• Title, Summary, Keyword: matrix stiffness method

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Determining the Size of a Hankel Matrix in Subspace System Identification for Estimating the Stiffness Matrix and Flexural Rigidities of a Shear Building (전단빌딩의 강성행렬 및 부재의 강성추정을 위한 부분공간 시스템 확인기법에서의 행켈행렬의 크기 결정)

  • Park, Seung-Keun;Park, Hyun Woo
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.2
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    • pp.99-112
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    • 2013
  • This paper presents a subspace system identification for estimating the stiffness matrix and flexural rigidities of a shear building. System matrices are estimated by LQ decomposition and singular value decomposition from an input-output Hankel matrix. The estimated system matrices are converted into a real coordinate through similarity transformation, and the stiffness matrix is estimated from the system matrices. The accuracy and the stability of an estimated stiffness matrix depend on the size of the associated Hankel matrix. The estimation error curve of the stiffness matrix is obtained with respect to the size of a Hankel matrix using a prior finite element model of a shear building. The sizes of the Hankel matrix, which are consistent with a target accuracy level, are chosen through this curve. Among these candidate sizes of the Hankel matrix, more proper one can be determined considering the computational cost of subspace identification. The stiffness matrix and flexural rigidities are estimated using the Hankel matrix with the candidate sizes. The validity of the proposed method is demonstrated through the numerical example of a five-story shear building model with and without damage.

Analysis of Design Parameter of Structural Modification using Change of Dynamic Characteristics (동특성 변화로부터 구조물의 변경된 설계파라미터 해석)

  • Oh Jae-Eung;Lee Jung-Woo;Lee Jung-Youn
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.4
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    • pp.387-392
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    • 2006
  • This paper predicts the modified mass and stiffness of structure using the sensitivity coefficients with the iterative method. The sensitivity coefficients are obtained by the change of the eigenvectors according to structural modification. The method is applied to an examples of a 3 degree of freedom system by modifying mass and stiffness. The predicted mass and stiffness are in good agreement with these from the structural reanalysis using the modified mass and stiffness.

Free vibration analysis of asymmetric shear wall-frame buildings using modified finite element-transfer matrix method

  • Bozdogan, Kanat B.
    • Structural Engineering and Mechanics
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    • v.46 no.1
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    • pp.1-17
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    • 2013
  • In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of $6{\times}6$ by transforming the obtained stiffness matrix. Thus, the dimension, which is $12n{\times}12n$ in classical finite elements, is reduced to the dimension of $6{\times}6$. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

The Rocking Response of Rectangular Fluid Storage Tank (구형 유체 저장 Tank의 Rocking응답)

  • 김재관
    • Proceedings of the Earthquake Engineering Society of Korea Conference
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    • pp.107-114
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    • 1997
  • A dynamic fluid-structure-soil interaction analysis method is developed to investigate the effects of rocking motion on the seismic response of the 3-D flexible rectangular liquid storage tanks founded on the deformable ground. The governing equation of 3-D rectangular tanks subjected to the translational and rocking motions is obtained by Rayleigh-Ritz method. The dynamic stiffness matrix of the rigid surface foundation resting on the surface of a stratum are calculated by hyperelement method. The seismic responses of a 3-D flexible tank model founded on the deformable ground is calculated by combining the governing equation of the structural motion with the dynamic stiffness matrix of the rigid surface foundation.

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Derivation of Exact Dynamic Stiffness Matrix of a Beam-Column Element on Elastic Foundation (균일하게 탄성지지된 보-기둥요소의 엄밀한 동적강성행렬 유도)

  • 김문영;윤희택;곽태영
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.15 no.3
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    • pp.463-469
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    • 2002
  • The governing equation and force-displacement rotations of a beam-column element on elastic foundation we derived based on variational approach of total potential energy. An exact static and dynamic 4×4 element stiffness matrix of the beam-column element is established via a generalized lineal-eigenvalue problem by introducing 4 displacement parameters and a system of linear algebraic equations with complex matrices. The structure stiffness matrix is established by the conventional direct stiffness method. In addition the F. E. procedure is presented by using Hermitian polynomials as shape function and evaluating the corresponding elastic and geometric stiffness and the mass matrix. In order to verify the efficiency and accuracy of the beam-column element using exact dynamic stiffness matrix, buckling loads and natural frequencies are calculated for the continuous beam structures and the results are compared with F E. solutions.

Static Analysis of Frame Structures Using Transfer of Stiffness Coefficient (강성계수의 전달을 이용한 골조구조물의 정적해석)

  • 최명수;문덕홍;정하용
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.1
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    • pp.9-18
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    • 2003
  • In static analysis of a variety of structures, the matrix method of structural analysis is the most widely used and powerful analysis method. However, this method has drawback requiring high-performance computers with many memory units and fast processing units in the case of analyzing accurately structures with a large number of degrees-of- freedom. Therefore, it's very difficult to analyze these structures accurately in personal computers. For overcoming the drawback of the matrix method of structural analysis, authors suggest the transfer stiffness coefficient method(TSCM). The TSCM is very suitable to a personal computer because the concept of the TSCM is based on the transfer of the stiffness coefficient for an analytical structure. In this paper, the static analysis algorithm for frame structures is formulated by the TSCM. We confirm the validity of the TSCM through the comparison of computation results by the TSCM, the NASTRAN, the matrix method of structural analysis and the analytical solution.

A new method to calculate the equivalent stiffness of the suspension system of a vehicle

  • Zhao, Pinbin;Yao, Guo-Feng;Wang, Min;Wang, Xumin;Li, Jianhui
    • Structural Engineering and Mechanics
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    • v.44 no.3
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    • pp.363-378
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    • 2012
  • The stiffness of a suspension system is provided by the bushings and the stiffness of the wheel center controls the suspension's elasto-kinematic (e-k) specification. So the stiffness of the wheel center is very important, but the stiffness of the wheel center is very hard to measure. The paper give a new method that we can use the stiffness of the bushings to calculate the equivalent stiffness of the wheel center, which can quickly and widely be used in all kinds of suspension structure. This method can also be used to optimize and design the suspension system. In the example we use the method to calculate the equivalent stiffness of the wheel center which meets the symmetric and positive conditions of the stiffness matrix.

Vibraiton and Power Flow Analysis for the Branched Piping System by Wave Approach (파동접근법을 이용한 분기된 배관계의 진동 및 파워흐름해석)

  • Koo, Gyeong-Hoe;Park, Yun-Sik
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.4
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    • pp.1225-1232
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    • 1996
  • In this paper the vibration and power flow analysis for the branched piping system conveying fluid are performed by wave approach. The uniform straight pipe element conveying fluid is formulated using the dynamic stiffness matrix by wave approach. The branched piping system conveying fluid can be easily formulated with considering of simple assumptions of displacements at the junction and continuity conditions of the pipe internal flow. The dynamic stiffness matrix for each uniform straight pipe element can be assembled by using the global assembly technique using in conventional finite element method. The computational method proposed in this paper can easily calculate the forced responses and power flow of the branched piping system conveying fluid regardless of finite element size and modal properties.

Static Analysis of Frame Structures Using Transfer of Stiffness Coefficient (강성계수의 전달을 이용한 골조구조물의 정적해석)

  • 문덕홍;최명수;정하용
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.287-294
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    • 2001
  • In static analysis of a variety of structures, the matrix method of structural analysis is the most widely used and powerful analysis method. However, this method has drawback requiring high-performance computers with many memory units and fast processing units in the case of analyzing complex and large structures accurately. Therefore, it's very difficult to analyze these structures accurately in personal computers. For overcoming the drawback of the matrix method of structural analysis, authors suggest transfer stiffness coefficient method(TSCM). The TSCM is very suitable to a personal computer because the concept of the TSCM is based on the transfer of the stiffness coefficient for an analytical structure. In this paper, the static analysis algorithm for frame structures is formulated by the TSCM. We confirm the validity of the proposed method through the compare of computation results by the TSCM and the NASTRAN.

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Free Vibration Analysis of Axisymmetric Conical Shell

  • Choi, Myung-Soo;Yeo, Dong-Jun;Kondou, Takahiro
    • Journal of the Korea Society For Power System Engineering
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    • v.20 no.2
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    • pp.5-16
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    • 2016
  • Generally, methods using transfer techniques, like the transfer matrix method and the transfer stiffness coefficient method, find natural frequencies using the sign change of frequency determinants in searching frequency region. However, these methods may omit some natural frequencies when the initial frequency interval is large. The Sylvester-transfer stiffness coefficient method ("S-TSCM") can always obtain all natural frequencies in the searching frequency region even though the initial frequency interval is large. Because the S-TSCM obtain natural frequencies using the number of natural frequencies existing under a searching frequency. In this paper, the algorithm for the free vibration analysis of axisymmetric conical shells was formulated with S-TSCM. The effectiveness of S-TSCM was verified by comparing numerical results of S-TSCM with those of other methods when analyzing free vibration in two computational models: a truncated conical shell and a complete (not truncated) conical shell.