Stresses due to a nucleus of thermo-elastic strain (i) in an infinite elastic solid with spherical cavity and (ii) in a solid elastic sphere

1957 ◽  
Vol 8 (2) ◽  
pp. 142-150 ◽  
Author(s):  
Brahma Sharma
Keyword(s):  
Spherical Cavity ◽  
Elastic Strain ◽  
Elastic Solid ◽  
Elastic Sphere

scholarly journals On generalized thermoelastic disturbances in an elastic solid with a spherical cavity

1991 ◽  
Vol 4 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Basudeb Mukhopadhyay ◽  
Rasajit Bera ◽  
Lokenath Debnath
Keyword(s):  
Laplace Transform ◽  
Classical Theory ◽  
Spherical Cavity ◽  
Dynamic Pressure ◽  
Elastic Solid ◽  
Dynamical Theory ◽  
The Laplace Transform ◽  
Generalized Thermoelastic ◽  
Short Time ◽  
The Waves

In this paper, a generalized dynamical theory of thermoelasticity is employed to study disturbances in an infinite elastic solid containing a spherical cavity which is subjected to step rise in temperature in its inner boundary and an impulsive dynamic pressure on its surface. The problem is solved by the use of the Laplace transform on time. The short time approximations for the stress, displacement and temperature are obtained to examine their discontinuities at the respective wavefronts. It is shown that the instantaneous change in pressure and temperature at the cavity wall gives rise to elastic and thermal disturbances which travel with finite velocities v1 and v2(>v1) respectively. The stress, displacement and temperature are found to experience discontinuities at the respective wavefronts. One of the significant findings of the present analysis is that there is no diffusive nature of the waves as found in classical theory.

V. On the bodily tides of viscous and semi-elastic spheroids, and on the ocean tides on a yielding nucleus

1878 ◽  
Vol 27 (185-189) ◽  
pp. 419-424
Keyword(s):  
Viscous Fluid ◽  
Thin Shell ◽  
Elastic Solid ◽  
The State ◽  
Internal Strain ◽  
Incompressible Viscous Fluid ◽  
Elastic Sphere ◽  
Ocean Tides ◽  
The Earth ◽  
Bodily Tides

Sir W. Thomson’s investigation of the bodily tides of an elastic sphere has gone far to overthrow the idea of a semi-fluid interior to the earth, yet geologists are so strongly impressed by the fact that enormous masses of rock have been poured out of volcanic vents in the earth’s surface, that the belief is not yet extinct that we live on a thin shell over a sea of molten lava. It appeared to me, therefore, to be of interest to investigate the consequences which would arise from the supposition that the matter constituting the earth is of a viscous or imperfectly elastic nature. In this paper I follow out these hypo-theses, and it will be seen that the results are fully as hostile to the idea of any great mobility of the interior of the earth as are those of Sir W. Thomson. I begin by showing that the equations of flow of an incompressible viscous fluid have precisely the same form as those of strain of an incompressible elastic solid, at least when inertia is neglected. Hence, every problem about the strains of the latter has its analogue touching the flow of the former. This being so, the solution of Sir W. Thomson’s problem of the bodily tides of an elastic sphere may be adapted to give the bodily tides of a viscous spheroid. Sir W. Thomson, however, introduces the effects of the mutual gravitation of the parts of the sphere, by a synthetical method, after he has found the state of internal strain of an elastic sphere devoid of gravitational power The parallel synthetical method becomes, in the case of the viscous spheroid, somewhat complex, and I have preferred to adapt the solution analytically so as to include gravitation.

scholarly journals Stress amplification in three-dimensional narrow zones created by cavities

2012 ◽  
Vol 39 (1) ◽  
pp. 71-97
Author(s):  
Stavros Syngellakis
Keyword(s):  
Spherical Cavity ◽  
Exact Analytical Solution ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Bending Moments ◽  
Series Solutions ◽  
Minimum Thickness ◽  
Narrow Region ◽  
Stress Amplification ◽  
Radial Tension

The paper is concerned with a particular case of stress amplification arising from the proximity of a spherical cavity to the boundary of a loaded elastic solid. The performed approximate analysis yields distributions of stresses and displacements in the narrow region formed between a spherical cavity and the faces of a thin flat layer subjected to a far field uniform radial tension. The narrow region is modelled as a circular plate of non-uniform thickness undergoing coupled membrane and flexural deformation. Series solutions are obtained for both membrane forces and bending moments leading to estimates for the stress concentration factor at minimum thickness. These predictions are found consistent with those obtained from both the exact analytical solution and finite element modelling of the problem. Cross-validated results from the two latter methods also provide trends for the stress amplification due to the narrowness of the region.

scholarly journals Tension of a Dissimilar Elastic Solid with a Spherical Cavity.

1999 ◽  
Vol 65 (629) ◽  
pp. 21-25
Author(s):  
Takeyuki MIYAKAWA ◽  
Hisao HASEGAWA
Keyword(s):  
Spherical Cavity ◽  
Elastic Solid
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