• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.12
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• pp.3020-3027
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• 1993

Curved beam element has received attention because of its own usefulness and its bearing on general curved elements like shells. In conventional curved beam elements stiffness matrix is overestimated and eigensolutions are poor. To avoid this phenomenon it is necessary to use a large number of elements and, as a result, the total number of degrees of freedom is increased. In this paper the two-noded, with three degrees of freedom at each node, in-plane curvature-based curbed beam element is employed in eigen-analysis of curved beam. It is shown that the curvature-based beam element is very efficient in vibration analysis and also that it is applicable to both thin and thick curved beams.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.10
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• pp.1049-1056
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• 2008

A method for the vibration analysis of curved beam conveying fluid with uniform velocity was presented. The dynamics of curved beam is based on the inextensible theory. Both in-plane motion and out-of-plane motion of curved beam were discussed. The finite element method was formulated to solve the governing equations. The natural frequencies calculated by the presented method were compared with those by analytical solution, straight beam theories and Nastran. As the velocity of fluid becomes larger, the results by straight beam model became different from those by curved beam model. And it was shown that the curved beam element should be used to predict the critical velocity of fluid exactly. The influence of fluid velocity on the frequency response function was also discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.310-323
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• 1990

A three-noded, with three degree-of-freedom at each node, in-plane curved beam element is formulated and employed in eigen-analysis of constant curvature beam. The conventional quadratic shape functions used in a three noded C .deg. type curved beam element produce such an undesirable large stiffness that a significant error is introduced in displacements and stresses. These phenomena are called 'Stiffness Locking Phenomena', which result from spurious strain energy due to inappropriate assumptions on independent isoparametric quadratic interpolation functions. Stiffness locking phenomena can be alleviated by using modified interpolation functions which get rid of spurious constraints of conventional interpolation functions. Eigenvalues and their modes as well as displacements and stresses may be locked because they are related to stiffness. Using modified curved beam element in eigenvalue problem of cantilever and arch, the property and performance of modified curved beam element are examined by numerical experimentations. In these eigen-analyses, mass matrices are calculated by using both modified and unmodified curved beam element, are compared with theoretical solutions. These comparisons show that the performance of the modified curved beam element is better than that of the unmodified curved beam element.

• Journal of KSNVE
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• v.6 no.1
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• pp.83-88
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• 1996

The significance of spectral element method is that it can treat the mass and stiffness distribution exactly in contrast to the conventional finite element method, and therefore the dynamic behaviors within each spectral element can be obtained exactly. The present study provides the derivation of the spectral element of a curved beam, while the previous ones presented that of a straight structure. Further, in order to verify the derived spectral element, the natural frequencies of a ring by the spectral element method are compared with those by the analytical method and those by the FEM. From the verification, derived spectral element is admissible. And the dynamic behaviors of curved beam are simulated by using the derived spectral element of a curved beam.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.10
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• pp.2535-2542
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• 1993

Two-noded curved beam elements, CMLC (field-consistent membrane and linear curvature) and IMLC(field-inconsistent membrane and linear curvature) are developed on the basis of Timoshenko's beam theory and curvilinear coordinate. The curved beam element is developed by the separation of the radial deflection into the bending deflection. In the CMLC element, field-consistent axial strain interpolation is adapted for removing the membrane locking. The CMLC element shows the rapid and stable convergence on the wide range of curved beam radius to thickness. The field-consistent axial strain and the separation of radial deformation produces the most efficient linear element possible.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2540-2545
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• 1996

It is well known that in typical displacement-based curved beam elements, the stiffness matrix is overestimated and as a result displacement predictions show gross error for the thin beam case. In this paper, a stain based curved beam element with 2 nodes is formulated based on shallow beam geometry. At the element level, the curvature and membrane strain fields are approximated independently and the displacement fields are obtained by integrating the strain fields. Three test problems are given to demonstrate the numerical performance of the element. Analysis results obtained reveal that the element is free for locking and very effectively applicable to deeply as well as shallowly curved beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.285-290
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• 2003

A method for the dynamic analysis of curved beam conveying fluid presents. The dynamics of curved beam is based on inextensible theory and the fluid in curved beam has uniform velocity. The equations of motion of curved beam are decoupled by in-plane motion and out-of$.$Plane motion. The solutions of equations are presented by a finite element method and validate by comparing the natural frequency with analytical solution, straight beam theories and Nastran. The influence of fluid velocity on the frequency response function is illustrated and discussed.

• Structural Engineering and Mechanics
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• v.19 no.1
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• pp.73-96
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• 2005

For the spatially coupled free vibration analysis of shear deformable thin-walled non-symmetric curved beam subjected to initial axial force, an exact dynamic element stiffness matrix of curved beam is evaluated. Firstly equations of motion and force-deformation relations are rigorously derived from the total potential energy for a curved beam element. Next a system of linear algebraic equations are constructed by introducing 14 displacement parameters and transforming the second order simultaneous differential equations into the first order simultaneous differential equations. And then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact $14{\times}14$ dynamic element stiffness matrix is determined using force-deformation relations. To demonstrate the accuracy and the reliability of this study, the spatially coupled natural frequencies of shear deformable thin-walled non-symmetric curved beams subjected to initial axial forces are evaluated and compared with analytical and FE solutions using isoparametric and Hermitian curved beam elements and results by ABAQUS's shell elements.

• Steel and Composite Structures
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• v.19 no.3
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• pp.635-659
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• 2015

In this study, natural frequency analysis of a large deflected cantilever laminated composite beam fixed at both ends, which forms the case of a pre-stressed curved beam, is investigated. The laminated beam is considered to have symmetric and asymmetric lay-ups and the effective flexural modulus of the beam is used in the analysis. In order to obtain the pre-stressed composite curved beam case, an external vertical concentrated load is applied at the free end of a cantilever laminated composite beam and then the loading point of the deflected beam is fixed. The non-linear deflection curve of the flexible beam undergoing large deflection is obtained by the Reversion Method. The curved laminated composite beam is modeled by using the Finite Element Method with a straight-beam element approach. The effects of orientation angle and vertical load on the natural frequency parameter for the first four modes are examined and the results obtained are given in graphics. It has been found that the effect of the load parameter, which forms the curved laminated beam, on the natural frequency parameter, almost disappears after a certain value of the load parameter. This certain value differs for each laminated curved beam and each vibration mode.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.559-566
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• 2003

In this study, we present a new highly accurate two-dimensional curved composite beam element. The present element, which is based on the Hellinger-Reissner variational principle and classical lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (9x9) element stiffness matrix. It should be noted that the stacking sequences without transverse deformation to the load plane makes a two dimensional analysis of curved composite beams practically useful . Several numerical examples confirm the superior locking-free behavior of the present higher-order laminated curved beam element.