• Journal of Aerospace System Engineering
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• v.12 no.6
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• pp.41-49
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• 2018

In this study, the theoretical dynamic characteristics of a thin-walled composite beam with a single-cell of chordwise asymmetric cross-section was studied. Mathematical modeling was done by considering the transverse shear effects, the warping restraint effects, the constant taper ratio in the longitudinal direction of the beam, and the geometrical cross-section ratio. The mass coefficients, stiffness coefficients, and Eigen frequencies of the selected section were investigated. In particular, the effects of the taper ratio and cross-section ratio of the model on the Eigen frequencies were analyzed and compared when the asymmetry of the section was considered and the warping function was not corrected.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2016-2024
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• 2005

In this work, a mixed beam approach that combines both the stiffness and the flexibility methods has been performed to analyze the coupled composite blades with closed, two-cell cross-sections. The Reissner's semi-complementary energy functional is used to derive the beam force-displacement relations. Only the membrane part of the shell wall is taken into account to make the analysis simple and also to deliver a clear picture of the mixed method. All the cross section stiffness coefficients as well as the distribution of shear across the section are evaluated in a closed-form through the beam formulation. The theory is validated against experimental test data, detailed finite element analysis results, and other analytical results for coupled composite blades with a two-cell airfoil section. Despite the simple kinematic model adopted in the theory, an accuracy comparable to that of two-dimensional finite element analysis has been obtained for cases considered in this study.

• Structural Engineering and Mechanics
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• v.11 no.4
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• pp.423-442
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• 2001

This paper presents a method of elastic-plastic analysis for planar steel frames that provides the accuracy of distributed plasticity methods with the computational efficiency that is greater than that of distributed plasticity methods but less than that of plastic-hinge based methods. This method accounts for the effect of spread of plasticity accurately without discretization through the cross-section of a beam-column element, which is achieved by the following procedures. First, nonlinear equations describing the relationships between generalized stresses and strains of the cross-section are derived analytically. Next, nonlinear force-deformation relationships for the beam-column element are obtained through lengthwise integration of the generalized strains. Elastic-plastic flexibility coefficients are then calculated by differentiating the above element force-deformation relationships. Finally, an elastic-plastic stiffness matrix is obtained by making use of the flexibility-stiffness transformation. Adding the conventional geometric stiffness matrix to the elastic-plastic stiffness matrix results in the tangent stiffness matrix, which can readily be used to evaluate the load carrying capacity of steel frames following standard nonlinear analysis procedures. The accuracy of the proposed method is verified by several examples that are sensitive to the effect of spread of plasticity.

• Journal of Aerospace System Engineering
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• v.2 no.1
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• pp.7-12
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• 2008

The three-dimensional finite element modeling of a composite rotor blade is very hard and requires much computation effort. The efficient method to model a composite beam is necessary for the dynamic and aeroelastic analyses of rotor blades. In this study, the beam modeling method of a composite rotor blade is studied using VABS. The computer program, VABS (Variational Asymptotic Beam Section Analysis), uses the variational asymptotic method to split a 3-D nonlinear elasticity problem into 2-D cross-sectional analysis and 1-D nonlinear beam problem. The VABS can produce the sectional stiffness coefficients of composite rotor blades with various cross section and initial twist/curvatures, and recover the original 3-D distribution of displacement/strain/stress fields. The results of various cross section beams show that VABS gives us the accurate results comparared to commercial codes and does not need much computation effort. It can be concluded that VABS provides the efficient method to establish the FE model of a composite rotor blade.

• Tribology and Lubricants
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• v.24 no.6
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• pp.291-296
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• 2008

In order to improve the leakage prediction and rotordynamic analysis of an annular seal with a smooth rotor and circumferentially grooved stator, CFD analysis using FLUENT has been performed to determine the groove penetration angle a which is the angle of separation line between control volumes II and III in groove section of Ha and Lee's three-control-volume theory. Validation to the present analysis using new penetration angle determined by the CFD analysis is achieved by comparisons with the results of published Ha and Lee's analysis. For the leakage prediction the present analysis shows slight improvement and CFD results yields the best. Direct damping and cross-coupled stiffness coefficients are predicted better to the experimental ones. However, direct stiffness coefficient is predicted worse.

• Structural Engineering and Mechanics
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• v.8 no.3
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Journal of Aerospace System Engineering
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• v.13 no.2
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• pp.51-59
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• 2019

Subsequently, Part I [1], which was about the single-cell model, a composite thin-walled beam with a multi-cell of chord-wise asymmetric cross-section, was selected in this study. Moreover, the theoretical dynamic characteristics of the model were analyzed. For this analysis, mathematical modeling was performed by considering the warping restraint effects, transverse shear effects, taper ratio and cross-section ratio. Similar to part I, the mass, stiffness coefficients and Eigen frequencies of the multi-cell section considered were investigated. In particular, the comparison between the multi-cell and single-cell sections and the effects of the cross-section ratio and taper ratio of the model on the Eigen frequencies were analyzed. However, the results compared when the asymmetry of the section was considered and warping function were not corrected.

• Structural Engineering and Mechanics
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• v.42 no.5
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• pp.715-728
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• 2012

This paper deals with determining the fundamental frequency of tall buildings that consist of framed tube, shear core, belt truss and outrigger systems in which the framed tube and shear core vary in size along the height of the structure. The effect of belt truss and outrigger system is modeled as a concentrated rotational linear spring at the belt truss and outrigger system location. Many cantilevered tall structures can be treated as cantilevered beams with variable cross-section in free vibration analysis. In this paper, the continuous approach, in which a tall building is replaced by an idealized cantilever continuum representing the structural characteristics, is employed and by using energy method and Hamilton's variational principle, the governing equation for free vibration of tall building with variable distributed mass and stiffness is obtained. The general solution of governing equation is obtained by making appropriate selection for mass and stiffness distribution functions. By applying the separation of variables method for time and space, the governing partial differential equation of motion is reduced to an ordinary differential equation with variable coefficients with the assumption that the transverse displacement is harmonic. A power-series solution representing the mode shape function of tall building is used. Applying boundary conditions yields the boundary value problem; the frequency equation is established and solved through a numerical process to determine the natural frequencies. Computer program has been developed in Matlab (R2009b, Version 7.9.0.529, Mathworks Inc., California, USA). A numerical example has been solved to demonstrate the reliability of this method. The results of the proposed mathematical model give a good understanding of the structure's dynamic characteristics; it is easy to use, yet reasonably accurate and suitable for quick evaluations during the preliminary design stages.

• Steel and Composite Structures
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• v.19 no.6
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• pp.1561-1580
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• 2015

No significant improvement has been observed on the seismic performance of the ordinary steel reinforced concrete (SRC) columns compared with the reinforced concrete (RC) columns mainly because I, H or core cross-shaped steel cannot provide sufficient confinement for core concrete. Two improved SRC columns by constructing with new-type section steel were put forward on this background: a cross-shaped steel whose flanges are in contact with concrete cover by extending the geometry of webs, and a rotated cross-shaped steel whose webs coincide with diagonal line of the column's section. The advantages of new-type SRC columns have been proved theoretically and experimentally, while construction measures and seismic behavior remain unclear when the new-type columns are joined onto SRC beams. Seismic behavior of SRC joints with new-type section steel were experimentally investigated by testing 5 specimens subjected to low reversed cyclic loading, mainly including the failure patterns, hysteretic loops, skeleton curves, energy dissipation capacity, strength and stiffness degradation and ductility. Effects of steel shape, load angel and construction measures on seismic behavior of joints were also analyzed. The test results indicate that the new-type joints display shear failure pattern under seismic loading, and steel and concrete of core region could bear larger load and tend to be stable although the specimens are close to failure. The hysteretic curves of new-type joints are plumper whose equivalent viscous damping coefficients and ductility factors are over 0.38 and 3.2 respectively, and this illustrates the energy dissipation capacity and deformation ability of new-type SRC joints are better than that of ordinary ones with shear failure. Bearing capacity and ductility of new-type joints are superior when the diagonal cross-shaped steel is contained and beams are orthogonal to columns, and the two construction measures proposed have little effect on the seismic behavior of joints.

• Wind and Structures
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• v.21 no.1
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• pp.105-117
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• 2015

This paper presents a numerical characterization of real railway overhead cables based on computational fluid dynamics (CFD). Complete analysis of the aerodynamic coefficients of this type of cross section yields a more accurate modelling of pressure loads acting on moving cables than provided by current approaches used in design. Thus, the characterization of certain selected commercial cables is carried out in this work for different wind speeds and angles of attack. The aerodynamic lift and drag coefficients are herein determined for two different types of grooved cables, which establish a relevant data set for the railway industry. Finally, the influence of this characterization on the fluid-structure interaction (FSI) is proved, the static behavior of a catenary system is studied by means of the finite element method (FEM) in order to analyze the effect of different wind angles of attack on the stiffness distribution.