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Andre Teofilo Beck - One of the best experts on this subject based on the ideXlab platform.
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timoshenko versus Euler Beam theory pitfalls of a deterministic approach
Structural Safety, 2011Co-Authors: Andre Teofilo Beck, Claudio Avila R Da SilvaAbstract:Abstract The selection criteria for Euler–Bernoulli or Timoshenko Beam theories are generally given by means of some deterministic rule involving Beam dimensions. The Euler–Bernoulli Beam theory is used to model the behavior of flexure-dominated (or “long”) Beams. The Timoshenko theory applies for shear-dominated (or “short”) Beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length Beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two Beam models is radically different in terms of uncertainty propagation. In the paper, some Beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo–Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko Beams than for Euler–Bernoulli Beams. On the other hand, propagation of the uncertainty for random Beam height is much larger for Euler Beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the Beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities.
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Timoshenko versus Euler Beam theory: Pitfalls of a deterministic approach
Structural Safety, 2011Co-Authors: Andre Teofilo Beck, Cláudio R. Ávila Da SilvaAbstract:The selection criteria for Euler-Bernoulli or Timoshenko Beam theories are generally given by means of some deterministic rule involving Beam dimensions. The Euler-Bernoulli Beam theory is used to model the behavior of flexure-dominated (or ""long"") Beams. The Timoshenko theory applies for shear-dominated (or ""short"") Beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length Beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two Beam models is radically different in terms of uncertainty propagation. In the paper, some Beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko Beams than for Euler-Bernoulli Beams. On the other hand, propagation of the uncertainty for random Beam height is much larger for Euler Beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the Beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.Sao Paulo State Foundation for Research - FAPESP[2008/10366-4]National Council for Research and Development - CNPq[305120/2006-9
Cláudio R. Ávila Da Silva - One of the best experts on this subject based on the ideXlab platform.
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Timoshenko versus Euler Beam theory: Pitfalls of a deterministic approach
Structural Safety, 2011Co-Authors: Andre Teofilo Beck, Cláudio R. Ávila Da SilvaAbstract:The selection criteria for Euler-Bernoulli or Timoshenko Beam theories are generally given by means of some deterministic rule involving Beam dimensions. The Euler-Bernoulli Beam theory is used to model the behavior of flexure-dominated (or ""long"") Beams. The Timoshenko theory applies for shear-dominated (or ""short"") Beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length Beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two Beam models is radically different in terms of uncertainty propagation. In the paper, some Beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko Beams than for Euler-Bernoulli Beams. On the other hand, propagation of the uncertainty for random Beam height is much larger for Euler Beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the Beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.Sao Paulo State Foundation for Research - FAPESP[2008/10366-4]National Council for Research and Development - CNPq[305120/2006-9
Claudio Avila R Da Silva - One of the best experts on this subject based on the ideXlab platform.
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timoshenko versus Euler Beam theory pitfalls of a deterministic approach
Structural Safety, 2011Co-Authors: Andre Teofilo Beck, Claudio Avila R Da SilvaAbstract:Abstract The selection criteria for Euler–Bernoulli or Timoshenko Beam theories are generally given by means of some deterministic rule involving Beam dimensions. The Euler–Bernoulli Beam theory is used to model the behavior of flexure-dominated (or “long”) Beams. The Timoshenko theory applies for shear-dominated (or “short”) Beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length Beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two Beam models is radically different in terms of uncertainty propagation. In the paper, some Beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo–Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko Beams than for Euler–Bernoulli Beams. On the other hand, propagation of the uncertainty for random Beam height is much larger for Euler Beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the Beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities.
Wanlin Guo - One of the best experts on this subject based on the ideXlab platform.
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thermal vibration of carbon nanotubes predicted by Beam models and molecular dynamics
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2010Co-Authors: Lifeng Wang, Wanlin GuoAbstract:The paper presents a detailed study on the thermal vibration of a single-walled carbon nanotube by using different Beam models of continuum mechanics, together with the law of energy equipartition, and the molecular dynamics simulations. The basic finding of the study is the relation, derived by using the Timoshenko Beam model and the law of energy equipartition, between the temperature and the root-of-mean-squared (RMS) amplitude of thermal vibration at any cross section of the carbon nanotube. The molecular dynamics simulations show that both the Euler Beam model and the Timoshenko Beam model can roughly predict the thermal vibration of lower order modes for a relatively long carbon nanotube. However, the Timoshenko Beam model, compared with the Euler Beam model, offers a much better prediction of the RMS amplitude of the thermal vibration near the fixed end of the carbon nanotube. For the thermal vibration of a relatively short carbon nanotube or higher order models of a relatively long carbon nanotube, the difference between the Timoshenko Beam and the Euler Beam in dynamic prediction becomes obvious, and the Timoshenko Beam model works much better than the Euler Beam model.
Lifeng Wang - One of the best experts on this subject based on the ideXlab platform.
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FREE VIBRATION ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES USING THE SMOOTHED FINITE ELEMENT METHOD
International Journal of Computational Methods, 2011Co-Authors: Lifeng Wang, Dong Han, Gui-rong Liu, Xiangyang CuiAbstract:This paper studies the resonant frequencies and the associated vibration modes of an individual double-walled carbon nanotube, using gradient smoothing technique. The study uses a double-elastic Beam based on the Euler Beam theory with the consideration of the intertube van der Waals interactions. A gradient smoothed formulation is deployed to deal with the fourth-order differential equation of the Euler Beam problems for dynamic analysis of the double-walled carbon nanotubes. In the double-thin Beam problems, a set of linear shape functions are adopted to approximate the displacement field. Smoothing domains are then formed for computing the smoothed curvature and bending moment field. Compared with analysis results of multi-Beam theory, numerical examples indicate that very accurate results could be yielded when a reasonable number of nodes were used. The results also showed that non-coaxial intertube resonance would be excited at the higher resonant frequencies of double-walled carbon nanotubes. In addition, free vibration of a double-walled carbon nanotube with inner wall simple supported and outer wall one end fixed and the other end free is studied.
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thermal vibration of carbon nanotubes predicted by Beam models and molecular dynamics
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2010Co-Authors: Lifeng Wang, Wanlin GuoAbstract:The paper presents a detailed study on the thermal vibration of a single-walled carbon nanotube by using different Beam models of continuum mechanics, together with the law of energy equipartition, and the molecular dynamics simulations. The basic finding of the study is the relation, derived by using the Timoshenko Beam model and the law of energy equipartition, between the temperature and the root-of-mean-squared (RMS) amplitude of thermal vibration at any cross section of the carbon nanotube. The molecular dynamics simulations show that both the Euler Beam model and the Timoshenko Beam model can roughly predict the thermal vibration of lower order modes for a relatively long carbon nanotube. However, the Timoshenko Beam model, compared with the Euler Beam model, offers a much better prediction of the RMS amplitude of the thermal vibration near the fixed end of the carbon nanotube. For the thermal vibration of a relatively short carbon nanotube or higher order models of a relatively long carbon nanotube, the difference between the Timoshenko Beam and the Euler Beam in dynamic prediction becomes obvious, and the Timoshenko Beam model works much better than the Euler Beam model.