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.

The Effect of an Axial Force on the Response of an Anisotropic Elastic Half Space to a Rolling Cylinder

1973 ◽  
Vol 40 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Half Space ◽  
Axial Force ◽  
Elastic Half Space ◽  
Applied Force ◽  
Finite Width ◽  
Infinite Length ◽  
Anisotropic Elastic

The problem of an inflated cylindrical tire of infinite length and constant finite width steadily rolling over the surface of an anisotropic elastic half space is examined. The influence of an applied force, acting along the axis of the cylinder, on the width of the region of slip at each end of the tire is determined. In particular, it is shown numerically that when a material exhibits certain anisotropy the presence of an axial force can considerably reduce the width of the zones of slip.

The response of an anisotropic elastic half-space to a rolling cylinder

1971 ◽  
Vol 70 (3) ◽  
pp. 467-484 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Shear Stress ◽  
Half Space ◽  
Elastic Anisotropy ◽  
Contact Region ◽  
Steady Motion ◽  
Elastic Half Space ◽  
Infinite Length ◽  
Anisotropic Elastic ◽  
Similar Class ◽  
Basic Equations

The problem of the steady motion of a heavy cylinder, of infinite length, over the surface of an elastic half-space has been examined by Craggs and Roberts(1), Clements(2) and Roberts (3). In papers (1) and (2) the surfaces of both the cylinder and the half-space are assumed to be smooth so that the shear stress over the region of contact is zero. With this assumption Craggs and Roberts analysed the motion for an isotropic half-space while Clements considered the case of an anisotropic half-space. In the paper by Roberts (3) various problems concerning the rolling of rigid and non-rigid cylinders over an isotropic elastic half-space are discussed. In this paper we consider a similar class of rolling cylinder problems for an anisotropic half-space. We begin, in section 2, by deriving the relevant basic equations for the stress and displacement while in section 3 some properties of certain constants occurring in the equations of section 2 are derived for use in later sections. The problem of the steady motion of an inflated tyre is discussed in section 4 under the assumptions that the tyre exerts a constant pressure over the contact region which is instantaneously at rest. The solution shows that, with these assumptions, the shear stress is infinite near the ends of the region of contact. This indicates that there will be slipping of the tyre over the half-space at both ends of the contact region. If these zones of slip are large compared with the total contact area then the assumption of a contact region which is instantaneously at rest is invalidated so that the solution may only be regarded as being applicable when the zones of slip are small. An expression to determine the width of the zones of slip is derived and this expression is used, together with the numerical results of section 5, to obtain information about the influence of anisotropy on the width of the zones of slip. In section 6 the problem of the inflated tyre is discussed with allowance made for a zone of slip at both ends of the region of contact. The results of this section could be expected, particularly when the zones of slipping are wide, to more accurately predict the response of the anisotropic half-space to the rolling tyre than the results of section 4. Unfortunately, in order to satisfactorily complete the analysis, it is necessary to restrict the class of anisotropic materials for which the results are applicable. As a consequence, the work of section 4 is in many ways preferable to that of section 6 in indicating the influence which elastic anisotropy has upon the results.

Steady Motion of a Rigid Strip Bonded to an Elastic Half Space

1971 ◽  
Vol 38 (2) ◽  
pp. 328-334 ◽  
Author(s):  
M. A. Oien
Keyword(s):  
Approximate Solution ◽  
Galerkin Method ◽  
Integral Equations ◽  
Half Space ◽  
Steady Motion ◽  
Elastic Half Space ◽  
Fredholm Integral Equations ◽  
Harmonic Waves ◽  
Forced Motion ◽  
Inertia Properties

The diffraction of harmonic waves by a movable rigid strip bonded to the surface of an elastic half space is divided into two more fundamental problems, the diffraction of waves by a fixed strip and the forced motion of an inertialess strip. These problems are formulated in terms of a pair of coupled Fredholm integral equations of the first kind. An approximate solution for the resultant loads acting on the strip is obtained using the Bubnov-Galerkin method. These loads provide a simple means of studying the excited motion of a movable strip having a variety of inertia properties.

Response of a plate and elastic half-space to harmonic waves

1982 ◽  
Vol 10 (2) ◽  
pp. 255-266 ◽  
Author(s):  
W. L. Whittaker ◽  
Paul Christiano
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Harmonic Waves

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.

Refraction of P- and S-Wave at the Interface of Micropolar Elasticity and Thermoelasticity with Voids

2018 ◽  
Vol 06 (03n04) ◽  
pp. 1850005
Author(s):  
R. Lianngenga ◽  
J. Lalvohbika ◽  
Lalawmpuia
Keyword(s):  
Thermal Expansion ◽  
Half Space ◽  
Plane Waves ◽  
Linear Thermal Expansion ◽  
Elastic Half Space ◽  
Micropolar Elasticity ◽  
S Wave ◽  
Incident Plane ◽  
Energy Ratios ◽  
Refracted Waves

The problem of incident plane waves at the interface of micropolar thermoelastic half-space with voids and micropolar elastic half-space with voids has been attempted. The amplitude and energy ratios of various reflected and refracted waves for the incident [Formula: see text]- and [Formula: see text]-waves are obtained with the help of appropriate boundary conditions at the interface. The effect of linear thermal expansion and microinertia on the amplitude and energy ratios due to the incident [Formula: see text]- and [Formula: see text]-waves are discussed. Numerically and analytically, these amplitude and energy ratios are computed to show the effect of linear thermal expansion and microinertia. It is observed that the effect of linear thermal expansion is less for incident [Formula: see text]-wave and the effect of microinertia is less for incident [Formula: see text]-wave.

The Approximate Distribution of Stress in a Finite Plate Having a Stress-Free Circular Cut-Out

1964 ◽  
Vol 68 (639) ◽  
pp. 204-208 ◽  
Author(s):  
H. Waters
Keyword(s):  
Outer Boundary ◽  
Practical Importance ◽  
Infinite Plate ◽  
Approximate Solutions ◽  
Finite Width ◽  
Infinite Length ◽  
Uniform Tension ◽  
Approximate Distribution ◽  
Axis Of Symmetry ◽  
Distribution Of Stress

The distribution of stress in a flat plate having a circular cut-out and subjected to known forces at its outer boundary is of considerable practical importance. Assuming that (i) the plate is thin, so that the problem is one of plane stress, and (ii) the material of which it is formed is isotropic and obeys Hooke's law, exact or approximate solutions have been obtained for a limited number of particular cases. Most of these solutions relate to a plate which is infinite in extent in one or more directions. The case of a plate of finite width and infinite length having a circular hole on the axis of symmetry was discussed by Howland, and by Howland and Stevenson. Wang gave an approximate solution for a perforated shear web, and Mindlin investigated the stress distribution around a hole near the edge of a semi-infinite plate under uniform tension.

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.

scholarly journals Static Deformation due to a Long Tensile Fault of Finite Width in an Isotropic Half-Space Welded with an Orthotropic Half-Space

2014 ◽  
Vol 9 ◽  
pp. 11-26
Author(s):  
Yogita Godara ◽  
Ravinder Kumar Sahrawat ◽  
Mahabir Singh
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Stress Function ◽  
Vertical Displacement ◽  
Elastic Half Space ◽  
Finite Width ◽  
Airy Stress Function ◽  
Two Phase ◽  
Phase Medium ◽  
Analytical Expressions

Closed-form analytical expressions for displacements and stresses at any point of a two-phase medium consisting of a homogeneous, isotropic, perfectly elastic half-space in welded contact with a homogeneous, orthotropic, perfectly elastic half-space caused by a tensile fault of finite width located at an arbitrary distance from the interface in the isotropic half-space are obtained. The Airy stress function approach is used to obtain the expressions for the stresses and displacements. The vertical tensile fault is considered graphically. The variations of the displacements with the distance from the fault and with depth for various cases have been studied graphically. Also horizontal and vertical displacement of the surface are presented graphically.

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