The Effect of Thickness Variations on the Behavior of Smooth Curved Pipes Under External Bending

1980 ◽  
Vol 102 (1) ◽  
pp. 45-48 ◽  
Author(s):  
J. Spence ◽  
G. E. Findlay
Keyword(s):  
Cross Sections ◽  
Theoretical Work ◽  
Small Displacement ◽  
Constant Thickness ◽  
Elliptical Cross ◽  
Classical Energy ◽  
Curved Pipes ◽  
Bending Stresses ◽  
Plane Bending ◽  
Thickness Variations

By various manufacturing techniques straight pipes with initially circular cross sections can be processed into smooth bends but usually with noncircular cross sections and with variations in thickness. These changes from the ideal are normally referred to as “ovality” and “thinning”; their influence on the subsequent behaviour of curved pipes is not yet fully understood. Here theoretical work on constant thickness circular and elliptical cross sections has been extended to cope with typical variations in thickness. The theory which is based on a classical energy approach is outlined for in-plane bending loading and is easily extended to cover out-of-plane bending. Linear elastic small displacement limitations apply. It is concluded that normally accepted values of thinning have virtually no effect on the flexibility due to bending of smooth pipe bends with or without initial ovality. Similarly, the peak meridional bending stresses were found to be insensitive to thickness variations.

Creep Analysis of Smooth Curved Pipes under in-plane Bending

1973 ◽  
Vol 15 (4) ◽  
pp. 252-265 ◽  
Author(s):  
J. Spence
Keyword(s):  
Circular Cross Section ◽  
Approximate Solutions ◽  
Constitutive Relationship ◽  
Constant Thickness ◽  
Stationary Condition ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Plane Bending ◽  
Stationary Creep ◽  
Stress Concentration Factors

Theoretical analyses are presented for the behaviour of a smooth circular cross-section thin-walled curved pipe of constant thickness when loaded by in-plane bending moments under isothermal creep conditions. Twin energy analyses, designated type 1 and type 2 respectively, are used in conjunction with an n-power stationary creep constitutive relationship. Approximate solutions are obtained by direct minimization techniques on a computer. Deformation results and stress-concentration factors relevant to the stationary condition based on straight-pipe values are reported for all practical geometries of pipe bends. The influence of the results on design and matters of total deformation and stress redistribution are briefly mentioned.

The influence of the variation in wall thickness of glass fibre reinforced plastic pipe bends subjected to in-plane bending

1992 ◽  
Vol 27 (2) ◽  
pp. 113-121 ◽  
Author(s):  
R Kitching ◽  
D R Hose
Keyword(s):  
Constant Thickness ◽  
Reinforced Plastic ◽  
Process Plant ◽  
Glass Fibre Reinforced Plastic ◽  
Glass Fibre Reinforced ◽  
Plane Bending ◽  
Chopped Strand Mat ◽  
Thickness Variations ◽  
Glass Reinforcement ◽  
Fourier Series Analysis

Glass reinforced plastic (GRP) pipe bends as used in the process plant industry are often made by hand lay-up and, because of overlapping of layers in the construction, are prone to thickness variations sometimes approaching ± 50 percent of the mean thickness. An existing Fourier series analysis for calculating flexibility factors and strain distributions in such components with constant thickness subjected to in-plane bending moments is extended to include typical thickness variations. Results are expressed in closed form, and their practical implications are discussed. The theoretical results are also discussed in relation to experiments on two GRP pipe bends having nominal inside pipe diameters of 250mm and mean pipe radii of 250mm where the resin was polyester and the E-glass reinforcement consisted of three layers of 0.6 kg m−2 chopped strand mat and one layer of 0.6kg m−2 woven rovings.

Stationary Creep Stresses for Elliptical Cross-Sectional Pipe Bends Subject to In-Plane Bending

1974 ◽  
Vol 96 (3) ◽  
pp. 162-170 ◽  
Author(s):  
J. Spence
Keyword(s):  
Elastic Beam ◽  
Constitutive Law ◽  
Constant Thickness ◽  
Straight Tube ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Curved Pipe ◽  
Linear Elastic ◽  
Plane Bending ◽  
Stationary Creep

A theoretical analysis is presented which allows the determination of the stationary creep stresses acting in a smooth curved pipe of initially elliptical cross section when subject to in-plane bending. The bend is assumed to be of constant thickness and “thin” compared with its cross-sectional axes. The analysis is based on an energy approach and uses a simple power-type creep constitutive law. Results are presented in nondimensional fashion in terms of the maximum linear elastic beam bending stress in a straight tube. A large range of possible geometries is covered.

scholarly journals Photoionization Cross-Sections of Carbon-Like N+ Near the K-Edge (390–440 eV)

Atoms ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 27
Author(s):  
Jean-Paul Mosnier ◽  
Eugene T. Kennedy ◽  
Jean-Marc Bizau ◽  
Denis Cubaynes ◽  
Ségolène Guilbaud ◽  
...  
Keyword(s):  
High Resolution ◽  
Cross Section ◽  
Cross Sections ◽  
Experimental Studies ◽  
Photoionization Cross Section ◽  
Theoretical Work ◽  
Rydberg Series ◽  
R Matrix ◽  
Resonance Strengths ◽  
Nitrogen Ion

High-resolution K-shell photoionization cross-sections for the C-like atomic nitrogen ion (N+) are reported in the 398 eV (31.15 Å) to 450 eV (27.55 Å) energy (wavelength) range. The results were obtained from absolute ion-yield measurements using the SOLEIL synchrotron radiation facility for spectral bandpasses of 65 meV or 250 meV. In the photon energy region 398–403 eV, 1s⟶2p autoionizing resonance states dominated the cross section spectrum. Analyses of the experimental profiles yielded resonance strengths and Auger widths. In the 415–440 eV photon region 1s⟶(1s2s22p2 4P)np and 1s⟶(1s2s22p2 2P)np resonances forming well-developed Rydberg series up n=7 and n=8 , respectively, were identified in both the single and double ionization spectra. Theoretical photoionization cross-section calculations, performed using the R-matrix plus pseudo-states (RMPS) method and the multiconfiguration Dirac-Fock (MCDF) approach were bench marked against these high-resolution experimental results. Comparison of the state-of-the-art theoretical work with the experimental studies allowed the identification of new resonance features. Resonance strengths, energies and Auger widths (where available) are compared quantitatively with the theoretical values. Contributions from excited metastable states of the N+ ions were carefully considered throughout.

Numerical Analysis of Branch Mechanical Response to Loading

2019 ◽  
Vol 45 (4) ◽  
Author(s):  
Barbora Vojáčková ◽  
Jan Tippner ◽  
Petr Horáček ◽  
Luděk Praus ◽  
Václav Sebera ◽  
...  
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Mechanical Response ◽  
Mechanical Analysis ◽  
Beam Deflection ◽  
Design System ◽  
Elliptical Cross ◽  
Static Mechanical ◽  
The Difference ◽  
Tree Uprooting

Failure of a tree can be caused by a stem breakage, tree uprooting, or branch failure. While the pulling test is used for assessing the first two cases, there is no device-supported method to assess branch failure. A combination of the optical technique, pulling test, and deflection curve analysis could provide a device-supported tool for this kind of assessment. The aim of the work was to perform a structural analysis of branch response to static mechanical loading. The analyses were carried out by finite element simulations in ANSYS using beam tapered elements of elliptical cross-sections. The numerical analyses were verified by the pulling test combined with a sophisticated optical assessment of deflection evaluation. The Probabilistic Design System was used to find the parameters that influence branch mechanical response to loading considering the use of cantilever beam deflection for stability analysis. The difference in the branch’s deflection between the simulation and the experiment is 0.5% to 26%. The high variability may be explained by the variable modulus of the elasticity of branches. The finite element (FE) sensitivity analysis showed a higher significance of geometry parameters (diameter, length, tapering, elliptical cross-section) than material properties (elastic moduli). The anchorage rotation was found to be significant, implying that this parameter may affect the outcome in mechanical analysis of branch behavior. The branch anchorage can influence the deflection of the whole branch, which should be considered in stability assessment.

Stresses and Deformations of Toroidal Shells of Elliptical Cross Section: With Applications to the Problems of Bending of Curved Tubes and of the Bourdon Gage

1952 ◽  
Vol 19 (1) ◽  
pp. 37-48
Author(s):  
R. A. Clark ◽  
T. I. Gilroy ◽  
E. Reissner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Practical Interest ◽  
Closed Shell ◽  
Open Shell ◽  
Elliptical Cross Section ◽  
Axially Symmetric ◽  
Elliptical Cross ◽  
Two Parameters ◽  
Toroidal Shells

Abstract This paper is concerned with the application of the theory of thin shells to several problems for toroidal shells with elliptical cross section. These problems are as follows: (a) Closed shell subjected to uniform normal wall pressure. (b) Open shell subjected to end bending moments. (c) Combination of the results for the first and second problems in such a way as to obtain results for the stresses and deformations in Bourdon tubes. In all three problems the distribution of stresses is axially symmetric but only in the first problem are the displacements axially symmetric. The magnitude of stresses and deformations for given loads depends in all three problems on the magnitude of the two parameters bc/ah and b/c where b and c are the semiaxes of the elliptical section, a is the distance of the center of the section from the axis of revolution, and h is the thickness of the wall of the shell. For sufficiently small values of bc/ah trigonometric series solutions are obtained. For sufficiently large values of bc/ah asymptotic solutions are obtained. Numerical results are given for various quantities of practical interest as a function of bc/ah for the values 2, 1, 1/2, 1/4 of the semiaxes ratio b/c. It is suggested that the analysis be extended to still smaller values of b/c and to cross sections other than elliptical.

Glaciological Problems Set by the Control of Dangerous Lakes in Cordillera Blanca, Peru. II. Movement of a Covered Glacier Embedded within a Rock Glacier

1977 ◽  
Vol 18 (79) ◽  
pp. 255-274 ◽  
Author(s):  
Louis Lliboutry
Keyword(s):  
Cross Sections ◽  
Rock Glacier ◽  
Measured Velocity ◽  
Elliptical Cross ◽  
Cordillera Blanca ◽  
The Holocene ◽  
Glacier Tongue ◽  
Proglacial Lake

AbstractIn front of Laguna Parón there is a huge moraine which turns through 90° in the middle of the valley and with a narrow covered glacier on the top. It has been studied by electrical exploration, and using the displacements of 43 marked boulders on the glacier. Assuming a uniform balance on the glacier tongue and semi-elliptical cross-sections, it has been possible to estimate this balance and the glacier thickness. A great amount of the measured velocity comes from the creep of the moraine itself, which seems 10 be a kind of rock glacier, probably without interstitial ire. It must have taken all the Holocene to be formed. During its complex history a proglacial lake must have formed at some time, the rupture of which explains the crooked form.

Chain Out of Plane Bending (OPB) Fatigue Joint Industry Project (JIP) Static Test Program and OPB Interlink Stiffness

2016 ◽  
Author(s):  
Lucile Rampi ◽  
Fata Dewi ◽  
Michel Francois ◽  
Arnaud Gerthoffert ◽  
Pedro Vargas
Keyword(s):  
Fatigue Loading ◽  
Time Frame ◽  
Small Time ◽  
Static Test ◽  
Fatigue Design ◽  
Out Of Plane ◽  
Bending Stresses ◽  
Plane Bending ◽  
Mooring Chain ◽  
Fatigue Mechanism

In 2002, several mooring chains of a deepwater offloading buoy failed prematurely within a very small time frame. These chains were designed according to conventional offshore fatigue assessment using API recommendations. With this first deepwater buoy application, a new mooring chain fatigue mechanism was discovered. High pretension levels combined with significant mooring chain motions caused interlink rotations that generated significant Out of Plane Bending (OPB) fatigue loading. Traditionally, interlink rotations are relatively harmless and generate low bending stresses in the chain links. The intimate mating contact that occurs due to the plastic deformation during the proof loading and the high pretension of the more contemporary mooring designs have been identified as aggravating factors for this phenomenon. A Joint Industry Project (JIP), gathering 26 different companies, was started in 2007 to better understand the Out of Plane Bending (OPB) mooring chain fatigue mechanism and to propose mooring chain fatigue design recommendations. This paper summarizes the quasi static OPB stiffness measurement campaign and the post processing work to derive the OPB interlink stiffness.

scholarly journals GEOMETRIC MODELING OF A SHAPE OF PARALLELOGRAM PLATES IN A PROBLEM OF FREE VIBRATIONS USING CONFORMAL RADII

2021 ◽  
pp. 143-159
Author(s):  
A.A. Chernyaev ◽  
Keyword(s):  
Cross Sections ◽  
Geometric Modeling ◽  
Interpolation Method ◽  
Geometric Characteristic ◽  
Free Vibrations ◽  
Theory Of Elasticity ◽  
Constant Thickness ◽  
Basic Frequency ◽  
Plate Vibrations ◽  
The Subject

The paper considers a method of geometric modeling applied when solving basic twodimensional problems of the theory of elasticity and structural mechanics, in particular the applied problems of engineering. The subject of this study is vibrations of thin elastic parallelogram plates of constant thickness. To determine a basic frequency of vibrations, the interpolation method based on the geometric characteristic of the shape of plates (membrane, cross sections of a rod) is proposed. This characteristic represents a ratio of interior and exterior conformal radii of the plate. As is known from the theory of conformal mappings, conformal radii are those obtained by mapping of a plate onto the interior and exterior of a unit disk. The paper presents basic terms, tables, and formulas related to the considered geometric method with a comparative analysis of the curve diagrams obtained using various interpolation formulas. The original computer program is also developed. The main advantage of the proposed method of determining the basic frequency of plate vibrations is a graphic representation of results that allows one to accurately determine the required solution on the graph among the other solutions corresponding to the considered case of parallelogram plates. Although there are many known approximate approaches, which are used to solve the considered problems, only geometric modeling technique based on the conformal radii ratio gives such an opportunity.

Study on non-local effects in dimers of circular and elliptical cross-sections

2021 ◽  
Author(s):  
Xi Zhang ◽  
Wenyuan Wu ◽  
Yanchun Gong ◽  
Suhong He ◽  
Fangping Wu ◽  
...  
Keyword(s):  
Absorption Spectrum ◽  
Electric Field ◽  
Cross Section ◽  
Cross Sections ◽  
Field Enhancement ◽  
Radius Of Curvature ◽  
Electric Field Enhancement ◽  
Nonlocal Effects ◽  
Elliptical Cross ◽  
Non Local

Abstract The nonlocal effects of dimers consisted of two cylinders are studied, whose cross section is elliptical. Importantly, the results with dimers whose cross section is circular are compared. For comparison, the curvature of the ellipse is set the same with the circle, and four different geometries are considered. The electric field enhancement at the gap center and the absorption spectrum of the dimers are calculated. For the second geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the first geometry, the frequencies corresponding to the peaks are totally different. Similarly, for the fourth geometry, either the electric field enhancement at the gap center or the absorption spectrum is approximately calculated using the third geometry, the disciplines of the peak values change as radius of curvature increases are totally different.

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