On the stress distributions due to force nuclei in an elastic solid bounded internally by a spherical hollow and in an elastic sphere

1960 ◽  
Vol 11 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Derek Collins
Keyword(s):  
Elastic Solid ◽  
Stress Distributions ◽  
Elastic Sphere ◽  
Spherical Hollow

The Stress Field Caused by a Circular Cylindrical Inclusion in a Transversely Isotropic Elastic Solid

2003 ◽  
Vol 70 (6) ◽  
pp. 825-831 ◽  
Author(s):  
H. Hasegawa ◽  
M. Kisaki
Keyword(s):  
Stress Field ◽  
Strain Energy ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Cylindrical Inclusion ◽  
Stress Distributions ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Isotropic Solid ◽  
Stress And Displacement Fields

Exact solutions are presented in closed form for the axisymmetric stress and displacement fields caused by a circular solid cylindrical inclusion with uniform eigenstrain in a transversely isotropic elastic solid. This is an extension of a previous paper for an isotropic elastic solid to a transversely isotropic solid. The strain energy is also shown. The method of Green’s functions is used. The numerical results for stress distributions are compared with those for an isotropic elastic solid.

Some axially symmetric stress distributions in elastic solids containing penny-shaped cracks I. Cracks in an infinite solid and a thick plate

1962 ◽  
Vol 266 (1326) ◽  
pp. 359-386 ◽  
Keyword(s):  
Integral Equations ◽  
Interior Point ◽  
Thick Plate ◽  
Elastic Solid ◽  
Point Force ◽  
Fredholm Integral Equations ◽  
Stress Distributions ◽  
Axially Symmetric ◽  
Single Crack ◽  
Elastic Solids

Some axially symmetric stress distributions in an infinite elastic solid and in a thick plate containing penny-shaped cracks are considered. It is shown that, by use of a representation for the displacement in an infinite elastic solid containing a single crack, representations for the displacements in an infinite solid containing two or more cracks and in a thick plate containing a single crack can be constructed and used to reduce the problems of determining the stresses in these solids to the solutions of Fredholm integral equations of the second kind. Various stress distributions investigated include those due to the opening of a crack in an infinite solid by a point force acting at an interior point of the solid and the opening of cracks in an infinite solid and a thick plate under the action of constant pressures over the cracks.

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.

A Contact Stress Problem for a Rigid Smooth Sphere in an Extended Elastic Solid

1965 ◽  
Vol 32 (3) ◽  
pp. 651-655 ◽  
Author(s):  
I-Chih Wang
Keyword(s):  
Legendre Polynomials ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Rigid Sphere ◽  
Stress Distributions ◽  
Dual Series Equations ◽  
Axisymmetric Elasticity ◽  
Rigid Smooth ◽  
Smooth Sphere

A three-dimensional axisymmetric elasticity problem pertaining to the contact stresses between a smooth rigid sphere and an infinite elastic solid with a smooth spherical cavity of the same diameter has been considered. Uniaxial loading is applied to the solid at infinity, resulting in a separation along a portion of the boundary between the sphere and the solid. The problem has been considered as a mixed boundary-value problem of elasticity. The angle of contact and the stress distributions along the contact surface are determined by solving a set of dual-series equations associated with Legendre polynomials. Numerical results are presented.

Some coplanar punch and crack problems in three-dimensional elastostatics

1963 ◽  
Vol 274 (1359) ◽  
pp. 507-528 ◽  
Keyword(s):  
Half Space ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Normal Derivative ◽  
Elastic Half Space ◽  
Fredholm Integral Equations ◽  
Stress Distributions ◽  
Crack Problems ◽  
Three Dimensional Space

Certain three-dimensional punch and crack problems for an elastic half-space and an infinite elastic solid respectively reduce to Dirichlet or Neumann problems in potential theory in which the potential is to be determined at all points of an infinite three-dimensional space, given its values or the values of its normal derivative on two or more coplanar circular regions. These problems are shown to be governed by infinite sets of Fredholm integral equations of the second kind, which can be solved approximately by iteration when the spacing between the circular regions is sufficiently large compared with their radii. The stress distributions in a half-space indented by two flat-ended circular punches and in an infinite solid containing two or more coplanar penny-shaped cracks opened under pressure are thus investigated.

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