• Title, Summary, Keyword: matrix stiffness method

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Analysis Of the Joint Structure of the Vehicle Body by Condensed Joint Matrix Method

  • Suh, Myung-Won;Yang, Won-Ho;Jonghwan Suhr
    • Journal of Mechanical Science and Technology
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    • v.15 no.12
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    • pp.1639-1646
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    • 2001
  • It is often necessary that the joints characteristics should be determined in the early stage of the vehicle body design. The researches on identification of joints in a vehicle body have been performed until the recent year. In this study, the joint characteristics of vehicle structure were expressed as the condensed matrix forms from the full joint stiffness matrix. The condensed joint stiffness matrix was applied to typical T-type and Edge-type joints, and the usefulness was confirmed. In addition, it was applied to the real center pillar model and the full vehicle body in order to validate the practical application.

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Application of Condensed Joint Matrix Method to the Joint Structure of Vehicle Body (축약 행렬법을 적용한 차체 결합부 해석)

  • 서종환;서명원;양원호
    • Transactions of the Korean Society of Automotive Engineers
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    • v.6 no.4
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    • pp.9-16
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    • 1998
  • The joint characteristics are necessary to be determined in the early stage of the vehicle body design. Researches on identification of joints in a vehicle body have been performed until the recent year. In this study, the joint characteristics of vehicle struct- ure were expressed as condensed forms from the full joint stiffness and mass matrix. The condensed joint stiffness and mass matrix were applied to typical T-type and Edge-type joints, and the usefulness was confirmed. In addition, those were applied to center pillar and full vehicle body to validate the practical application.

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Dynamic stiffness matrix of composite box beams

  • Kim, Nam-Il
    • Steel and Composite Structures
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    • v.9 no.5
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    • pp.473-497
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    • 2009
  • For the spatially coupled free vibration analysis of composite box beams resting on elastic foundation under the axial force, the exact solutions are presented by using the power series method based on the homogeneous form of simultaneous ordinary differential equations. The general vibrational theory for the composite box beam with arbitrary lamination is developed by introducing Vlasov°Øs assumption. Next, the equations of motion and force-displacement relationships are derived from the energy principle and explicit expressions for displacement parameters are presented based on power series expansions of displacement components. Finally, the dynamic stiffness matrix is calculated using force-displacement relationships. In addition, the finite element model based on the classical Hermitian interpolation polynomial is presented. To show the performances of the proposed dynamic stiffness matrix of composite box beam, the numerical solutions are presented and compared with the finite element solutions using the Hermitian beam elements and the results from other researchers. Particularly, the effects of the fiber orientation, the axial force, the elastic foundation, and the boundary condition on the vibrational behavior of composite box beam are investigated parametrically. Also the emphasis is given in showing the phenomenon of vibration mode change.

Numerical modelling of nonlinear behaviour of prestressed concrete continuous beams

  • Lou, Tiejiong;Lopes, Sergio M.R.;Lopes, Adelino V.
    • Computers and Concrete
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    • v.15 no.3
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    • pp.373-389
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    • 2015
  • The development of a finite element model for the geometric and material nonlinear analysis of bonded prestressed concrete continuous beams is presented. The nonlinear geometric effect is introduced by the coupling of axial and flexural fields. A layered approach is applied so as to consider different material properties across the depth of a cross section. The proposed method of analysis is formulated based on the Euler-Bernoulli beam theory. According to the total Lagrangian description, the constructed stiffness matrix consists of three components, namely, the material stiffness matrix reflecting the nonlinear material effect, the geometric stiffness matrix reflecting the nonlinear geometric effect and the large displacement stiffness matrix reflecting the large displacement effect. The analysis is capable of predicting the nonlinear behaviour of bonded prestressed concrete continuous beams over the entire loading stage up to failure. Some numerical examples are presented to demonstrate the validity and applicability of the proposed model.

Frequency-Dependent Element Matrices for Vibration Analysis of Piping Systems (배영계의 진동해소를 위한 주파수종속 요표행렬)

  • 양보석;안영홍;최원호
    • Journal of Ocean Engineering and Technology
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    • v.6 no.2
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    • pp.125-132
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    • 1992
  • This paper presents an approach for the derivation of frequency-dependent element matrices for vibration analysis of piping systems containing a moving medium. The dynamic stiffness matrix is deduced from transfer matrix, and, in turn, the frequency-dependent element matrices are derived. Numerical examples show that method gives more accurate results than those obtained using the conventional static shape function based element matrices.

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A Study on Estimated Stiffness and Mass Matrices from Modal Data at Measured Points (측정 모달 데이터를 이용한 골조의 강성행렬 및 질량행렬 추정에 관한 연구)

  • Han, Dong-Ho;Lee, Chy-Hyoung;Yoon, Sung-Kee
    • Journal of the Korean Association for Spatial Structures
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    • v.2 no.2
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    • pp.59-67
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    • 2002
  • In this study, a method that estimates stiffness and mass matrices of shear building from modal test data is presented. This method applied of building depends on the number of measurement points that are less in number than the total structural degrees of freedom, and on the first two orders of structural mode measured. By means of this method it is possible to use modal data of unmeasurable points to estimate total stiffness and mass matrices of structure. Some examples are studied in this paper, and its result shows that this method is reliable.

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Damage assessment in periodic structures from measured natural frequencies by a sensitivity and transfer matrix-based method

  • Zhu, Hongping;Li, Lin;Wang, Dansheng
    • Structural Engineering and Mechanics
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    • v.16 no.1
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    • pp.17-34
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    • 2003
  • This paper presents a damage assessment procedure applied to periodic spring mass systems using an eigenvalue sensitivity-based method. The damage is directly related to the stiffness reduction of the damage element. The natural frequencies of periodic structures with one single disorder are found by adopting the transfer matrix approach, consequently, the first order approximation of the natural frequencies with respect to the disordered stiffness in different elements is used to form the sensitivity matrix. The analysis shows that the sensitivity of natural frequencies to damage in different locations depends only on the mode number and the location of damage. The stiffness changes due to damage can be identified by solving a set of underdetermined equations based on the sensitivity matrix. The issues associated with many possible damage locations in large structural systems are addressed, and a means of improving the computational efficiency of damage detection while maintaining the accuracy for large periodic structures with limited available measured natural frequencies, is also introduced in this paper. The incomplete measurements and the effect of random error in terms of measurement noise in the natural frequencies are considered. Numerical results of a periodic spring-mass system of 20 degrees of freedom illustrate that the proposed method is simple and robust in locating single or multiple damages in a large periodic structure with a high computational efficiency.

Evaluation of Stiffness Matrix of 3-Dimensional Elements for Isotropic and Composite Plates (등방성 및 복합재 플레이트용 16절점 요소의 강성행렬 계산)

  • 윤태혁;김정운;이재복
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.10
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    • pp.2640-2652
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    • 1994
  • The stiffness of 6-node isotropic element is stiffer than that of 8-node isotropic element of same configuration. This phenomenon was called 'Relative Stiffness Stiffening Phenomenon'. In this paper, an equation of sampling point modification which correct this phenomenon was derived for the composite plate, as well as an equation for an isotropic plate. The relative stiffness stiffening phenomena of an isotropic plate element could be corrected by modifying Gauss sampling points in the numerical integration of stiffness matrix. This technique could also be successfully applied to the static analyses of composite plate modeled by the 3-dimensional 16-node elements. We predicted theoretical errors of stiffness versus the number of layers that result from the reduction of numerical integration order. These errors coincide very well with the actual errors of stiffness. Therefore, we can choose full integration of reduced integration based upon the permissible error criterion and the number of layers by using the thoretically predicted error.

Computational Modeling of the Bearing Coupling Section of Machine Tools (공작기계 베어링 결합부의 전산 모델링)

  • Kim, Hyun-Myung;Seo, Jae-Wu;Park, Hyung-Wook
    • Journal of the Korean Society for Precision Engineering
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    • v.29 no.10
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    • pp.1050-1055
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    • 2012
  • The bearing coupling section of machine tools is the most important factor to determine their static/dynamic stiffness. To ensure the proper performance of machine tools, the static/dynamic stiffness of the rotating system has to be predicted on the design stage. Various parameters of the bearing coupling section, such as the spring element, node number and preload influence the characteristics of rotating systems. This study focuses on the prediction of the static and dynamic stiffness of the rotating system with the bearing coupling section using the finite element (FE) model. MATRIX 27 in ANSYS has been adopted to describe the bearing coupling section of machine tools because the MATRIX 27 can describe the bearing coupling section close to the real object and is applicable to various machine tools. The FE model of the bearing couple section which has the sixteen node using MATRIX 27 was constructed. Comparisons between finite element method (FEM) predictions and experimental results were performed in terms of the static and dynamic stiffness.

Stiffness Analysis of a Low-DOF Parallel Manipulator including the Elastic Deformations of Both Joints and Links (ICCAS 2005)

  • Kim, Han-Sung;Shin, Chang-Rok;Kyung, Jin-Ho;Ha, Young-Ho;Yu, Han-Sik;Shim, Poong-Soo
    • 제어로봇시스템학회:학술대회논문집
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    • pp.631-637
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    • 2005
  • This paper presents a stiffness analysis method for a low-DOF parallel manipulator, which takes into account of elastic deformations of joints and links. A low-DOF parallel manipulator is defined as a spatial parallel manipulator which has less than six degrees of freedom. Differently from the case of a 6-DOF parallel manipulator, the serial chains in a low-DOF parallel manipulator are subject to constraint forces as well as actuation forces. The reaction forces due to actuations and constraints in each limb can be determined by making use of the theory of reciprocal screws. It is shown that the stiffness model of an F-DOF parallel manipulator consists of F springs related to the reciprocal screws of actuations and 6-F springs related to the reciprocal screws of constraints, which connect the moving platform to the fixed base in parallel. The $6{times}6$ stiffness matrix is derived, which is the sum of the stiffness matrices of actuations and constraints. The six spring constants can be precisely determined by modeling the compliance of joints and links in a serial chain as follows; the link can be considered as an Euler beam and the stiffness matrix of rotational or prismatic joint can be modeled as a $6{times}6$ diagonal matrix, where one diagonal element about the rotation axis or along the sliding direction is zero. By summing the elastic deformations in joints and links, the compliance matrix of a serial chain is obtained. Finally, applying the reciprocal screws to the compliance matrix of a serial chain, the compliance values of springs can be determined. As an example of explaining the procedure, the stiffness of the Tricept parallel manipulator has been analyzed.

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