Euler-Bernoulli beam theory

Bauchau, Olivier A.; Craig, James I.

doi:10.1007/978-90-481-2516-6_5

Cited by 165 publications

(117 citation statements)

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“…, 26. Moreover, in equation (8), N ⇤ was taken equal to 1 and the weights ↵ j (l) were defined as in [18], i.e., at the beam ends we took 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 and finally…”

Section: Simulation Resultsmentioning

confidence: 99%

“…The model used to simulated the beam vibration is based on a Timoshenko type p-version finite element and was introduced in [12] see also [13]). We used this model to obtain the data w(x, t),ẇ(x, t) andẅ(x, t) from which y(x, t) and A(x, t) in (26) are constructed and then given as inputs in their discrete versions to the 2D HNN (8). For the sake of completeness, the main steps of the formulation are described here.…”

Section: Simulation Modelmentioning

confidence: 99%

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A 2D Hopfield Neural Network approach to mechanical beam damage detection

Almeida

Alonso

Ribeiro

et al. 2015

Multidim Syst Sign Process

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The aim of this paper is to present a method based on a 2D Hopfield Neural Network for online damage detection in beams subjected to external forces. The underlying idea of the method is that a significant change in the beam model parameters can be taken as a sign of damage occurrence in the structural system. In this way, damage detection can be associated to an identification problem. More concretely, a 2D Hopfield Neural Network uses information about the way the beam vibrates and the external forces that are applied to it to obtain time-evolving estimates of the beam parameters at the di↵erent beam points. The neural network organizes its input information based on the Euler-Bernoulli model for beam vibrations. Its performance is tested with vibration data generated by means of a di↵erent model, namely Timonshenko's, in order to produce more realistic simulation conditions.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Modelmentioning

confidence: 99%

A 2D Hopfield Neural Network approach to mechanical beam damage detection

Almeida

Alonso

Ribeiro

et al. 2015

Multidim Syst Sign Process

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“…This does not significantly affect the flow (fluid velocity and pressure); however, changes the solid response, see Figure 7. Similar to the mode shapes of an Euler-Bernoulli beam [49], the (transient) nonlinear solid model exhibits deformation modes corresponding to the natural frequencies of the solid material.…”

Section: Transient Fluid and Transient Nonlinear Solid In 3dmentioning

confidence: 90%

A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms

Hessenthaler

Balmus

Röhrle

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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Fluid-structure interaction (FSI) problems are pervasive in the computational engineering community. The need to address challenging FSI problems has led to the development of a broad range of numerical methods addressing a variety of application-specific demands. While a range of numerical and experimental benchmarks are present in the literature, few solutions are available that enable both verification and spatiotemporal convergence analysis. In this paper, we introduce a class of analytic solutions to FSI problems involving shear in channels and pipes. Comprised of 16 separate analytic solutions, our approach is permuted to enable progressive verification and analysis of FSI methods and implementations, in two and three dimensions, for static and transient scenarios as well as for linear and hyperelastic solid materials. Results are shown for a range of analytic models exhibiting progressively complex behavior. The utility of these solutions for analysis of convergence behavior is further demonstrated using a previously published monolithic FSI technique. The resulting class of analytic solutions addresses a core challenge in the development of novel FSI algorithms and implementations, providing a progressive testbed for verification and detailed convergence analysis.

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“…The records of the archaeologists suggest that this would have been one of the tallest occupied buildings in the world at the time and the foundation is still impressive almost 1,000 years later. The solid mechanics theory of beams commonly known as beam theory and it has a main role in structural analysis as it provides simple tools to analyze numerous structures [3]. This study was mainly conducted by using Euler -Bernouli beam theorem in order to prove its application during our ancestor's period.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore experiments had proved that following assumptions are valid for long and slender beams. According to Bauchau and Craig [3] the cross-section must infinitely rigid in its own plane. Secondly the cross-section of the beam remains plane after deformation and finally the cross-section must remain normal to the deformed axis of the beam.…”

Section: Introductionmentioning

confidence: 99%

The Structural Analysis of King Parakramabahu's Palace

Ranaweera¹,

Lilushan²,

Randenigama³

et al. 2017

cea

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King Parakramabahu, in Polonnaruwa monarch who built the 'Parakrama Samudra' had a magnificent seven storied palace called 'Vijayanta Prasada' or 'Vijayothpaya', the palace of God Sakra. This study has investigated the structural configuration of the palace through historical data and observation of existing part of the palace. The chronicles Chulawansa and Mahawansa has described the palace as seven storied building with thousand chambers. Though the main building possibly cannot hold such a number of chambers, considering the whole palace complex this number seems a possible. The research was being conducted using the existing brick wall and was used to identify the column beam configuration and how the load path was distributed. During the research the load path from the upper floors to the ground was also investigated. The dimensions of all the existing structural components were taken into consideration. The results revealed that the upper floors could have been made out of timber such as Weera and Palu and the existing wall must have held the massive wooden structure that form the floor of the upper level. The study was conducted in order to prove that the ancestors who lived 1000 years ago also used a method similar to Euler -Bernouli beam theorem for constructions.

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Euler-Bernoulli beam theory

Cited by 165 publications

References 0 publications

A 2D Hopfield Neural Network approach to mechanical beam damage detection

A 2D Hopfield Neural Network approach to mechanical beam damage detection

A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms

The Structural Analysis of King Parakramabahu's Palace

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