An experimental study on the contact problem of spherical indentation on the anisotropic elastic half-space based on imaging

The two-dimensional contact problem for a semi-infinite anisotropic elastic media is reconsidered here by using the formalism of Es he I by et al. (1953) and Stroh (1958). The approach of analytic function continuation is employed to investigate the half-space contact problem with various mixed boundary conditions applied to the half-space. A key point of the solution procedure suggested in the present paper is its dependence on a general eigenvalue problem involving a Hermitian matrix. This eigenvalue problem is analogous to the one encountered when investigating the behavior of an interface crack (Ting, 1986). As an application, the interaction between a dislocation and a contact strip is solved. The compactness of the results shows their potential for utilization to solve the problem of contact of a damaged anisotropic half-space.

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Transient contact problem for spherical shell and elastic half-space

Shell Structures: Theory and Applications Volume 4 ◽

10.1201/9781315166605-67 ◽

2017 ◽

pp. 301-304

Author(s):

E.Yu. Mikhailova ◽

G.V. Fedotenkov ◽

D.V. Tarlakovskii

Keyword(s):

Contact Problem ◽

Spherical Shell ◽

Half Space ◽

Elastic Half Space ◽

Transient Contact

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

Bulletin of the National Engineering Academy of the Republic of Kazakhstan ◽

10.47533/2020.1606-146x.31 ◽

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.

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