• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.6
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• pp.503-508
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• 2007

In this study, the aeroelastic response and stability of bearingless rotors are investigated using a large deflection beam theory. The outboard main blade, flexbeam, and torque tube are all assumed to be an elastic beam undergoing arbitrary large displacements and rotations. The finite element equations of motion obtained from Hamilton's principle. Two-dimensional quasi-steady strip theory is used to evaluate aerodynamic forces. In hover, the modal approach method based on coupled rotating natural modes is used for the stability analysis. In forward flight, the nonlinear periodic blade steady response is obtained by integrating the full finite element equation in time through a coupled trim procedure with a vehicle trim. The results of the full finite element analysis using the large deflection beam theory are compared with those of a previously published modal analysis using the moderate deflection-type beam theory.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.115-121
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• 2007

The aeroelastic analysis of rotor blades with trailing edge flaps, focused on reducing vibration while minimizing control effort, are investigated using large deflection-type beam theory in forward flight. The rotor blade aerodynamic forces are calculated using two-dimensional quasi-steady strip theory. For the analysis of forward flight, the nonlinear periodic blade steady response is obtained by integrating the full finite element equation in time through a coupled trim procedure with a vehicle trim. The objective function, which includes vibratory hub loads and active flap control inputs, is minimized by an optimal control process. Numerical simulations are performed for the steady-state forward flight of various advance ratios. Also, numerical results of the steady blade and flap deflections, and the vibratory hub loads are presented for various advance ratios and are compared with the previously published analysis results obtained from modal analysis based on a moderate deflection-type beam theory.

• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Advances in Computational Design
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• v.7 no.2
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• pp.99-112
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• 2022

This research has been devoted to examine nonlinear static bending analysis of smart beams with nano dimension exposed to thermal environment. The beam elastic properties are corresponding to piezo-magnetic material of different compositions. The large deflection analysis of the beam has been performed assuming that the beam is exposed to transverse uniform pressure. Based on the rule of Hamilton, the governing equations have been derived for a nonlocal thin beam and solved using differential quadrature method. Temperature variation effect on nonlinear deflection of the smart beams has been studied. Also, the beam deflection is shown to be affected by electric voltage, magnetic intensity and material composition.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.1
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• pp.99-105
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• 2006

In this study, nonlinear static and dynamic aeroelastic analyses for a high-aspect-ratio wing have been performed. To achieve these aims, the transonic small disturbance (TSD) theory for the aerodynamic analysis and the large deflection beam theory considering a geometrical nonlinearity for the structural analysis are applied, respectively. For the coupling between fluid and structure, the transformation of a displacement from the structural mesh to the aerodynamic grid is performed by a shape function which is used for the finite element and the inverse transformation of force by work equivalent load method. To validate the current method, the present analysis results of a high-aspect-ratio wing are compared with the experimental results. Static deformations in the vertical and torsional directions caused by an angle of attack and gravity loading are compared with experimental results. Also, static and dynamic aeroelastic characteristics are investigated. The comparisons of the flutter speed and frequency between a linear and nonlinear analysis are presented.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.585-594
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• 2021

Ductility is very important parameter in seismic design of RC members such as beams where it allows RC beams to dissipate the seismic energy. In this field, the curvature ductility has taken a large part of interest compared to the deflection ductility. For this reason, the present paper aims to propose a general formula for predicting the deflection ductility factor of RC beams under mid-span load. Firstly, the moment area theorem is used to develop a model in order to calculate the yield and the ultimate deflections; then this model is validated by using some results extracted from previous researches. Secondly, a general formula of deflection ductility factor is written based on the developed deflection expressions. The new formula is depended on curvature ductility factor, beam length, and plastic hinge length. To facilitate the use of this formula, a parametric study on the curvature ductility factor is conducted in order to write it in simple manner without the need for curvature calculations. Therefore, the deflection ductility factor can be directly calculated based on beam length, plastic hinge length, concrete strength, reinforcement ratios, and yield strength of steel reinforcement. Finally, the new formula of deflection ductility factor is compared with the model previously developed based on the moment area theorem. The results show the good performance of the new formula.

• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.463-474
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• 1995

When a tubular cantilever beam is loaded by a dynamic force applied transversely at its tip, the strain hardening of the material tends to increase the load carrying capacity and local buckling and cross-sectional overlization occurring in the tube section tends to reduce the moment carrying capacity and results in structural softening. A theoretical model is presented in this paper to analyze the deformation of a tubular beam in a dynamic response mode. Based on a large deflection analysis, the hardening/softening M-${\kappa}$ relationship is introduced. The main interest is on the curvature development history and the deformed configuration of the beam.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.3
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• pp.31-36
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• 2006

In this study, nonlinear static aeroelastic analysis system for a high-aspect-ratio wing are developed using the transonic small disturbance (TSD) and large deflection beam theory and validated. For the coupling between fluid and structure, the transformation of displacement from the structural mesh to aerodynamic one is performed by the shape function of the beam finite element and the inverse transformation of force by work equivalent load concept. Also, for the static aeroelastic analysis of the wing the use of TSD aerodynamics are justified. The validation of the system includes one of the efficient transformation methods of force and displacement.

• International Journal of Ocean System Engineering
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• v.2 no.3
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• pp.195-199
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• 2012

This paper reports a new analytical method to calculate the planar displacement of structures. The cross-sections were assumed to remain in plane and the deflection curve was evaluated using the curvature values geometrically, despite being solved with differential equations. The deflection curve was parameterized with the arc-length of the curvature values, and was taken as an assembly of chains of circular arcs. Fast and accurate solutions of complex deflections can be obtained easily. This paper includes a comparison of the nonlinear displacements of an elastic tapered cantilever beam with a uniform moment distribution among the proposed analytical method, numerical method of the theory and large deflection FEM solutions.

• Journal of the korean Society of Automotive Engineers
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• v.4 no.3
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• pp.56-68
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• 1982

This paper presents analytic solutions of defection and their resonance diagrams for a uniform beam of infinite length subjected to an constant axial force and moving transverse load simultaneously. Steady solutions are obtained by a time-independent coordinate moving with the load. The supporting foundation includes damping effects. The influences of the axial force, the damping coefficient and the load velocity on the beam response are studied. The limiting cases of no damping and critical damping are also investigate. The profiles of the deflection of the beam are shown graphically for several values of the load speed, the axial force and damping parameters. Form the results, following conclusions have been reached. 1. The critical velocity .THETA.cr decreases as the axial compressive force increases, but increases as the axial tensile force increase. 2. At the critical velocity .THETA.cr the deflection have a tendency to decrease as the axial tensile force increases and to increase gradually as the axial compressive force increases. 3. In case if relatively small dampings, the deflection increases suddenly as the velocity of the moving load approaches the critical velocity, and it reachs its maximum at the critical velocity, and it decreases and become greatly affected by the axial force as the velocity increases further. 4. in case of relatively large dampings, as the velocity increases the deflection decreases gradually and it is affected little by the axial load.