The stresses produced in an elastic half-space by a normal step loading over a circular area analytical and numerical results

Wave Motion ◽  
1990 ◽  
Vol 12 (2) ◽  
pp. 107-127 ◽  
Author(s):  
F.G. Laturelle
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Circular Area ◽  
Step Loading

XIII.—Layered Systems Subjected to Asymmetric Surface Shears

1963 ◽  
Vol 66 (3) ◽  
pp. 140-149
Author(s):  
R. A. Westmann
Keyword(s):  
General Solution ◽  
Half Space ◽  
Elastic Layer ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Shearing Force ◽  
Layered Systems ◽  
Circular Area ◽  
Stress Components

SynopsisThis paper formulates a general solution, within the scope of classical elastostatic theory, for the problem of layered systems subjected to asymmetric surface shears. As an illustrative example the solution for the problem of an elastic layer supported on an elastic half-space is presented for the particular loading consisting of a surface shearing force uniformly distributed over a circular area. Numerical results are included indicating some displacement and stress components of interest.

Subsurface and Surface Cracking Due to Hertzian Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 347-351 ◽  
Author(s):  
L. M. Keer ◽  
M. D. Bryant ◽  
G. K. Haritos
Keyword(s):  
Crack Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Vertical Crack ◽  
Subsurface Crack ◽  
Surface Cracking ◽  
Crack Geometry

Numerical results are presented for a cracked elastic half-space surface-loaded by Hertzian contact stresses. A horizontal subsurface crack and a surface breaking vertical crack are contained within the half-space. An attempt to correlate crack geometry to fracture is made and possible mechanisms for crack propagation are introduced.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

An Efficient Semi-Analytical Method to Compute Displacements and Stresses in an Elastic Half-Space with a Hemispherical Pit

2015 ◽  
Vol 7 (3) ◽  
pp. 295-322 ◽  
Author(s):  
Valeria Boccardo ◽  
Eduardo Godoy ◽  
Mario Durán
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Half Space ◽  
Plane Surface ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Quadratic Functional ◽  
Infinite Plane ◽  
Equilibrium Equations ◽  
Finite Element Software

AbstractThis paper presents an efficient method to calculate the displacement and stress fields in an isotropic elastic half-space having a hemispherical pit and being subject to gravity. The method is semi-analytical and takes advantage of the axisymmetry of the problem. The Boussinesq potentials are used to obtain an analytical solution in series form, which satisfies the equilibrium equations of elastostatics, traction-free boundary conditions on the infinite plane surface and decaying conditions at infinity. The boundary conditions on the free surface of the pit are then imposed numerically, by minimising a quadratic functional of surface elastic energy. The minimisation yields a symmetric and positive definite linear system of equations for the coefficients of the series, whose particular block structure allows its solution in an efficient and robust way. The convergence of the series is verified and the obtained semi-analytical solution is then evaluated, providing numerical results. The method is validated by comparing the semi-analytical solution with the numerical results obtained using a commercial finite element software.

Impulsive Loading on an Elastic Half-Space

1954 ◽  
Vol 21 (3) ◽  
pp. 294-295
Author(s):  
J. H. Huth ◽  
J. D. Cole
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Impulsive Loading ◽  
Wave System ◽  
Step Loading

Abstract This brief note considers the wave system resulting from a step loading on an elastic half-space. A similar problem was treated by H. Lamb in 1904, but his interest was in surface tremors rather than the stresses treated herein.

Dynamic Response of a Rigid Foundation Subjected to a Distance Blast

2012 ◽  
Author(s):  
Deji Ojetola ◽  
Hamid R. Hamidzadeh
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Integral Transform ◽  
Numerical Technique ◽  
Formal Solution ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Rigid Foundation ◽  
Transform Method

Blasts and explosions occur in many activities that are either man-made or nature induced. The effect of the blasts could have a residual or devastating effect on the buildings at some distance within the vicinity of the explosion. In this investigation, an analytical solution for the time response of a rigid foundation subjected to a distant blast is considered. The medium is considered to be an elastic half space. A formal solution to the wave propagations on the medium is obtained by the integral transform method. To achieve numerical results for this case, an effective numerical technique has been developed for calculation of the integrals represented in the inversion of the transformed relations. Time functions for the vertical and radial displacements of the surface of the elastic half space due to a distant blast load are determined. Mathematical procedures for determination of the dynamic response of the surface of an elastic half-space subjected to the blast along with numerical results for displacements of a rigid foundation are provided.

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.

Propagation of Torsional Surface Waves in Heterogeneous Half-Space with Irregular Free Surface

2020 ◽  
Vol 9 (2) ◽  
pp. 128-131
Author(s):  
Mahmoud M. Selim
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Half Space ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Surface Irregularity ◽  
Closed Form Solutions ◽  
The Earth ◽  
Waves Propagation ◽  
Torsional Surface Waves

This study is an attempt to show the impacts of free surface irregularity on the torsional surface waves propagating in heterogeneous, elastic half-space. The surface irregularity is taken in the parabolic form at the surface of the half-space. The governing equation and corresponding closed form solutions are derived. Then, the phase velocity of torsional surface waves is obtained analytically and the influences of surface irregularity are studied in detail. Numerical results analyzing the torsional surface waves propagation are discussed and presented graphically. The analytical solutions and numerical results reveal that, the surface irregularity and heterogeneity have notable effects on the torsional surface waves propagation in the elastic half-space. Since the Earth crust is heterogeneous medium with irregular surface, thus it is important to consider the effects of heterogeneity and surface irregularity on velocity of torsional surface waves propagating in the Earth medium.

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