The Interaction Between a System of Circular Punches on an Elastic Half Space

1982 ◽  
Vol 49 (2) ◽  
pp. 341-344 ◽  
Author(s):  
G. M. L. Gladwell ◽  
V. I. Fabrikant
Keyword(s):  
Half Space ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Concentrated Load ◽  
Circular Punch

Galin derived an expression for the pressure produced under a rigid circular punch by the application of a concentrated load at another point of the half space. This result is used to derive approximate relationships among the forces, moments, and indentations for a system of punches on an elastic half space. The results are compared with a number of earlier approximate solutions.

A concave indenter on a piezoelectromagneto-elastic substrate or a layer elastically supported

2012 ◽  
Vol 47 (6) ◽  
pp. 362-378 ◽  
Author(s):  
Bogdan Rogowski
Keyword(s):  
Half Space ◽  
Elastic Foundation ◽  
Contact Region ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
Solution Technique ◽  
Elementary Functions ◽  
Full Field ◽  
Full Contact ◽  
Two Parameter

Indentation of piezoelectromagneto-elastic half-space or a layer on a two-parameter elastic foundation by a cylindrical indenter with a slightly concave base is considered. Full-field magnetoelectro-elastic solutions in elementary functions are obtained for the case of full contact and half-space. If the axial load is small, the contact area will be an annulus the outer circumference of which coincides with the edge of the punch. The inner circumference will shrink with increasing load and there will be a critical load above which the stratum makes contact with the entire punch base. The contact problem for high loads can therefore be treated by classical methods. The more interested case in which the load is less the critical value and the contact region is annulus remains. By use the methods of triple integral equations and series solution technique the solution for an indentured substrate over an annular contact region is also given. For parabolic and conical concave punches the exact or approximate solutions are obtained for full contact or annular contact region, respectively. For the layer on two-parameter elastic foundation and concave punch approximate solution is established.

Steady Motion of a Plate on an Elastic Half Space

1973 ◽  
Vol 40 (2) ◽  
pp. 478-484 ◽  
Author(s):  
M. A. Oien
Keyword(s):  
Half Space ◽  
Steady Motion ◽  
Approximate Solutions ◽  
Elastic Half Space ◽  
General Nature ◽  
Finite Width ◽  
Infinite Length ◽  
Harmonic Waves ◽  
Vibrational Modes ◽  
Incident Plane

The response of a smooth Bernoulli-Euler plate of finite width and infinite length in contact with an elastic half space to incident plane harmonic waves propagating normally to the infinite axis of the plate is considered. Upon expanding the motion of the plate in a series of vibrational modes, approximate solutions for the response of the plate and the elastic half space are obtained separately using the Bubnov-Galerkin method. Numerical results are presented illustrating the general nature of the response of the plate and showing that individual vibrational modes of the plate are not excited to resonance.

On two-dimensional waves in an elastic half-space

1960 ◽  
Vol 56 (3) ◽  
pp. 269-285 ◽  
Author(s):  
J. W. Craggs
Keyword(s):  
Half Space ◽  
Elastic Waves ◽  
Analytic Solutions ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Two Dimensional ◽  
Surface Traction ◽  
Concentrated Load ◽  
Dynamic Similarity

ABSTRACTTwo-dimensional elastic waves in a half-space 0 ≤ r < ∞, 0 ≤ θ ≤ π are examined under the assumption of dynamic similarity, so that the stresses depend only on r/t, θ. Analytic solutions are given for constant surface traction on θ = 0, 0 < r/t < V, where V is constant, the rest of the surface being unloaded, and for a concentrated load at r = 0.Numerical results are quoted for the particular case V → ∞, corresponding to a load on half the bounding plane.

An Arbitrary Tangential Load Underneath a Smooth Circular Punch

1990 ◽  
Vol 57 (3) ◽  
pp. 596-599 ◽  
Author(s):  
V. I. Fabrikant
Keyword(s):  
Exact Solution ◽  
Transversely Isotropic ◽  
Elastic Half Space ◽  
Reciprocal Theorem ◽  
Tangential Load ◽  
Concentrated Load ◽  
Circular Punch ◽  
Angular Displacements ◽  
The Reciprocal Theorem ◽  
First Time

The problem of a smooth circular punch penetrating a transversely isotropic elastic half space and interacting with an arbitrarily located tangential concentrated load is considered. For the first time, a closed-form exact solution is obtained for the stress distribution under the punch as well as for the linear and angular displacements of the punch. The solution is based on the results previously obtained by the author and combined with the reciprocal theorem. A numerical example is presented as an illustration.

On the Unbonded Contact Between Plates and an Elastic Half Space

1969 ◽  
Vol 36 (2) ◽  
pp. 198-202 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Approximate Solution ◽  
Tensile Stress ◽  
Half Space ◽  
Elastic Plate ◽  
Elastic Half Space ◽  
Elastic Support ◽  
Elastic Region ◽  
Concentrated Load

In this paper an approximate solution is presented for the radius of contact between an elastic plate and a semi-infinite elastic half space. The plate is assumed to rest on the supporting half space without bond, and to be pressed against the elastic region by a concentrated load. In the absence of bonding no tensile stress can be transmitted across the interface between the plate and its elastic support so that contact takes place only within a circle centered about the concentrated load. Outside of this circle the plate lifts up and is no longer in contact with the elastic region.

Torsion of a circular punch attached to an elastic half-space with a coating with periodically depth-varying elastic properties

2015 ◽  
Vol 86 (7) ◽  
pp. 1247-1254 ◽  
Author(s):  
Andrey S. Vasiliev ◽  
Michael V. Swain ◽  
Sergey M. Aizikovich ◽  
Evgeniy V. Sadyrin
Keyword(s):  
Half Space ◽  
Elastic Properties ◽  
Elastic Half Space ◽  
Circular Punch

The dynamic problem of a circular punch at the boundary of an elastic half-space

1971 ◽  
Vol 7 (2) ◽  
pp. 151-159
Author(s):  
V. L. Lobysev ◽  
V. I. Saigina ◽  
Yu. S. Yakovlev
Keyword(s):  
Half Space ◽  
Dynamic Problem ◽  
Elastic Half Space ◽  
Circular Punch
Sign in / Sign up

Export Citation Format

Share Document