• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.9 s.180
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• pp.2191-2201
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• 2000

End effects due to sectional deformations of thin-walled beams with closed cross section are analysed by a one-dimensional theory. In particular, end effects associated with warping (out of plane m otion) and distortion (in plane motion) are investigated. The exact solutions as a vector form are newly derived to reveal slowly-decaying nature of the end effects in a thin-walled beam loaded by a couple. Several examples of thin-walled beams under various loading conditions indicate that the local end effect zone due to warping and distortion is approximately ten times the typical beam width.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. 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. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.414-419
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• 2001

In this research, reliability based optimum design is presented for the thin walled beam structures. Deterministic and stochastic optimum design are compared for the thin walled beam structures. Monte Carlo simulation is used for stochastic optimum design with consideration of probabilistic distribution of representative section properties of the thin walled beams with the Response Surface Method.

• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.2
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• pp.57-68
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• 1998

For free vibration of monosymmetric thin-walled circular arches including restrained warping effect, the elastic strain and kinetic energy is derived by introducing displacement fields of circular arches in which all displacement parameters are defined at the centroid axis. The cubic Hermitian polynomials are utilized as shape functions for development of the curved thin-walled beam element having eight degrees of freedom. Analytical solution for free vibration behaviors of simply supported thin-walled curved beam element is presented by evaluating elastic stiffness and mass matrices. In order to illustrate the accuracy and practical usefulness of this study, analytical and numerical solutions for free vibration of circular arches are presented and compared with solutions analyzed by the FEM using straight beam element.

• Journal of KSNVE
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• v.9 no.6
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• pp.1193-1199
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• 1999

This paper deals with the free vibrations of circular curved beams with thin-walled cross-section. The differential equation for the coupled flexural-torsional vibrations of such beams with warping is solved numerically to obtain natural frequencies and mode shapes. The Runge-Kutta and determinant search methods, respectively, are used to solve the governing differential equation and to compute the eigenvalues. The lowest three natural frequencies and corresponding mode shapes are calculated for the thin-walled horizontally curved beams with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of opening angle of beam, warping parameter, and two different values of slenderness ratios are considered. Numerical results are compared with existing exact and numerical solutions by other methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1033-1039
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• 2006

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analyses. For this, the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to tl1e solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Journal of Advanced Navigation Technology
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• v.16 no.2
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• pp.367-374
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• 2012

A dynamic simulation and test of frame with thin walled closed section beams considering warping conditions have been performed. When a beam is subjected under torsional moment, the cross section will deform an warping as well as twist. For some thin-walled sections warping will be large, and accompanying warping restraint will induce axial and shear stresses and reduce the twist of beam which stiffens the beam in torsion. This paper presents that an warping restraint factor in finite element model effects the behavior of beam deformation and dynamic mode shape. The computer modelling of frame is discussed in linear beam element model and linear thin shell element model, also presents a correlation between computer predicted and actual experimental results for static deflection, natural frequencies and mode shapes of frame.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.589-604
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• 2005

To overcome the drawback of currently available curved beam theories having non-symmetric thin-walled cross sections, a curved beam theory based on centroid-shear center formulation is presented for the spatially coupled free vibration and elastic analysis. For this, the displacement field is expressed by introducing displacement parameters defined at the centroid and shear center axes, respectively. Next the elastic strain and kinetic energies considering the thickness-curvature effect and the rotary inertia of curved beam are rigorously derived by degenerating the energies of the elastic continuum to those of curved beam. And then the equilibrium equations and the boundary conditions are consistently derived for curved beams having non-symmetric thin-walled cross section. It is emphasized that for curved beams with L- or T-shaped sections, this thin-walled curved beam theory can be easily reduced to the solid beam theory by simply putting the sectional properties associated with warping to zero. In order to illustrate the validity and the accuracy of this study, FE solutions using the Hermitian curved beam elements are presented and compared with the results by previous research and ABAQUS's shell elements.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.195-210
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• 2011

Bernoulli-Euler beam theory is used to develop an exact dynamic stiffness matrix for the flexural-torsional coupled motion of a three-dimensional, axially loaded, thin-walled beam of doubly asymmetric cross-section. This is achieved through solution of the differential equations governing the motion of the beam including warping stiffness. The uniform distribution of mass in the member is also accounted for exactly, thus necessitating the solution of a transcendental eigenvalue problem. This is accomplished using the Wittrick-Williams algorithm. Finally, examples are given to confirm the accuracy of the theory presented, together with an assessment of the effects of axial load and loading eccentricity.

• Journal of Korean Society of Steel Construction
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• v.14 no.1
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• pp.31-40
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• 2002

Free vibration of a thin-walled laminated composite beam is studied. A general analytical model applicable to the dynamic behavior of a thin-walled channel section composite is developed. This model is based on the classical lamination theory, and accounts for the coupling of flexural and torsional modes for arbitrary laminate stacking sequence configuration. i.e. unsymmetric as well as symmetric, and various boundary conditions. A displacement-based one-dimensional finite element model is developed to predict natural frequencies and corresponding vibration modes for a thin-walled composite beam. Equations of motion are derived from the Hamilton's principle. Numerical results are obtained for thin-walled composite addressing the effects of fiber angle. modulus ratio. and boundary conditions on the vibration frequencies and mode shapes of the composites.