• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.345-352
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• 2001

Derivation procedures of exact static element stiffness matrix of shear deformable thin-walled straight beams are rigorously presented for the spatial buckling analysis. An exact static element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The buckling loads are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.528-533
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• 1995

An analyical method is proposed to construct a clamp jointed structure as an equivalent stiffness matrix element in the finite element modal analysis of a complex beam structure. Static structural analysis was first made for the detail finite element model of the clamp joint. Utilizing the results of this analysis, the equivalent stiffness matrix element was buildup by using the flexibility influence coefficient method and Guyan condensation. The proposed method was applied to finite element modal analysis of a clamp jointed cantilever beam. And the finite element analysis results were compared to those experimental modal analysis. Comparison shows doog agreement each other Furthermore the effects of normal contact(or clamping) load on the equivalent stiffness matrix was also examined. The equivalent stiffness matrix showed little change in spite of the remakable increase in the contact load on the clamp joint.

• 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.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• Journal of Korean Society of Steel Construction
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• v.14 no.4
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• pp.509-518
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• 2002

In order to perform the spatial buckling and static analysis of the nonsymmetric thin-walled beam-column element, improved exact static stiffness matrices were evaluated using equilibrium equation and force-deformation relationships. This numerical technique was obtained using a generalized linear eigenvalue problem, by introducing 14 displacement parameters and system of linear algebraic equations with complex matrices. Unlike the evaluation of dynamic stiffness matrices, some zero eigenvalues were included. Thus, displacement parameters related to these zero eigenvalues were assumed as polynomials, with their exact distributions determined using the identity condition. The exact displacement functions corresponding to three loadingcases for initial stress-resultants were then derived, by consistently combining zero and nonzero eigenvalues and corresponding eigenvectors. Finally, exact static stiffness matrices were determined by applying member force-displacement relationships to these displacement functions. The buckling loads and displacement of thin-walled beam were evaluated and compared with analytic solutions and results using ABAQUS' shell element or straight beam element.

• Proceedings of the KSR Conference
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• 2005.11a
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• pp.1165-1170
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• 2005

In order to perform the spatial buckling analysis of the curved beam element with nonsymmetric thin-walled cross section, exact static stiffness matrices are evaluated using equilibrium equations and force-deformation relations. Contrary to evaluation procedures of dynamic stiffness matrices, 14 displacement parameters are introduced when transforming the four order simultaneous differential equations to the first order differential equations and 2 displacement parameters among these displacements are integrated in advance. Thus non-homogeneous simultaneous differential equations are obtained with respect to the remaining 8 displacement parameters. For general solution of these equations, the method of undetermined parameters is applied and a generalized linear eigenvalue problem and a system of linear algebraic equations with complex matrices are solved with respect to 12 displacement parameters. Resultantly displacement functions are exactly derived and exact static stiffness matrices are determined using member force-displacement relations. The buckling loads are evaluated and compared with analytic solutions or results by ABAQUS's shell element.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3007-3019
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• 1993

For the same configuration, the stiffness of 6-node two dimensional isoparametric is stiffer than that of 8-node two dimensional isoparametric element. This phenomenon may be called 'Relative Stiffness Stiffening Phenomenon.' In this paper, the relative stiffness stiffening phenomenon was studied, and could be corrected by modifying the position of Gauss integral points used in the numerical integration of the stiffness matrix. For the same deformation (bending) energy of 6-node and 8-node two dimensional isoparametric elements, Gauss integral points of 6-node element have to move closer, in comparison with those of 8-node element, in the case of numerical integration along the thickness direction.