Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

Beck, André Teófilo; Silva, Cláudio R.A. da

doi:10.1016/j.strusafe.2010.04.006

Cited by 32 publications

(9 citation statements)

References 4 publications

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“…Interestingly, an opposite behavior was observed by the authors when studying bending of stochastic Euler-Bernoulli beams. These observations have led to interesting conclusions about the comparative uncertainty propagation properties of Timoshenko and Euler-Bernoulli beam models [33]. For both examples, the Galerkin scheme presented very fast convergence rates to the first and second order moments of transverse and angular displacement fields.…”

Section: Discussionmentioning

confidence: 86%

“…For Euler-Bernoulli beams, an opposite behavior was observed by the authors [22]: Euler-Bernoulli beams are more sensitive to uncertainties in cross-section height than to uncertainties in elastic properties. These observations have led to interesting conclusions about the comparative uncertainty propagation properties of the two beam models [33].…”

Section: Example 2: Random Beam Cross-section Heightmentioning

confidence: 92%

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Chaos–Galerkin solution of stochastic Timoshenko bending problems

Silva

Beck

2011

Computers & Structures

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Section: Discussionmentioning

confidence: 86%

Section: Example 2: Random Beam Cross-section Heightmentioning

confidence: 92%

Chaos–Galerkin solution of stochastic Timoshenko bending problems

Silva

Beck

2011

Computers & Structures

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“…A great number of theoretical and experimental studies have been done by many researchers (Guan et al, 2003;Li et al, 2004;Fan et al, 2013). In terms of the complexity of the model, most of the early models are uncoupled vibration models, like axial (Lubinski, 1988;Elsayed and Phung, 2005;Li et al, 2007), lateral (Beck and da Silva, 2010;Ghasemloonia et al, 2012) and torsional (Challamel et al, 2000;Besselink et al, 2011;Arjun Patil andTeodoriu, 2013a, Arjun Patil andTeodoriu, 2013b) vibration models. These simplified models allow researchers to understand how the single external excitations influence the vibration of drill string.…”

Section: Introductionmentioning

confidence: 99%

Study on Dynamic Characteristics of Drill String Considering Rock-Breaking Process

Liang

Guan

et al. 2021

Front. Earth Sci.

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Using various tools to obtain downhole data to reach a precise pore pressure model is an important means to predict overpressure. Most downhole tools are connected to the lower end of drill string and move with it. It is necessary to understand the motion state and dynamic characteristics of drill string, which will affect the use of downhole tools. In this paper, a drilling process considering rock-breaking process in vertical wells is simulated using finite element method. In the simulation, gravity is applied to the whole drill string. The contact force between PDC bit and formation is the weight on bit (WOB). And a rotation speed is applied to the upper end of drill string. Analysis of the results shows that the vibration amplitude of bottom hole WOB (contact force between PDC bit and formation, which is the real WOB in drilling process) is bigger than the amplitude of wellhead WOB (acquired through conversion using Hook load, which is on behalf of the WOB obtained on drilling site). Both wellhead WOB and bottom hole WOB decline with a fluctuation in drilling process. In small initial WOB and low rotation speed conditions, the fluctuation of wellhead WOB focuses on low frequency, the fluctuation of bottom hole WOB focus on high frequency, and the phase of them are not identical. In large initial WOB and high rotation speed conditions, the fluctuation of wellhead WOB and bottom hole WOB both become more irregular. As for wellhead torque and bottom hole torque, the fluctuation of them mainly focuses on low frequency. And in high rotation speed conditions, wellhead torque may become negative. The research results are beneficial to the usage of downhole tools.

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“…The validity of these hypothesis greatly depends of the characteristics of the beam, for as stated in Beck et al [5], the choice of one hypothesis or the other involves generally the geometry of the beam.…”

Section: Introductionmentioning

confidence: 99%

3D small strain large deflection beam shape sensing including poisson effect

Schaefer

Chagnon

Moreau–Gaudry

2020

Engineering Structures

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This article presents a new method to monitor beam shapes from strain measures. The beam is instrumented with strain sensors placed on its surface with an angle of orientation. The method developed is a 3D large deflection beam shape reconstruction based on a beam model incorporating Poisson effect and is thus able to take into account bending, torsion, shearing and tensile-compression deformations. Exemple of application on circular beams is conducted with beam shape reconstructed from FEM simulations strain measures. Results show that, compared to beam shape sensing methods using axial strain, the beam shape method proposed provides a significant increase in the reconstruction accuracy when the beam is subject to deformations containing torsion.

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Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

Cited by 32 publications

References 4 publications

Chaos–Galerkin solution of stochastic Timoshenko bending problems

Chaos–Galerkin solution of stochastic Timoshenko bending problems

Study on Dynamic Characteristics of Drill String Considering Rock-Breaking Process

3D small strain large deflection beam shape sensing including poisson effect

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