On the parametric large deflection study of Euler–Bernoulli cantilever beams subjected to combined tip point loading

Tari, Hafez

doi:10.1016/j.ijnonlinmec.2012.09.004

Cited by 51 publications

(36 citation statements)

References 9 publications

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“…This approach does not simply linearize the system governing equation, but provides solution convergence for nonlinear portion of the governing equation employing Adomian polynomials. Taylor expansion technique [64,65] [66].…”

Section: Analytical Methodmentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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Abstract. The paper presents a review on large deflection behavior of curved beams, as manifested through the responses under static loading. The term large deflection behavior refers to the inherent nonlinearity present in the analysis of such beam system response. The analysis leads to the field of geometric nonlinearity, in which equation of equilibrium is generally written in deformed configuration. Hence, the domain of large deflection analysis treats beam of any initial configuration as curved beam. The term curved designates the geometry of center line of beam, distinguishing it from the usual straight or circular arc configuration. Different methods adopted by researchers, to analyze large deflection behavior of beam bending, have been taken into consideration. The methods have been categorized based on their application in various formats of problems. The nonlinear response of a beam under static loading is also a function of different parameters of the particular problem. These include boundary condition, loading pattern, initial geometry of the beam, etc. In addition, another class of nonlinearity is commonly encountered in structural analysis, which is associated with nonlinear stress-strain relations and known as material nonlinearity. However the present paper mainly focuses on geometric nonlinear analysis of beam, and analysis associated with nonlinear material behavior is covered briefly as it belongs to another class of study. Research works on bifurcation instability and vibration responses of curved beams under large deflection is also excluded from the scope of the present review paper.

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Section: Analytical Methodmentioning

confidence: 99%

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Ghuku

Saha

2017

IJET

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“…The Euler-Bernoulli bending for finite deflections has been extensively used in the scientific literature, since the work of Bisshopp and Drucker (1945), which have defined the differential equation to be solved involving the exact curvature for large displacements, since the assumptions from elementary beam theory are no longer valid. Based on this differential equation, various works dealing with finite Euler-Bernoulli bending have been performed (see, among many others, Jenkins et al (1966); Holden (1972); Mattiasson (1981); Lee (2002); Chen (2010); Tari (2013)). …”

Section: Numerical Analysis Of Highly Deformable Elastoplastic Beams mentioning

confidence: 99%

Numerical analysis of highly deformable elastoplastic beams

Pascon

2015

Lat. Am. j. solids struct.

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“…So far, a large number of theoretical methods have been proposed to determine the large deflections of Euler-Bernoulli beams due to geometric and material nonlinearity. For example, for a simply-supported beam, elliptic integrals are applied to calculate large deflections for a centrally-loaded simply-supported beam (e.g., [1][2][3]). When a simply-supported beam is subjected to moment at ends, large deflections have been calculated in [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…JID:CRAS2B AID:3409 /FLA [m3G; v1.180; Prn:6/06/2016; 18:03] P.6(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) …”

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confidence: 99%

Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending

2016

Comptes Rendus. Mécanique

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Three-point bending of a beam is studied based on the Timoshenko beam theory. Large deflection and large rotation of a beam resting on simple supports with friction are calculated for a concentrated force acting at the midspan. Using the Lagrangian kinematic relations, a system of non-linear differential equations are obtained for a prismatic sheardeformable Timoshenko beam. Exact solutions for the deflection, horizontal displacement, and rotation of cross-section are derived analytically. Two deflections of small and large scale exist under three-point bending. The solutions corresponding to linearized model coincide with the well-known solutions to the classical Timoshenko beams. Numerical calculations are carried out to show the effect of the important parameters such as shear rigidity of the beam and the coefficient of friction at the contact position between the beam and supports on the deflection. The load-deflection curves are graphically presented. A comparison of large deflections and large rotations with their classical counterparts and with experimental data is made. The obtained results are useful in safety design of linear and non-linear beams subject to three-point bending.

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On the parametric large deflection study of Euler–Bernoulli cantilever beams subjected to combined tip point loading

Cited by 51 publications

References 9 publications

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

A Review on Stress and Deformation Analysis of Curved Beams under Large Deflection

Numerical analysis of highly deformable elastoplastic beams

Large deflection and rotation of Timoshenko beams with frictional end supports under three-point bending

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