scholarly journals Application of low-order potential solutions to higher-order vertical traction boundary problems in an elastic half-space

2018 ◽  
Vol 5 (5) ◽  
pp. 180203 ◽  
Author(s):  
Adam G. Taylor ◽  
Jae H. Chung
Keyword(s):  
Boundary Condition ◽  
Half Space ◽  
Granular Media ◽  
Elastic Half Space ◽  
Higher Order ◽  
Classical Solutions ◽  
Internal Stresses ◽  
Normal Surface ◽  
Soil Medium ◽  
Traction Distribution

New solutions of potential functions for the bilinear vertical traction boundary condition are derived and presented. The discretization and interpolation of higher-order tractions and the superposition of the bilinear solutions provide a method of forming approximate and continuous solutions for the equilibrium state of a homogeneous and isotropic elastic half-space subjected to arbitrary normal surface tractions. Past experimental measurements of contact pressure distributions in granular media are reviewed in conjunction with the application of the proposed solution method to analysis of elastic settlement in shallow foundations. A numerical example is presented for an empirical ‘saddle-shaped’ traction distribution at the contact interface between a rigid square footing and a supporting soil medium. Non-dimensional soil resistance is computed as the reciprocal of normalized surface displacements under this empirical traction boundary condition, and the resulting internal stresses are compared to classical solutions to uniform traction boundary conditions.

scholarly journals Surface Displacements due to a Steadily Moving Point Force

1996 ◽  
Vol 63 (2) ◽  
pp. 245-251 ◽  
Author(s):  
J. R. Barber
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Point Force ◽  
Two Dimensional ◽  
Normal Surface ◽  
Displacement Fields ◽  
Linear Superposition ◽  
Surface Displacements ◽  
Stress And Displacement Fields

Closed-form expressions are obtained for the normal surface displacements due to a normal point force moving at constant speed over the surface of an elastic half-space. The Smirnov-Sobolev technique is used to reduce the problem to a linear superposition of two-dimensional stress and displacement fields.

The Interface Crack Problem of Bonded Piezoelectric and Elastic Half-Space Under Transient Electromechanical Loads

2002 ◽  
Vol 69 (3) ◽  
pp. 244-253 ◽  
Author(s):  
S. A. Meguid ◽  
X. Zhao
Keyword(s):  
Boundary Condition ◽  
Intensity Factor ◽  
Boundary Conditions ◽  
Half Space ◽  
Interface Crack ◽  
Singular Integral ◽  
Crack Problem ◽  
Elastic Half Space ◽  
Electric Displacement Intensity Factor ◽  
Impermeable Boundary

The interface crack problem of bonded piezoelectric and elastic half-space under transient electromechanical loads is considered. Both the permeable and impermeable boundary conditions are examined and discussed. Based on the use of integral transform techniques, the problem is reduced either to a singular integral equation for the permeable boundary condition or to two coupled singular integral equations for the impermeable boundary condition, which can be solved using Chebyshev polynomial expansions. Numerical results are provided to show the effect of the applied electric fields, the electric boundary conditions along the crack faces and a free surface on the resulting dynamic stress intensity factor and electric displacement intensity factor.

Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

2000 ◽  
Vol 68 (2) ◽  
pp. 162-168 ◽  
Author(s):  
L. M. Brock
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Arbitrary Constant ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Poisson Effect ◽  
Wave Speeds ◽  
Wave Patterns ◽  
Infinitesimal Deformations ◽  
Surface Loads

A plane-strain study of a prestressed isotropic compressible neo-Hookean half-space subjected to shear and normal surface loads is performed. The loads are either stationary and applied for an instant, or travel at an arbitrary constant speed. The transient process is viewed as the superposition of infinitesimal deformations upon large, and exact expressions for the displacements, within and upon, the half-space are obtained. These, and the associated wave patterns, demonstrate the anisotropy induced by prestress. The wave speeds themselves are sensitive to prestress; in particular, Rayleigh waves disappear beyond a critical compressive prestress. A critical tensile prestress also exists, beyond which a negative Poisson effect occurs.

scholarly journals CONTACT OF MULTI-LEVEL PERIODIC SYSTEM OF INDENTERS WITH COATED ELASTIC HALF-SPACE

2019 ◽  
Vol 17 (2) ◽  
pp. 149 ◽  
Author(s):  
Irina G. Goryacheva ◽  
Elena V. Torskaya
Keyword(s):  
Half Space ◽  
Periodic System ◽  
Mutual Effect ◽  
Elastic Half Space ◽  
Internal Stresses ◽  
Contact Density ◽  
Nominal Pressure ◽  
Multi Level ◽  
Numerical Analytical Method ◽  
Contact Spots

The contact of a periodic system of spherical indenters of different heights and radii of curvature with two-layered elastic half-space is considered. Numerical-analytical method is developed to determine contact pressure distribution and internal stresses taking into account mutual effect of contact spots. The results for relatively hard and soft coatings are analyzed for different values of input parameters: nominal pressure, contact density, coating thickness.

The role of soil anisotropy on SH wave scattering by a lined circular elastic tunnel in an elastic half-space soil medium

2019 ◽  
Vol 125 ◽  
pp. 105721 ◽  
Author(s):  
Zailin Yang ◽  
Guanxixi Jiang ◽  
Cheng Sun ◽  
Tongsuo Tang ◽  
Yong Yang
Keyword(s):  
Half Space ◽  
Wave Scattering ◽  
Elastic Half Space ◽  
Sh Wave ◽  
Soil Medium

scholarly journals Exponentially Decaying Pressure Pulse Moving With Constant Velocity on the Surface of a Layered Elastic Material (Superseismic Layer, Subseismic Half Space)

1970 ◽  
Vol 37 (1) ◽  
pp. 141-152 ◽  
Author(s):  
J. P. Wright ◽  
M. L. Baron
Keyword(s):  
Half Space ◽  
Constant Velocity ◽  
Moving Load ◽  
Elastic Half Space ◽  
Normal Surface ◽  
Entire Plane ◽  
Normal Loading ◽  
Wave Speeds ◽  
S Waves ◽  
Typical Configuration

The response of a layered elastic half space to a progressing exponentially decaying normal surface pressure is evaluated for a case in which the constant velocity V of the moving pressure is greater than that of the P and S waves, respectively, in the upper layer (superseismic) and smaller than these wave speeds in the underlying half space (subseismic). It is assumed that a steady state exists with respect to coordinate axis attached to the moving load. The superseismic-subseismic geometry results in a stress field that extends over the entire plane, with sharp shocks possible only in that portion of the layer that lies behind the front of the progressing normal loading. A computer program for evaluating stresses and velocities at points in the medium was developed and results are presented for a typical configuration of interest.

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