• Steel and Composite Structures
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• 제19권3호
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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.

• Steel and Composite Structures
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• 제27권5호
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• pp.567-576
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• 2018

The objective of this work is to analyze large deflections of a fiber reinforced composite cantilever beam under point loads. In the solution of the problem, finite element method is used in conjunction with two dimensional (2-D) continuum model. It is known that large deflection problems are geometrically nonlinear problems. The considered non-linear problem is solved considering the total Lagrangian approach with Newton-Raphson iteration method. In the numerical results, the effects of the volume fraction and orientation angles of the fibre on the large deflections of the composite beam are examined and discussed. Also, the difference between the geometrically linear and nonlinear analysis of fiber reinforced composite beam is investigated in detail.

• International Journal of Aeronautical and Space Sciences
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• 제9권2호
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• pp.41-47
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• 2008

The nonlinear structural analyses of high-aspect-ratio structures were performed. For the high-aspect-ratio structures, it is important to understand geometric nonlinearity due to large deflections. To consider geometric nonlinearity, finite element analyses based on the large deflection beam theory were introduced. Comparing experimental data and the present nonlinear analysis results, the current results were proved to be very accurate for the static and dynamic behaviors for both isotropic and anisotropic beams.

• Structural Engineering and Mechanics
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• 제54권3호
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• pp.433-451
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• 2015

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

• 한국기계연구소 소보
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• 통권18호
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• pp.131-136
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• 1988

A small-deflected beam can be easily solved by assuming a linear system. But a large-deflected beam can not be solved by superposition of the displacements, because the system is nonlinear. The solutions for the large-deflection problems can not be obtained directly from elementary beam theory for linearized systems since the basic assumptions are no longer valid. Specifically, elementary theory neglects the square of the first derivative in the beam curvature formula and provides no correction for the shortening of the moment-arm cause by transverse deflection. These two effects must be considered to analyze the large deflection. Through the correction of deflected geometry and internal axial force, the proposed new approach is developed from the linearized beam theory. The solutions from the proposed approach are compared with exact solutions.

• 대한기계학회논문집
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• 제19권8호
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• pp.1889-1900
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• 1995

In this study, a large deflection analysis of a plane frame composed of a thin-walled tube in investigated. When bent, a thin-walled tube is usually controlled by local buckling and subsequent bending collapse of the section. So load resistance reaches the yield level in a thin-walled rectangular tube. This relationship can be divided into three regimes : elastic, post-buckling and crippling. In this paper, this relationship is theoretically presented to be capable of describing nonlinearities and a stiffness matrix is derived by introducing a compound beam-spring element. A numerical analysis uses a constant incremental energy method and the solution is obtained by modifying stiffness matrix at elastic/inelastic stage. This analytical results, load-deflection paths show a good agreement with the test results.

• International Journal of Aeronautical and Space Sciences
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• 제8권1호
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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.

• International Journal of Aeronautical and Space Sciences
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• 제7권1호
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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.

• Advances in Computational Design
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• 제7권2호
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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.

• 한국항공우주학회지
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• 제35권6호
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• pp.503-508
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• 2007

본 연구에서는 대변형 보이론을 이용하여 무베어링 로터 시스템의 공력탄성학적 안정성 해석을 수행하였다. 무베어링 로터 시스템의 유연보, 토오크 튜브, 그리고 메인 블레이드를 각각 탄성 운동을 하는 보로 가정하고, 1차원 보 요소로 모델링을 하였다. 외력으로는 2차원 준-정상 공기력 모델을 적용하였으며, 보의 유한 요소 지배방정식은 헤밀턴 원리(Hamilton's Principle)를 이용하여 얻었다. 공력탄성학적 안정성 해석을 수행하기 위하여 정지 비행시는 모달 접근법을, 전진 비행시는 주기적인 특성을 갖는 비선형 정적 트림해를 얻기 위해 동체 평형을 고려한 연계 평형 해석을 통한 완전 유한요소 방정식을 이용하였다. 본 연구에서 구한 결과를 기존의 적정변형 보이론에 모달 접근법을 이용한 무베어링 로터 시스템의 결과와 비교하였다.