Stresses in spheres with concentric spherical cavities under diametral compression by three-dimensional photoelasticity

1966 ◽  
Vol 6 (5) ◽  
pp. 244-250 ◽  
Author(s):  
H. Pih ◽  
H. Vanderveldt
Keyword(s):  
Three Dimensional ◽  
Diametral Compression ◽  
Spherical Cavities

On the Axisymmetric Problem of the Theory of Elasticity for an Infinite Region Containing Two Spherical Cavities

1952 ◽  
Vol 19 (1) ◽  
pp. 19-27
Author(s):  
E. Sternberg ◽  
M. A. Sadowsky
Keyword(s):  
Axisymmetric Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Field ◽  
Dimensional Problem ◽  
Spherical Cavities ◽  
Infinite Region ◽  
In Series ◽  
The Common ◽  
Axis Of Symmetry

Abstract This paper contains a solution in series form for the stress distribution in an infinite elastic medium which possesses two spherical cavities of the same size. The loading consists of tractions applied to the cavities, as well as of a uniform field of tractions at infinity, and both are assumed to be symmetric with respect to the common axis of symmetry of the cavities and with respect to the plane of geometric symmetry perpendicular to this axis. The loading is otherwise unrestricted. The solution is based upon the Boussinesq stress-function approach and apparently constitutes the first application of spherical dipolar co-ordinates in the theory of elasticity. Numerical evaluations are given for the case in which the surfaces of the cavities are free from tractions and the stress field at infinity is hydrostatic. The results illustrate the interference of two sources of stress concentration in a three-dimensional problem. The approach used here may be extended to cope with the general equilibrium problem for a region bounded by two nonconcentric spheres.

Stress Interference in Three-Dimensional Torsion

1965 ◽  
Vol 32 (1) ◽  
pp. 21-25 ◽  
Author(s):  
R. A. Eubanks
Keyword(s):  
Stress Concentration ◽  
Displacement Field ◽  
Series Solution ◽  
Three Dimensional ◽  
Pure Torsion ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Spherical Cavities ◽  
Infinite Extent ◽  
Axis Of Symmetry

An explicit series solution is presented for the stress and displacement fields in an elastic body of infinite extent containing two equidiameter spherical cavities. At large distances from the cavities the displacement field coincides with that which arises from pure torsion about the axis of symmetry. Numerical results are presented in graphs which demonstrate the interference of the two sources of stress concentration.

Early stages of infiltration in two- and three-dimensional systems

Soil Research ◽  
1969 ◽  
Vol 7 (3) ◽  
pp. 213 ◽  
Author(s):  
JR Philip
Keyword(s):  
Three Dimensional ◽  
Delta Function ◽  
The Third ◽  
Spherical Cavities ◽  
Leading Term ◽  
Flow Components ◽  
Function Approximations ◽  
Short Time ◽  
Practical Implications ◽  
Linear Integrodifferential Equation

The paper establishes the series solution of problems of infiltration from cylindrical and spherical cavities. The leading term is the fundamental horizontal absorption solution. The second term, representing linearly additive interactions of gravity and m-dimensionality (m = 2, 3), follows at once from known solutions for one-dimensional infiltration and for m-dimensional absorption. The third term is evaluated by solution of an ordinary linear integrodifferential equation. Higher terms involve circumferential flow components, and partial equations must be solved to evaluate them. For small enough times these higher terms are negligible. Physically, this implies that flow is essentially radial at such times; mathematically, that, taken no further than the third term, the solution applies indifferently to infiltration from cavities and from semicircular furrows (m = 2) and hemispherical basins (m = 3). The relation between this solution and the linearized and delta-function approximations is explored. The practical implications for sorptivity determinations based on short-time infiltration from furrows and basins are examined.

THE LOCATION OF SPHERICAL CAVITIES USING A TRIPOTENTIAL RESISTIVITY TECHNIQUE

Geophysics ◽  
1969 ◽  
Vol 34 (5) ◽  
pp. 780-784 ◽  
Author(s):  
G. M. Habberjam
Keyword(s):  
Magnetic Field ◽  
Apparent Resistivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Spherical Body ◽  
Numerical Results ◽  
Detailed Account ◽  
Conducting Sphere ◽  
Spherical Cavities ◽  
Conductivity Contrast

The surface gravitational and magnetic field anomalies due to a contrasting spherical body at depth are well known and appear in geophysical textbooks. The corresponding problem of the anomaly in apparent resistivity arising from such a body, owing to its conductivity contrast, is less frequently referred to because of the lengthy potential solutions involved. In electrical interpretation, few potential solutions exist for buried bodies of limited three‐dimensional extent, and consequently the simplest of these problems, the buried sphere, has received particular attention. Following early work by Hummel (1928), Webb (1931) produced potential solutions for this problem, and more recently Lipskaya (1949) has derived solutions and computed extensive numerical results. For the particular case of an infinitely conducting sphere, Van Nostrand (1953) has computed comprehensive numerical solutions, and more recently Van Nostrand and Cook (1966) presented a very detailed account of work on the buried sphere.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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