The Half-Space Under Pressure Distributed Over an Elliptical Portion of Its Plane Boundary

1960 ◽  
Vol 27 (1) ◽  
pp. 111-119 ◽  
Author(s):  
H. Deresiewicz
Keyword(s):  
Pressure Distribution ◽  
Half Space ◽  
Principal Axis ◽  
Major Axis ◽  
Minor Axis ◽  
Plane Boundary ◽  
Uniform Pressure ◽  
Principal Stresses ◽  
The Difference ◽  
Normal Deflection

In determining the safety of foundations the assumption is usually made that the pressure distribution on the ground, in general unknown, is closely approximated by a constant one. Mathematically, the problem is thereby reduced to finding the components of stress and displacement in a half-space due to a uniform pressure on a portion of its plane boundary. The present paper contains an investigation of this problem for the case of loading over an area bounded by an ellipse. Two of the results are: (a) On the normal to the loading area through its center, the two principal stresses in planes parallel to the undeformed surface, compressive on and near the surface, become tensile within a depth smaller than the length of the corresponding principal axis of the loading area; (b) the normal deflection of the surface is greater at the extremity of the minor axis of the loading area than at the extremity of the major axis, the difference between the two values increasing with the ellipticity of the bounding curve.

The Great Ellipse Solution for Distances and Headings to Steer between Waypoints

1999 ◽  
Vol 52 (3) ◽  
pp. 421-424 ◽  
Author(s):  
P. R. Walwyn
Keyword(s):  
Circle Method ◽  
Major Axis ◽  
Great Circle ◽  
Minor Axis ◽  
Geodesic Curve ◽  
Present Position ◽  
The Earth ◽  
Shortest Distance ◽  
The Difference ◽  
A Minor

The normal Great Circle method of computing the shortest distance between two positions on the Earth – e.g. from an aircraft's present position (PP) to a waypoint (WP) – is not accurate enough to meet present-day requirements for aircraft Nav–Attack systems.On the surface of an Ellipsoid (or Spheroid), the true ‘shortest distance’ is along a geodesic curve between the two points, but the computation of this curve is complex, and as shown by R. Williams at Reference, the difference between the geodesic and Great Ellipse distances between two points is negligible (<0·01 nm).The Great Ellipse through two points on a spheroid is defined as the ellipse that passes through the two points and the centre of the spheroid; it therefore has a major axis equal to the Earth's, and a minor axis that is between the Earth's major axis (for two points on the Equator) and minor axis (for two points on the same, or diametrically opposite, longitudes). Thus the problem of deciding on which Great Ellipse the two points lie is equivalent to determining the magnitude of the minor axis β of the ellipse on which they both lie.

scholarly journals Out of sight, out of mind? The impact of correlated clustering in substructure lensing

2021 ◽  
Author(s):  
Alexandres Lazar ◽  
James S Bullock ◽  
Michael Boylan-Kolchin ◽  
Robert Feldmann ◽  
Onur Çatmabacak ◽  
...  
Keyword(s):  
Dark Matter ◽  
Principal Axis ◽  
Major Axis ◽  
Line Of Sight ◽  
Gravitational Lenses ◽  
Local Clustering ◽  
Analytic Expression ◽  
Halo Masses ◽  
The Impact

Abstract A promising route for revealing the existence of dark matter structures on mass scales smaller than the faintest galaxies is through their effect on strong gravitational lenses. We examine the role of local, lens-proximate clustering in boosting the lensing probability relative to contributions from substructure and unclustered line-of-sight (LOS) haloes. Using two cosmological simulations that can resolve halo masses of Mhalo ≃ 109 M⊙ (in a simulation box of length Lbox ∼ 100 Mpc) and 107 M⊙ (Lbox ∼ 20 Mpc), we demonstrate that clustering in the vicinity of the lens host produces a clear enhancement relative to an assumption of unclustered haloes that persists to &gt;20 Rvir. This enhancement exceeds estimates that use a two-halo term to account for clustering, particularly within 2 − 5 Rvir. We provide an analytic expression for this excess, clustered contribution. We find that local clustering boosts the expected count of 109 M⊙ perturbing haloes by ${\sim }35{{\ \rm per\ cent}}$ compared to substructure alone, a result that will significantly enhance expected signals for low-redshift (zl ≃ 0.2) lenses, where substructure contributes substantially compared to LOS haloes. We also find that the orientation of the lens with respect to the line of sight (e.g. whether the line of sight passes through the major axis of the lens) can also have a significant effect on the lensing signal, boosting counts by an additional $\sim 50{{\ \rm per\ cent}}$ compared to a random orientations. This could be important if discovered lenses are biased to be oriented along their principal axis.

Design of Turning Area for LNG Terminal Base on Computer Simulation

2012 ◽  
Vol 215-216 ◽  
pp. 1236-1240
Author(s):  
Yao Tian Fan
Keyword(s):  
Computer Simulation ◽  
Theoretical Calculation ◽  
Cost Effective ◽  
Major Axis ◽  
Minor Axis ◽  
Computer Simulator

Design of turning area for sea port is generally done according to the outcome of theoretical calculation or real-ship trial. However, these methods only take into account some limited respects for planning a port or are not so cost-effective. In this paper, computer simulator is used for optimizing the size of turning area for Yangshan LNG terminal. The outcome indicates that the major axis and minor axis of the turning area can meet the requirement of Q-Max LNG carrier berthing operation and it is suggested to do such maneuvering in some given conditions related to wind, current, tide, visibility and wave.

The Measurement of Stresses in Composites

1986 ◽  
Vol 1 (2) ◽  
pp. 15-21 ◽  
Author(s):  
J. B. Cohen
Keyword(s):  
Three Dimensional ◽  
Stress System ◽  
Principal Stresses ◽  
Reasonable Time ◽  
Complete Measurement ◽  
Useful Life ◽  
Diffraction Peaks ◽  
The Difference ◽  
Full Investigation ◽  
Hydrostatic Component

AbstractAlthough there is mounting interest in the measurement of stresses in composite materials after fabrication and/or use, few measurements to date have not taken into account the three dimensional nature of the stress system in such materials. Most data give only the net stress, that is, the difference between principal stresses. A procedure for a more complete measurement (in a reasonable time) is developed here, including the separation of macrostresses and microstresses. If time does not permit a full investigation, measurements of the lattice parameters of the component phases provide a simple way to sample the hydrostatic component due to differential thermal contraction. The Barrett-Predecki method of adding filler is particularly promising for stress measurements in those composites whose component phases do not give appropriate diffraction peaks. This procedure could also be used for monitoring stresses during the useful life of such materials.

Effect of Mach number on the acoustic field of 2:1 elliptic-slot jet

2001 ◽  
Vol 105 (1043) ◽  
pp. 9-16 ◽  
Author(s):  
S. B. Verma ◽  
E. Rathakrishnan
Keyword(s):  
Mach Number ◽  
Fundamental Frequency ◽  
Acoustic Field ◽  
Major Axis ◽  
Shock Structure ◽  
Minor Axis ◽  
Noise Levels ◽  
Underexpanded Jets ◽  
Barrel Shock ◽  
Mach Numbers

Abstract The shock-structure and the related acoustic field of underexpanded jets undergoes significant changes as the Mach number Mj is increased. The present investigation is carried out to study the effect of Mach number on an underexpanded 2:1 elliptic-slot jet. Experimental data are presented for fully expanded Mach numbers ranging from 1.3 to 2.0. It is observed that the ‘cross-over’ point at the end of the first cell at low Mach numbers gets replaced by a normal shock at a highly underexpanded condition resulting in the formation of a ‘barrel’ shock along the minor-axis side with a ‘bulb’ shock formed along the major-axis side. The above change in shock structure is accompanied by a related change in the acoustic field. The amplitude of fundamental frequency along the minor-axis side grows with Mj but falls beyond Mj = 1.75. Along the major-axis side, however, the fundamental frequency does not exist at low Mach numbers. It appears at Mj = 1.75 but then falls at Mj = 2.0. The related azimuthal directivity of overall noise levels (OASPL) shows significant changes with Mj.

Comparison of the Flame Characteristics of Turbulent Circular and Elliptic Jets in a Crossflow

2002 ◽  
Vol 124 (3) ◽  
pp. 197-203 ◽  
Author(s):  
S. R. Gollahalli ◽  
D. Pardiwalla
Keyword(s):  
Flame Structure ◽  
Flux Ratio ◽  
Major Axis ◽  
Minor Axis ◽  
No Production ◽  
Sampling System ◽  
Computer Data ◽  
Rate Of Increase ◽  
Jet Velocity ◽  
Lower Limits

This study was directed to understand the coupling effects of the noncircular geometry of the burner and a crossflow on the combustion of gas jets. This paper compares the characteristics of turbulent propane jet flames from circular (diameter=0.45 cm) and elliptic (major axis/minor axis=3) burners of equivalent exit area in a crossflow. The elliptic burner was oriented with its major axis or minor axis aligned with the crossflow. Experiments were conducted in a wind tunnel provided with optical and probe access and capable of wind speeds up to 12.5 m/s. The burners were fabricated with metal tubes. Instrumentation included a Pt-Pt/13% Rh thermocouple, a quartz-probe gas sampling system, chemiluminescent and nondispersive infrared analyzers, a video-recorder, and a computer data acquisition system. The measurements consisted of the upper and lower limits of jet velocity for a stable flame, flame configuration, and visible length. Flame structure data including temperature profiles and concentration profiles of CO2,O2, CO, and NO were obtained in a two-zone flame configuration (at jet to crossflow momentum flux ratio=0.11), where a planar recirculation exists in the wake of the burner tube followed by an axisymmetric tail. The relative emission indicators of CO and NO were estimated from the composition data. Results show that the upper and lower limits of the fuel jet velocity increase with the crossflow velocity for all burners, and the rate of increase is highest for the elliptic burner with its minor axis aligned with the crossflow. That burner configuration also produces the longest flame. The relative emission indicators show that the CO production is lower and NO production is higher with elliptic burners than with circular burners in crossflow.

Quantitative diagenetic analyses of Edmontosaurus regalis (Dinosauria: Hadrosauridae) postcranial elements from the Danek Bonebed, Upper Cretaceous Horseshoe Canyon Formation, Edmonton, Alberta, Canada: implications for allometric studies of fossil organisms

2014 ◽  
Vol 51 (11) ◽  
pp. 1007-1016 ◽  
Author(s):  
Mackenzie Baert ◽  
Michael E. Burns ◽  
Philip J. Currie
Keyword(s):  
Cross Section ◽  
Upper Cretaceous ◽  
Strong Relationship ◽  
Major Axis ◽  
Minor Axis ◽  
Morphological Features ◽  
Fossil Assemblages ◽  
Fossil Vertebrate ◽  
Horseshoe Canyon Formation ◽  
Upper Campanian

For fossil assemblages, quantitative size and shape studies are often complicated by diagenetic distortion. Different vertebrate elements, although subjected to similar burial stresses, exhibit deformations based upon their original shapes; this hypothesis is tested here by quantitatively comparing deformed humeri and femora from the Danek Bonebed (a monodominant Edmontosaurus regalis bonebed from the upper Campanian Horseshoe Canyon Formation in Edmonton, Alberta, Canada) with samples of undeformed humeri and femora from modern and fossil assemblages. Analyses suggest that at the Danek Bonebed a strong relationship exists between element length and circumference despite being distorted by crushing deformation. Major and minor axes of the midshaft cross section, however, were not uniformly distorted. Although their anatomical position did not change, the major axis became longer relative to the minor axis in distorted specimens. A regression based on the undeformed humeri was not able to accurately predict circumference in the Danek humeri. Further study might quantify the deformation of other bones in the Danek Bonebed and could be extended to other assemblages and genera. Caution should be taken when conducting studies in which diagenetic crushing may have altered morphological features of fossil vertebrate remains.

Stem eccentricity in coastal western hemlock

1981 ◽  
Vol 11 (3) ◽  
pp. 715-718 ◽  
Author(s):  
Robert M. Kellogg ◽  
Francis J. Barber
Keyword(s):  
Major Axis ◽  
Western Hemlock ◽  
Eccentricity Ratio ◽  
Angular Rotation ◽  
Minimum Diameter ◽  
Breast Height ◽  
Second Growth ◽  
The Difference ◽  
Average Eccentricity ◽  
Practical Field

Stem eccentricity in second-growth western hemlock (Tsugaheterophylla (Raf.) Sarg.) from southern coastal British Columbia appears to be the rule rather than the exception. Although the difference was small, the average eccentricity ratios (ratios of minimum diameter inside bark (DIB) to maximum DIB) for two Lower Mainland sites were significantly larger than those of two Vancouver Island sites. The average eccentricity ratio of all 87 trees studied was 0.929, with a standard deviation of 0.0231. The angular rotation of the major axis of the stem cross section varied greatly, and was positively related to the average stem eccentricity ratio within 5-m log lengths for each stem. Average eccentricity of the whole stem was relatively independent of diameter at breast height (DBH), age, stem height, and eccentricity at breast height. It does not appear that a practical field technique could be devised for the rapid estimation of average stem eccentricity in western hemlock.

scholarly journals Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
Kh. Lotfy ◽  
A. Gohaly
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Elastic Layer ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Magnetic Field Effect ◽  
Plane Boundary ◽  
Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

Anisotropy Gas Reservoir Drainage Radius and Quantitative Well Interference Study

2013 ◽  
Vol 275-277 ◽  
pp. 1285-1291 ◽  
Author(s):  
Zheng Long Gao ◽  
Hong Fu Fan ◽  
Zhi Bin Gao
Keyword(s):  
Production Rate ◽  
Major Axis ◽  
Productivity Analysis ◽  
Analysis Method ◽  
Equivalent Radius ◽  
Average Value ◽  
Drainage Radius ◽  
Well Spacing ◽  
Cumulative Production ◽  
The Difference

Unstable productivity analysis method was used to obtain the equivalent radius of 77 wells and the result shows that the equivalent radius ranges from 30 to 970m with an average value of 230m in McKittrick Hills. The difference range of the radius is mainly caused by varying formation properties, gas saturation, production time, etc. Permeability anisotropy changes the drainage from round to ellipse. The major axis and the minor axis of the ellipse are determined by the ratio of major and minor permeability. Current pressure distribution was obtained and was found to be consistent with the modified drainage results, which demonstrates that the unstable productivity analysis method is applicable in the study of gas well drainage radius. An interference well and an observation well’s model was constructed to study well interference quantitatively. When the well spacing is larger than 750m, the productivity will be reduced by 20%. The production rate of interference well is more sensitive to the cumulative production of observation well, when the production rate of interference well is below 16.8×104m3/d.

Sign in / Sign up

Export Citation Format

Share Document