Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

Brojan, Miha; Čebron, Matjaž; Kosel, Franc

doi:10.1007/s10409-012-0053-3

Cited by 16 publications

(6 citation statements)

References 7 publications

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“…The solution method is based on a simple formulation and is therefore easy to understand and use. Furthermore, it can be generalized to employ nonlinear material response or other physical behavior without major difficulties, [1,[25][26][27].…”

Section: Introductionmentioning

confidence: 99%

A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler-Bernoulli and large displacement theory. The problem is solved numerically using RungeKutta-Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms.

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Section: Introductionmentioning

confidence: 99%

A simple method for determining large deflection states of arbitrarily curved planar elastica

2013

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“…9 Deflection of a rubber material beam in comparison between experiment [8], numerical results [8], and the proposed beam method Fig. 10 Stress-strain curves of a rubber material [8] and the approximated for the proposed beam method for Fig. 9 multi-nonlinear elastic stiffnesses are shown in Fig.…”

Section: Capabilitiesmentioning

confidence: 99%

“…Elastomers are also part of this kind of materials. In the experiment of Brojan et al such an elastomer is tested as a material for a beam structure [8]. Brojan et al developed also a comprehensive method to analyse such stiffness relation in beams.…”

Section: Introductionmentioning

confidence: 99%

Aeroelastic method to investigate nonlinear elastic wing structures

et al. 2022

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Stiffness directions of wing structures are already part of the optimisation in aircraft design. Aircraft like the A350 XWB and the Boeing 787 mainly consist of such composite material, whose stiffness directions can be optimised. To proceed with this stiffness optimisation, the aim of this work is to modify and optimise also the linear stress-strain relation. On that account, the Hooke’s law is exchanged by a multi-linear formulation to analyse any nonlinear elastic structural technology on wing structures. The wing structures, which are used to investigate the nonlinear behaviour, are deduced from a mid-range and a long-range aircraft configuration. These wings are analysed with an extended beam method and coupled with a VLM solution to calculate the aeroelastical loading. The proposed beam method is capable of analysing any multi-linear wing structure technology. A degressive structural behaviour shows up a good potential to reduce the bending moment which is one of the main drivers of the structural weight.

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“…Then, the computational procedure continues with the verification of the adopted value of ρ h , namely it calculates the difference between the initial and final values of the length of the beam, verifying that it is under a set level; contrary, δ h is incremented and the algorithm is restarted. Finally, the value of δ v is computed with the equation indicated in (17).…”

Section: Problem Formulationmentioning

confidence: 99%

Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

Borboni¹,

Santis²,

Solazzi³

et al. 2016

Open mechan. eng. J.

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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.Different authors worked on non-linear elastic materials with different constitutive models [21], i.e. , considering large deflections of cantilever beams under different loading conditions at the free end. Furthermore literature proposed different works on non-linear materials with variable constitutive model [23].This work proposes a study on a cantilever beam with a Ludwick elastic constitutive law that is non-linear and asymmetric under large deflections. Different implementations of these results can be performed for applicative purposes, i.e. in the design of compliant mechanisms or microactuators with large deflections [24 -26]. PROBLEM DESCRIPTIONThis work investigates a cantilever beam with the following characteristics: its length, at initial conditions, is L, the cross-section does not change over the time and is rectangular, the characteristic measures of the cross-section are b and h, finally the beam is subjected to a vertical constant load F at the free bound.This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/legalcode), which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

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Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

Cited by 16 publications

References 7 publications

A simple method for determining large deflection states of arbitrarily curved planar elastica

A simple method for determining large deflection states of arbitrarily curved planar elastica

Aeroelastic method to investigate nonlinear elastic wing structures

Ludwick Cantilever Beam in Large Deflection Under Vertical Constant Load

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