The Axisymmetric Thermoelastic Problem in Bispherical Coordinates

1967 ◽  
Vol 34 (1) ◽  
pp. 146-152
Author(s):  
W. E. Warren ◽  
J. A. Weese
Keyword(s):  
Half Space ◽  
Spherical Cavity ◽  
Thermal Conditions ◽  
Separation Distance ◽  
The Body ◽  
Graphical Form ◽  
Zero Temperature ◽  
Spherical Cavities ◽  
Thermoelastic Problems ◽  
Bispherical Coordinates

Analytical methods are developed for treating steady-state axisymmetric thermoelastic problems defined in bispherical coordinates. Possible geometrical configurations include the infinite space with two spherical cavities of arbitrary radii and separation distance, the half-space with a spherical cavity, and the thick-walled shell having eccentric spherical boundaries. Thermal conditions must be prescribed at the surface of the body such that the temperature distribution is uniquely determined. The surfaces of the body are traction free. Numerical results for a half-space containing a spherical cavity heated to constant temperature with zero temperature on the plane and at infinity are presented in graphical form for representative geometrical variations.

On the Axisymmetric Thermoelastic Problem in Bispherical Coordinates

1967 ◽  
Vol 34 (4) ◽  
pp. 975-978
Author(s):  
W. E. Warren ◽  
J. A. Weese
Keyword(s):  
Elastic Medium ◽  
Interference Effect ◽  
Separation Distance ◽  
Thermoelastic Problem ◽  
The Other ◽  
Zero Temperature ◽  
Uniform Temperature ◽  
Thermoelastic Analysis ◽  
Spherical Cavities ◽  
Bispherical Coordinates

Results of the thermoelastic analysis of an infinite elastic medium containing two arbitrary-sized spherical cavities with arbitrary separation distance are presented graphically. Of particular interest is the interference effect of one cavity on the other. The cavity surfaces are assumed to be held at uniform temperature while zero temperature prevails at infinity. Examples treated include those for which the cavity surfaces are stress-free and those for which individually self-equilibrated rigid liners are bonded to the cavity surfaces.

scholarly journals Spinning rough disc moving in a rarefied medium

2010 ◽  
Vol 466 (2119) ◽  
pp. 2033-2055 ◽  
Author(s):  
Alexander Plakhov ◽  
Tatiana Tchemisova ◽  
Paulo Gouveia
Keyword(s):  
The Body ◽  
Two Dimensional ◽  
Zero Temperature ◽  
Optimal Mass Transport ◽  
Dense Gases ◽  
Magnus Effect ◽  
Inverse Effect ◽  
Transversal Force ◽  
The Moment ◽  
Complementary Mechanism

We study the Magnus effect: deflection of the trajectory of a spinning body moving in a gas. It is well known that in rarefied gases, the inverse Magnus effect takes place, which means that the transversal component of the force acting on the body has opposite signs in sparse and relatively dense gases. The existing works derive the inverse effect from non-elastic interaction of gas particles with the body. We propose another (complementary) mechanism of creating the transversal force owing to multiple collisions of particles in cavities of the body surface. We limit ourselves to the two-dimensional case of a rough disc moving through a zero-temperature medium on the plane, where reflections of the particles from the body are elastic and mutual interaction of the particles is neglected. We represent the force acting on the disc and the moment of this force as functionals depending on ‘shape of the roughness’, and determine the set of all admissible forces. The disc trajectory is determined for several simple cases. The study is made by means of billiard theory, Monge–Kantorovich optimal mass transport and by numerical methods.

scholarly journals Field Study Of A Radiant Heating System For Sleep Thermal Comfort And Potential Energy Saving

2021 ◽  
Author(s):  
Christopher L. K. Wang
Keyword(s):  
Potential Energy ◽  
Thermal Comfort ◽  
Energy Saving ◽  
Energy Savings ◽  
Thermal Environment ◽  
Residential Buildings ◽  
Thermal Conditions ◽  
Heating System ◽  
The Body ◽  
Radiant Temperature

As sleep is unconscious, the traditional definition of thermal comfort with conscious judgment does not apply. In this thesis sleep thermal comfort is defined as the thermal condition which enables sleep to most efficiently rejuvenate the body and mind. A comfort model was developed to stimulate the respective thermal environment required to achieve the desired body thermal conditions and a new infrared sphere method was developed to measure mean radiant temperature. Existing heating conditions according to building code conditions during sleeping hours was calculated to likely overheat a sleeping person and allowed energy saving potential by reducing nighttime heating set points. Experimenting with existing radiantly and forced air heated residential buildings, it was confirmed that thermal environment was too hot for comfortable sleep and that the infrared sphere method shows promise. With the site data, potential energy savings were calculated and around 10% of energy consumption reduction may be achieved during peak heating.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity. IV

1969 ◽  
Vol 309 (1498) ◽  
pp. 331-344
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Liquid Layer ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Time Dependent ◽  
Stoneley Waves ◽  
Solid Interface

The effect of a liquid layer overlying a solid half-space excited by harmonically varying stresses on the surface of an embedded spherical cavity is examined. The Stoneley waves along the liquid/solid interface are studied in some detail. The results are then extended to the case of an exponential shock.

Dynamic response of an elastic half-space to time-dependent surface tractions over an embedded spherical cavity. III (With comments on a paper by R. D. Gregory)

1969 ◽  
Vol 309 (1498) ◽  
pp. 313-329 ◽  
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Rayleigh Waves ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Time Dependent ◽  
Plane Boundary ◽  
Surface Motion ◽  
Harmonic Solution ◽  
Time Harmonic

Discussion of the problem of an elastic half-space with spherical cavity is continued in respect of Rayleigh waves on the plane boundary. Displacements in the initial and first group of higher order Rayleigh waves are derived by using the time-harmonic solution developed in part I of this series with attention confined to the case of time-harmonic normal stress at the cavity. These are employed to find also the response to an exponential shock at the cavity and graphs are presented showing the surface motion due to the initial Rayleigh waves. Finally, in an appendix to the paper, some comments are given on a recent paper by R. D. Gregory on the problem of the half-space with cavity.

scholarly journals An Axisymmetric Contact Problem of an Elastic Half-Space with a Spherical Cavity.

1991 ◽  
Vol 57 (543) ◽  
pp. 2664-2671
Author(s):  
Takao AKIYAMA ◽  
Toshiaki HARA ◽  
Toshikazu SHIBUYA ◽  
Takashi KOIZUMI
Keyword(s):  
Contact Problem ◽  
Half Space ◽  
Spherical Cavity ◽  
Elastic Half Space ◽  
Axisymmetric Contact Problem

Pure Flexure of a Layered Orthotropic Shell-Elasticity Study of a Tire-Related Problem

1973 ◽  
Vol 46 (1) ◽  
pp. 294-304
Author(s):  
M. Levinson ◽  
H. Demiray ◽  
S. C. Sheung
Keyword(s):  
Cylindrical Shell ◽  
Related Problem ◽  
Orthotropic Shell ◽  
Matrix Material ◽  
Incompressible Material ◽  
The Body ◽  
Graphical Form ◽  
Pure Bending ◽  
Incompressible Materials ◽  
Tread Rubber

Abstract This paper presents the analysis of the plane strain, pure bending of a portion of a three-layered cylindrical shell which is taken as a simple model of a part of a belted pneumatic tire. The two inner layers, representing the body and belts, respectively, are modeled as orthotropic, incompressible materials whose properties can be found from the appropriate cord and matrix material propties in a manner given in an Appendix. The outer layer, representing the tread rubber, is considered to be an isotropic, incompressible material. We concern ourselves with the study of the stresses tending to separate the various layers. These stresses, for two particular cases, are found to be strongly dependent on the crown angles of the cords in the body and belt layers. The results are presented in graphical form with the separation stress as a function of the body crown angle and with the belt crown angle entering as a parameter.

The borehole transient electromagnetic response of a three‐dimensional fracture zone in a conductive half‐space

Geophysics ◽  
1988 ◽  
Vol 53 (11) ◽  
pp. 1469-1478 ◽  
Author(s):  
Richard C. West ◽  
Stanley H. Ward
Keyword(s):  
Half Space ◽  
Fracture Zone ◽  
Geophysical Methods ◽  
Practical Interest ◽  
The Body ◽  
Secondary Response ◽  
Direct Integral ◽  
Transient Electromagnetic ◽  
Integral Equation Formulation ◽  
Tem Method

Borehole geophysical methods can be useful in detecting subsurface fracture zones and mineral deposits which are nearby, but not intersected by boreholes. One electrical borehole technique which can be applied to this problem is the surface‐to‐borehole transient electromagnetic (TEM) method. In this method a transmitting loop is deployed on the surface while a receiving coil is moved down a borehole. A conductive, horizontal, tabular body in a homogeneous half space was chosen to simulate a 3-D fracture zone or mineral deposit within the earth. Theoretical borehole TEM responses for several models of practical interest were computed using a direct integral‐equation formulation. The anomalous TEM response (secondary response) is the result of a complex interaction between vortex and galvanic currents within the body. Distortion of the secondary response by the conductive host does not affect the estimate of the depth to the horizontal body but it does lead to erroneous estimates of the conductivity and size of the body. Increasing the resistivity of the host decreases the host effects and increases the peak response of the body. Decreasing the separation between the body and borehole or decreasing the depth of the body increases the secondary response. The decrease in the vortex response due to the decreased coupling when a transmitting loop is offset from the body is nearly countered by an increase in the galvanic response at late times; however, this phenomenon is model‐dependent. This study indicates promise for the borehole TEM method, but the application of the technique is limited by the hardware and modest modeling capabilities presently available.

ELECTROMAGNETIC SCATTERING BY CONDUCTORS IN THE EARTH NEAR A LINE SOURCE OF CURRENT

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 101-131 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Line Source ◽  
Numerical Technique ◽  
The Body ◽  
Scale Model ◽  
Electromagnetic Response ◽  
Field Phase ◽  
Horizontal Magnetic Field ◽  
Depth Of Burial

A theoretical solution is developed for the electromagnetic response of a two‐dimensional inhomogeneity in a conductive half‐space, in the field of a line source of current. The solution is in the form of an integral equation, which is reduced to a matrix equation, and solved numerically for the electric field in the body. The electric and magnetic fields at the surface of the half‐space are found by integrating the half‐space Green’s functions over the scattering currents. One advantage of this particular numerical technique is that it is necessary to solve for scattering currents only in the conductor and not throughout the half‐space. The response of a thin, vertical conductor is studied in some detail. Because the only interpretational aids available previously were scale model results for conductors in free space, the results presented here should be useful in interpreting data and in designing new EM systems. As expected, anomalies decay rapidly as depth of burial is increased, due to attenuation in the conductive half‐space. Depth of exploration appears to be greatest for measurements of horizontal magnetic field phase, while vertical field phase is diagnostic of conductivity. Horizontal location and depth of burial are best determined through measurements of vertical or horizontal magnetic field amplitude.

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