scholarly journals Dimensionless Analytical Solution and New Design Formula for Lateral-Torsional Buckling of I-Beams under Linear Distributed Moment via Linear Stability Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-23 ◽  
Author(s):  
Wen-Fu Zhang ◽  
Ying-Chun Liu ◽  
Ke-Shan Chen ◽  
Yun Deng
Keyword(s):  
Analytical Solution ◽  
Linear Stability ◽  
Stability Theory ◽  
Numerical Solutions ◽  
Beam Theory ◽  
Linear Stability Theory ◽  
Lateral Torsional Buckling ◽  
Torsional Buckling ◽  
Design Formula ◽  
Critical Moment

Even for the doubly symmetric I-beams under linear distributed moment, the design formulas given by codes of different countries are quite different. This paper will derive a dimensionless analytical solution via linear stability theory and propose a new design formula of the critical moment of the lateral-torsional buckling (LTB) of the simply supported I-beams under linear distributed moment. Firstly, the assumptions of linear stability theory are reviewed, the dispute concerning the LTB energy equation is introduced, and then the thinking of Plate-Beam Theory, which can be used to fully resolve the challenge presented by Ojalvo, is presented briefly; secondly, by introducing the new dimensionless coefficient of lateral deflection, the new dimensionless critical moment and Wagner’s coefficient are derived naturally from the total potential energy. With these independent parameters, the new dimensionless analytical buckling equation is obtained; thirdly, the convergence performance of the dimensionless analytical solution is discussed by numerical solutions and its correctness is verified by the numerical results given by ANSYS; finally, a new trilinear mathematical model is proposed as the benchmark of formulating the design formula and, with the help of 1stOpt software, the four coefficients used in the proposed dimensionless design formula are determined.

Multicellular natural convection in a vertical slot

1983 ◽  
Vol 126 ◽  
pp. 91-121 ◽  
Author(s):  
Yee Lee ◽  
Seppo A. Korpela
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Linear Stability ◽  
Stability Theory ◽  
Numerical Solutions ◽  
Travelling Waves ◽  
Linear Stability Theory ◽  
Vertical Slot

In this article we present numerical solutions to multicellular natural convection in a vertical enclosure. The calculated streamlines faithfully represent what has been seen in the laboratory by smoke traces in air and particle traces in oils. The calculated isotherms for air correspond to reported interferometric patterns. Solutions exhibiting travelling waves for water were calculated near conditions where they should occur according to linear stability theory. Heat-transfer results for air are given and their dependence on the aspect ratio of the enclosure exhibited.

Stability of vertical natural convection boundary layers: some numerical solutions

1971 ◽  
Vol 48 (4) ◽  
pp. 625-646 ◽  
Author(s):  
C. A. Hieber ◽  
B. Gebhart
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Linear Stability ◽  
Stability Theory ◽  
Numerical Solutions ◽  
Numerical Procedure ◽  
Thermal Capacity ◽  
Linear Stability Theory ◽  
Neutral Stability ◽  
Convection Boundary

Linear stability theory is applied to the natural convection boundary layer arising from a vertical plate dissipating a uniform heat flux. By using a numerical procedure which is much simpler than those previously employed on this problem, computer solutions are obtained for a much larger range of the Grashof number (G). For a Prandtl number (σ) of 0·733, it is found that, asG→ ∞: the effect of temperature coupling vanishes more rapidly than that of viscosity; the upper branch of the neutral curve is oscillatory but does approach a finite non-zero inviscid asymptote. For moderate and large values of σ, a loop appears in the neutral stability curve as a result of the merging of two unstable modes. As σ → ∞, the mode associated with the uncoupled (i.e. Orr–Sommerfeld) problem rapidly becomes less unstable than that arising from the temperature coupling, with the stability characteristics being independent of the thermal capacity of the plate. For small values of σ, only one unstable mode is found to exist with the coupling effect being negligible in the case of large thermal capacity plates but markedly destabilizing when the thermal capacity is small.By obtaining numerical results out toG≈ 1010for the cases σ = 0·733 and 6·7, it becomes possible to attempt to directly relate the theory to the actual observance of turbulent transition. Based upon comparison with available experimental data, empirical correlations are obtained between the linear stability theory and the régimes in which: (i) the boundary layer is first noticeably oscillatory; (ii) the mean (temporal) flow quantities first deviate significantly from those of laminar flow.

scholarly journals Convolutional neural network for transition modeling based on linear stability theory

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Muhammad I. Zafar ◽  
Heng Xiao ◽  
Meelan M. Choudhari ◽  
Fei Li ◽  
Chau-Lyan Chang ◽  
...  
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Linear Stability ◽  
Stability Theory ◽  
Linear Stability Theory ◽  
Transition Modeling

On the linear stability theory of Bénard–Marangoni convection

1989 ◽  
Vol 1 (7) ◽  
pp. 1123-1127 ◽  
Author(s):  
Rafael D. Benguria ◽  
M. Cristina Depassier
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Marangoni Convection ◽  
Linear Stability Theory

scholarly journals Films over topography: from creeping flow to linear stability, theory and experiments, a review

2018 ◽  
Vol 229 (4) ◽  
pp. 1451-1451
Author(s):  
H. Irschik ◽  
M. Krommer ◽  
C. Marchioli ◽  
G. J. Weng ◽  
M. Ostoja-Starzewski
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Creeping Flow ◽  
Linear Stability Theory ◽  
Theory And Experiments
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