement of efficiency which is related to computer memory and computing time. The present study focuses on the implementation of the MLSC on the direct time response analysis and the frequency response analysis of structural dynamic problems. For the transient time response analysis, the MLSC is combined with the Newmark's time integration scheme. Numerical examples demonstrate the efficiency of the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.19 no.2 s.72
• /
• pp.213-219
• /
• 2006

Topology optimization problem requires numerous repeated evaluations of objective function and design sensitivity for elements within design domain with various density distributions. The recently proposed two-level condensation scheme(TLCS) is very promising for the construction of reduced system and for an accurate and efficient analysis concerned about eigenvalue and dynamic problems. We used the two-level dynamic condensation scheme for the analysis and sensitivity computation part in the structural topology optimization problem. The results of the topology optimization for the reduced system show the TLCS provides high accuracy and computation efficiency compared to the full scale system within engineering accuracy.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1316-1321
• /
• 2003

The systematic method to construct equivalent static load from the given dynamic load is proposed in the present study. Previously reported works to construct equivalent static load were based on ad hoc methods. They may results in unreliable structural design. The present study proposes a selection scheme of degrees of freedom(d.o.f) for imposing the equivalent static loads. The d.o.fs are selected by Two-level condensation scheme(TLCS). TLCS consists of two two-steps. The first step is the energy estimation in element-level and the second step consists of the traditional sequential elimination precudure. Through several numerical examples, the efficiency and reliability of proposed scheme is verified.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.10a
• /
• pp.19-26
• /
• 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
• /
• 2007.04a
• /
• pp.631-636
• /
• 2007

Eigenvalue reduction schemes approximate the lower eigenmodes that represent the global behavior of the structures. In the, we proposed a two-level condensation scheme(TLCS) for the construction of a reduced system. In first step, the of candidate elements by energy estimation, Rayleigh quotient, through Ritz vector calculation, and next, the primary degrees of freedom is selected by sequential elimination from the degrees of freedom connected 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 higher modes intermediate range. Also, it possible to control the accuracy of the eigenvalues and eigenmodes of the reduced system. Numerical examples demonstrate performance of proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.21 no.5
• /
• pp.439-450
• /
• 2008

In this study, the reduced system for the dynamic analysis is proposed and the selection criterion of the primary degrees of freedom is presented considering the relation between natural frequency and external loading frequency. A well-constructed reduced system can assure the accurate representation of the dynamic behavior under arbitrary dynamic loads. For selecting the primary degrees of freedom of the reduced system, we employ the robust two-level condensation scheme of which the reliability has been proven through previous study. In the numerical examples, the reliability of the dynamic analysis based on the reduced system is demonstrated through comparing with those of global system.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.453-458
• /
• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

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

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.30 no.9 s.252
• /
• pp.1070-1077
• /
• 2006

In the present study, sizing and shape optimizations are performed based on the reduced system of large-scaled problem. In the analysis part to achieve efficiency and reliability of computation, two-level condensation scheme is applied. In the construction of reduced system of large scaled problems, it is much more efficient to use sub-domain method. Thus, in the present paper, two-level reduction method combined with sub-domain method is employed. Once the reduced system is constructed, it is straightforward to obtain design sensitivities from the analysis results of the reduced system We use semi-analytic method to obtain design sensitivities. Performance of the efficiency and reliability of the present reduction method in the structural optimization problem is demonstrated through the numerical examples. The present framework of reduction method should serve as a fast and reliable design tool in analysis and design of large-scaled dynamic problems.

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