Plane Punch Indentation of Anisotropic Elastic Half Space

1990 ◽  
Vol 57 (1) ◽  
pp. 84-90 ◽  
Author(s):  
J. W. Klintworth ◽  
W. J. Stronge
Keyword(s):  
Stress Distribution ◽  
Half Space ◽  
Elastic Half Space ◽  
Basic Solutions ◽  
Anisotropic Elastic ◽  
Punch Problem

The stress distribution within a planar anisotropic half space is determined for normal or tangential displacements imposed over a small part of the surface. The general punch problem is then considered as a combination of these basic solutions. Results are presented for the normal, tangential, and rotary indentation of an arbitrarily-oriented half space by a flat frictional punch.

Regular Pyramid Punch Problem

1992 ◽  
Vol 59 (3) ◽  
pp. 519-523 ◽  
Author(s):  
G. G. Bilodeau
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Half Space ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Reasonable Assumption ◽  
Punch Problem

An approximate solution is found for a regular pyramidal punch indenting, without friction, an elastic half-space. The method is based on the reasonable assumption of the stress distribution and of the region of contact. The force-indentation relationship is obtained for a regular pyramidal punch. The results compare well with direct numerical results.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

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.

scholarly journals Reduced model for the surface dynamics of a generally anisotropic elastic half-space

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190590 ◽  
Author(s):  
Yibin Fu ◽  
Julius Kaplunov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Travelling Waves ◽  
Moving Load ◽  
Multiple Scale ◽  
Elastic Half Space ◽  
Surface Dynamics ◽  
Near Surface ◽  
Surface Resonance ◽  
Anisotropic Elastic

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v  −  v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

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