• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.91-103
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• 1995

An analysis to determine shear centers for anisotropic elastic thin-walled composite beams, cantilevered and loaded transversely at the free end is presented. The shear center is formulated based on familiar strength of material procedures analogous to those for isotropic beams. These procedures call for a balancing of torsional moments on the cross sectional surface and lead to a condition of zero resultant torsional couple. As a consequence, due the presence of anisotropic coupling, certain non-classical effects are manifested and are illustrated in two example problems. The most distinguishing result is that twisting may occur for composite beams even if shear forces are applied at the shear center. The derived shear center locations do not depend on any specific anisotropic bending theories per se, but only on the values of bending and shear stresses which such theories produce.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.6
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• pp.238-246
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• 2000

In this paper, an optimization method of thin walled beam structures is proposed, Stiffnesses of a thin walled beam are characterized by the thickness of thin plates and the shape of the typical section of the beam. Explicit formula for section properties such as area, area moment of inertia, and torsional constants are derived using the response surface method. The explicit formula can be used for the optimal design of a structural system which consists of complicated thin walled beams. A vehicle structural system is optimized to demonstrate the proposed method.

• Composites Research
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• v.19 no.5
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• pp.1-6
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• 2006

In this study, a closed-form analysis has been developed for the transverse shear behavior of thin-walled composite beams with closed cross-sections. The shear flow distributions and cross-section stiffness coefficients are derived analytically by using a mixed beam approach. The theory has been applied to single-celled composite box-beams with elastic couplings. The location of the shear center and the effect of transverse shear deformation on the static behavior of composite beams are investigated in the framework of the analysis. The present results are validated against those of a two-dimensional finite element analysis and a good correlation has been obtained for box-beam cases considered in this study.

• 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 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.

• Advances in aircraft and spacecraft science
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• v.1 no.3
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.5
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• pp.492-501
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• 2010

Equations of motion of thin-walled composite H-type cross-section beams incorporating a number of nonclassical effects of transverse shear and primary and secondary warping, and anisotropy of constituent materials are derived. The vibrational characteristics of a composite thin-walled beam exhibiting the circumferentially asymmetric stiffness system(CAS) and the circumferentially uniform stiffness system(CUS) are exploited in connection with the bending-transverse shear coupling and the bending-twist coupling resulting from directional properties of fiber reinforced composite materials.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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• pp.2637-2645
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• 2000

We propose a new one-dimensional theory for thin-walled curved box beams having rectangular cross sections, in which torsional, out-of-plane bending, warping and distortional deformations are coupled. The major difference between the present theory and existing theories lies in that the present theory takes into account additional distortion as well as warping. To verify the present theory, a standard finite element based on the present theory is developed and used for numerical analysis. A couple of numerical examples indeed confirm that the consideration of warping and distortional deformations is very important.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.95-98
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• 2003

In this work, a closed-form analysis is performed to obtain the stiffness coefficients of thin-walled composites beams with elliptical profiles. The analytical model includes the effects of elastic couplings, shell wall thickness, torsion warping and constrained warping. Reissner's semi-complementary energy functional is used to derive the beam force-displacement relations. The theory is validated against MSC/NASTRAN results for coupled composites beams with single-cell elliptical sections. Very good correlation has been noticed for the test cases considered.