Extreme deformations of the cantilever Euler Elastica under transverse aerodynamic load

Misseroni, D.; Barbieri, Ettore; Pugno, Nicola

doi:10.1016/j.eml.2020.101110

Cited by 5 publications

(3 citation statements)

References 34 publications

(37 reference statements)

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“…It is evident that the Galerkin method can be equally powerful for nonlinear problems arising from applications in many fields. The elastica problem has a long and rich history, but it is still a hot topic related to the flexure and buckling of beams and rods; accurate results are essentially obtained from the elliptic functions [38,39]. The procedure and solution from this study show that with the Galerkin method, a new technique to solve similar nonlinear differential equations is available, and it can be much simpler to obtain reasonably accurate solutions.…”

Section: Equation Of Flexure Of An Elastic Beam and Its Solutionmentioning

confidence: 89%

The Approximate Solution of Nonlinear Flexure of a Cantilever Beam with the Galerkin Method

Zhang

Wang

et al. 2022

Applied Sciences

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For the optimal design and accurate prediction of structural behavior, the nonlinear analysis of large deformation of elastic beams has broad applications in various engineering fields. In this study, the nonlinear equation of flexure of an elastic beam, also known as an elastica, was solved by the Galerkin method for a highly accurate solution. The numerical results showed that the third-order solution of the rotation angle at the free end of the beam is more accurate and efficient in comparison with results of other approximate methods, and is perfectly consistent with the exact solution in elliptic functions. A general procedure with the Galerkin method is demonstrated for efficient solutions of nonlinear differential equations with the potential for adoption and implementation in more applications.

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Section: Equation Of Flexure Of An Elastic Beam and Its Solutionmentioning

confidence: 89%

The Approximate Solution of Nonlinear Flexure of a Cantilever Beam with the Galerkin Method

Zhang

Wang

et al. 2022

Applied Sciences

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“…Several attempts of providing experimental evidence to the concept using air or fluid flow from a nozzle [147][148][149] or using a rocket motor [150,151] were at least in part successful, nevertheless criticized from different points of view. A completely new approach was initiated by Bigoni & Noselli [129], in which the follower force was created by exploiting Coulomb friction on a freely rotating wheel, as sketched in figure 4a,b.…”

Section: Recent Progress On Flutter (A) the Quest For Follower Forcesmentioning

confidence: 99%

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Bigoni,

Dal Corso,

Kirillov

et al. 2023

Proc. R. Soc. A.

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The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated.

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“…In addition, we are considering quasi-static conditions. Experimentally, such situations are tricky to reproduce and the system becomes unstable for large loads (Misseroni et al, 2021). The shape of the elastica can be found by solving…”

Section: Equilibrium Equationsmentioning

confidence: 99%

Peeling under large bending deformations: Follower versus fixed loads. A unified approach for concentrated or distributed loads

Barbieri

Botto

2022

International Journal of Solids and Structures

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Extreme deformations of the cantilever Euler Elastica under transverse aerodynamic load

Cited by 5 publications

References 34 publications

The Approximate Solution of Nonlinear Flexure of a Cantilever Beam with the Galerkin Method

The Approximate Solution of Nonlinear Flexure of a Cantilever Beam with the Galerkin Method

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

Peeling under large bending deformations: Follower versus fixed loads. A unified approach for concentrated or distributed loads

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