In-Plane Bending of Curved Circular Tubes

1968 ◽  
Vol 90 (4) ◽  
pp. 666-670 ◽  
Author(s):  
D. H. Cheng ◽  
H. J. Thailer
Keyword(s):  
Experimental Data ◽  
General Solution ◽  
Compatibility Condition ◽  
Circular Tube ◽  
Series Expansions ◽  
Center Line ◽  
Complementary Energy ◽  
Circular Tubes ◽  
Binomial Expansion ◽  
Plane Bending

A general solution is presented for a thin, curved circular tube under in-plane bending. It includes the solution given by Clark and Reissner as a particular case in which the ratio of the radius of the tube to the radius of its center line is very small. The series expansions satisfy the equilibrium equation for any radius ratio while the compatibility condition is guaranteed by minimizing the complementary energy. The minimization is achieved in the manner of Raileigh-Ritz whereas the evaluation of integrals are facilitated by the use of binomial expansion. Numerical results correlate well with the experimental data. The solution is more rapidly convergent as compared to the existing analytical methods.

In-Plane Bending of a U-Shaped Circular Tube With End Constraints

1970 ◽  
Vol 92 (4) ◽  
pp. 792-796 ◽  
Author(s):  
Henry J. Thailer ◽  
David H. Cheng
Keyword(s):  
General Solution ◽  
Potential Energy ◽  
Circular Tube ◽  
Total Potential Energy ◽  
Center Line ◽  
Bending Moments ◽  
Series Form ◽  
Total Potential ◽  
In Series ◽  
Plane Bending

A general solution is presented for a thin, curved, circular tube containing rigid end constraints, subjected to in-plane bending moments. Inextensibility of the meridional center line is assumed. The displacements are expanded in series form and the equations of equilibrium are guaranteed by minimizing the total potential energy. The minimization is achieved in the manner of Rayleigh-Ritz. Analytical results are compared with published experimental results and existing axisymmetric theory.

On Bending of Curved Circular Tubes

1970 ◽  
Vol 92 (1) ◽  
pp. 62-66 ◽  
Author(s):  
David H. Cheng ◽  
Henry J. Thailer
Keyword(s):  
Stress Distribution ◽  
General Solution ◽  
Circular Tube ◽  
Radius Ratio ◽  
Experimental Results ◽  
Asymptotic Solutions ◽  
Asymptotic Formulas ◽  
Circular Tubes

Based on the improved general solution for a thin, circular tube subjected to in-plane end moments, the effect of the radius ratio on the stress distribution, rigidity, and stress intensification factors is studied. The existing asymptotic solutions are reexamined and modified to reflect the effect of the radius ratio. The modified asymptotic formulas are compared with the existing experimental results.

Combined Free and Forced Convection in Inclined Circular Tubes

1976 ◽  
Vol 98 (2) ◽  
pp. 322-324 ◽  
Author(s):  
J. A. Sabbagh ◽  
A. Aziz ◽  
A. S. El-Ariny ◽  
G. Hamad
Keyword(s):  
Experimental Data ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Circular Tube ◽  
Circular Tubes ◽  
Theoretical Predictions ◽  
Free And Forced Convection ◽  
Axial Heat ◽  
Peripheral Temperature

The problem of combined free and forced convection in an inclined circular tube with uniform peripheral temperature and axial heat flux has been studied experimentally. For fixed Pr and Ra, experimental data showing the effect of tube inclination and Reynolds number on temperature and axial velocity profiles are reported and found to agree qualitatively with the theoretical predictions [7]. Also shown is the variation of Nusselt number with inclination angle for Ra Re = 30,000. No optimum angle for maximum Nusselt number was found.

Deteriorated turbulent heat transfer (DTHT) of gas up-flow in a circular tube: Experimental data

2008 ◽  
Vol 51 (13-14) ◽  
pp. 3259-3266 ◽  
Author(s):  
J.I. Lee ◽  
P. Hejzlar ◽  
P. Saha ◽  
P. Stahle ◽  
M.S. Kazimi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Circular Tube ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat

Stresses in Curved, Circular Thin-Wall Tubes

1963 ◽  
Vol 30 (1) ◽  
pp. 134-135
Author(s):  
E. A. Utecht
Keyword(s):  
Thin Wall ◽  
Bending Moments ◽  
Circular Tubes ◽  
Out Of Plane ◽  
Thin Walled ◽  
Plane Bending

Curves are presented which give stress intensification factors for curved, thin-walled circular tubes under various combinations of in-plane and out-of-plane bending moments.

scholarly journals The radiation instability in modified gravity

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150060
Author(s):  
Spiros Cotsakis ◽  
Dimitrios Trachilis
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Modified Gravity ◽  
Evolution Equations ◽  
Formal Series ◽  
Series Expansions ◽  
General Polynomial ◽  
Theories Of Gravity ◽  
Polynomial Extensions

We study the problem of the instability of inhomogeneous radiation universes in quadratic Lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the resulting solutions have a smaller number of arbitrary functions than that required in a general solution. These results continue to hold for more general polynomial extensions of general relativity.

scholarly journals Plastic Deformation of Metal Tubes Subjected to Lateral Blast Loads

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kejian Song ◽  
Yuan Long ◽  
Chong Ji ◽  
Fuyin Gao
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Plastic Flow ◽  
Cross Section ◽  
Circular Tube ◽  
Circular Tubes ◽  
Simply Supported ◽  
Different Dimensions ◽  
Thin Walled ◽  
Wave Induced

When subjected to the dynamic load, the behavior of the structures is complex and makes it difficult to describe the process of the deformation. In the paper, an analytical model is presented to analyze the plastic deformation of the steel circular tubes. The aim of the research is to calculate the deflection and the deformation angle of the tubes. A series of assumptions are made to achieve the objective. During the research, we build a mathematical model for simply supported thin-walled metal tubes with finite length. At a specified distance above the tube, a TNT charge explodes and generates a plastic shock wave. The wave can be seen as uniformly distributed over the upper semicircle of the cross-section. The simplified Tresca yield domain can be used to describe the plastic flow of the circular tube. The yield domain together with the plastic flow law and other assumptions can finally lead to the solving of the deflection. In the end, tubes with different dimensions subjected to blast wave induced by the TNT charge are observed in experiments. Comparison shows that the numerical results agree well with experiment observations.

Transient Critical Heat Fluxes of Subcooled Water Flow Boiling in SUS304-Circular Tubes With Various Twisted-Tape Inserts (Influence of Twist Ratio)

2014 ◽  
Vol 6 (3) ◽  
Author(s):  
Koichi Hata ◽  
Katsuya Fukuda ◽  
Suguru Masuzaki
Keyword(s):  
Circular Tube ◽  
Flow Boiling ◽  
Heat Fluxes ◽  
Effective Length ◽  
Twisted Tape ◽  
Subcooled Flow Boiling ◽  
Circular Tubes ◽  
Twisted Tapes ◽  
Subcooled Flow ◽  
Twist Ratio

The transient critical heat fluxes (transient CHFs) in SUS304-circular tubes with various twisted-tape inserts are systematically measured for mass velocities (G = 3988–13,620 kg/m2s), inlet liquid temperatures (Tin = 287.55–313.14 K), outlet pressures (Pout = 805.11–870.23 kPa) and exponentially increasing heat inputs (Q = Q0 exp(t/τ), exponential periods, τ, of 28.39 ms to 8.43 s) by the experimental water loop comprised of a multistage canned-type circulation pump controlled by an inverter. The SUS304-circular tube of inner diameter (d = 6 mm), heated length (L = 59.4 mm), effective length (Leff = 49.4 mm), L/d (=9.9), Leff/d (=8.23), and wall thickness (δ = 0.5 mm) with average surface roughness (Ra = 3.89 μm) is used in this work. The SUS304 twisted-tapes with twist ratios, y [H/d = (pitch of 180 deg rotation)/d], of 2.40 and 4.45 are used. The transient critical heat fluxes for SUS304-circular tubes with the twisted-tapes of y = 2.40 and 4.45 are compared with authors' transient CHF data for the empty SUS304-circular tube and a SUS304-circular tube with the twisted-tape of y = 3.37, and the values calculated by authors' transient CHF correlations for the empty circular tube and the circular tube with twisted-tape insert. The influences of heating rate, twist ratio and swirl velocity on the transient CHF are investigated into details and the widely and precisely predictable correlations of the transient CHF against inlet and outlet subcoolings for the circular tubes with various twisted-tape inserts are given based on the experimental data. The correlations can describe the transient CHFs for SUS304-circular tubes with various twisted-tapes of twist ratios (y = 2.40, 3.37, and 4.45) in the wide experimental ranges of exponential periods (τ = 28.39 ms to 8.43 s) and swirl velocities (usw = 5.04–20.72 m/s) obtained in this work within −26.19% to 14.03% difference. The mechanism of the subcooled flow boiling critical heat flux in a circular tube with twisted-tape insert is discussed.

An Evaluation of the Mechanical Behaviour of Imperfect Aluminium Tubes

2005 ◽  
Author(s):  
Pieter F. J. Henning ◽  
Leon Pretorius ◽  
Rudolph F. Laubscher
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Mechanical Behaviour ◽  
3D Model ◽  
Reaction Force ◽  
Circular Tubes ◽  
Geometric Changes ◽  
Method Model ◽  
Spiral Grooves

In this research the effect of geometric changes introduced on Al 6063-T6 circular tubes in the form of horizontal and spiral grooves, (Fig. 2 and Fig. 3) is assessed. The horizontal and spiral grooves were cut into the tube to a depth of half the wall thickness of the tubes, while the pitch was varied for both the horizontal and spiral grooves, and the cut width was kept constant. These tubes were axially compressed, and load vs. displacement and Energy vs. displacement graphs were generated from the captured experimental data for the tubes. A Finite Element Method model is presented for each of the experimentally tested tubes. 2D models for the uncut and horizontally grooved tubes and a 3D model for the spiral cut tube were generated and analyzed. Reaction force vs. displacement and energy vs. displacement graphs are presented for the different analyses. A comparison is made between the numerically and experimentally determined gradients of the energy vs. displacement graphs for each of the tubes analyzed. This forms the basis for an energy absorber design with application in the transport industry currently under consideration.

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