Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behaviour

Solano-Carrillo, E.

doi:10.1016/j.ijnonlinmec.2008.11.007

Cited by 25 publications

(12 citation statements)

References 11 publications

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“…Governing equation of large deflection beam problem is generally derived in the framework of Euler-Bernoulli beam theory [71][72][73][74][75][76]. Mathematical manipulation transforms the nonlinear governing equation in some special forms.…”

Section: Analytical Methodmentioning

confidence: 99%

See 1 more Smart Citation

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%

“…They exhibit linear relation between stress and strain within its elastic limit. However, several metals undergo work hardening and show nonlinearity in stress-strain relation within elastic limit [72,85]. Stress-strain relation for this Ludwick type nonlinear material is generally modeled by the relation…”

Section: Isotropic Materialsmentioning

confidence: 99%

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

Ghuku

Saha

2017

IJET

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“…Then, the non-linear ODE indicated in (15) is solved approximately with an Euler approach under the initial conditions described in (16).…”

Section: (13) (14)mentioning

confidence: 99%

“…Other authors [15] described thin cantilever beams composed by bimodulus Ludwick type material under the presence of a mechanical moment applied at the free-end. A semi-exact solution was achieved [16] for cantilever beams composed by Ludwick material in large deformations and subjected to a double vertical load: the first was distributed on the beam and the second concentrated at the free end. Then non-prismatic cantilever beams composed by a generalized Ludwick material [17] were described in the presence of large deflections and external constant mechanical loads.…”

Section: Introductionmentioning

confidence: 99%

Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

Borboni¹,

Santis²,

Solazzi³

et al. 2016

TOMEJ

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Abstract:The aim of this paper is to calculate the horizontal and vertical displacements of a cantilever beam in large deflections. The proposed structure is composed with Ludwick material exhibiting a different behavior to tensile and compressive actions. The geometry of the cross-section is constant and rectangular, while the external action is a vertical constant load applied at the free end. The problem is nonlinear due to the constitutive model and to the large deflections. The associated computational problem is related to the solution of a set of equation in conjunction with an ODE. An approximated approach is proposed here based on the application Newton-Raphson approach on a custom mesh and in cascade with an Eulerian method for the differential equation.

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“…Bayakara et al [8] investigated the effect of bimodulus Ludwick type material behavior on the horizontal and vertical deflections at the free end of a thin cantilever beam under an end moment. A semi-exact solution was obtained by Solano-Carrillo [9] for large deflection of cantilever beams made of Ludwick type material subjected to a combined action of a uniformly distributed load and to a vertical concentrated force at the free end. Brojan et al [10] studied the large deflections of nonlinearly elastic non-prismatic cantilever beams made of materials obeying the generalized Ludwick constitutive law.…”

Section: Introductionmentioning

confidence: 99%

Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end

Borboni

Santis

2014

Meccanica

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The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated constant vertical load, to a concentrated constant horizontal load and to a concentrated constant bending torque at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler-Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper.

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Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behaviour

Cited by 25 publications

References 11 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

Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

Large deflection of a non-linear, elastic, asymmetric Ludwick cantilever beam subjected to horizontal force, vertical force and bending torque at the free end

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