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.

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.

Constant Temperature at the Surface of an Initially Uniform Temperature, Variable Conductivity Half Space

1971 ◽  
Vol 93 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Leonard Y. Cooper
Keyword(s):  
Temperature Distribution ◽  
Half Space ◽  
Constant Temperature ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Transient Temperature ◽  
Uniform Temperature ◽  
Transient Temperature Distribution ◽  
Temperature Variable ◽  
Variable Conductivity

The transient temperature distribution resulting from a constant and uniform temperature being imposed on the surface of an initially uniform temperature, variable conductivity half space is studied. Various solution expansion ideas are discussed. These are utilized in the solution of an example problem, and the resulting approximate analytic solutions representations are compared to exact numerical results. One of these approximations is found to be superior to the others, and, in fact, it is shown to yield useful results over a range of variables where the nonlinearities of the problem are significant.

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.

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.

Impact and Moving Loads on a Slightly Curved Elastic Half Space

1959 ◽  
Vol 26 (4) ◽  
pp. 491-498
Author(s):  
A. C. Eringen ◽  
J. C. Samuels
Keyword(s):  
Half Space ◽  
Fourier Transforms ◽  
Normal Load ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Moving Loads ◽  
Special Cases ◽  
Indefinite Integral ◽  
Wavy Boundary ◽  
Boundary Curves

Abstract Two-dimensional Fourier transforms are employed to treat the two-dimensional dynamic problem of elastic half space having a slightly wavy boundary. The various boundary curves considered include square and triangular bumps and holes, and sinusoidal and periodic boundaries. The number of different types of surface loadings considered are: (a) Normal tractions and zero shear, (b) impulsive normal tractions and zero shear, (c) suddenly applied normal tractions and zero shear, (d) concentrated normal load and zero shear, (e) concentrated impulsive load and zero shear, (f) pulsating normal load and zero shear, (g) moving loads, (h) pulsating moving loads, (i) vertical and horizontal loads, (j) moving vertical loads. Stress and displacement components for special cases of the loads described in (a, c, f, and g) acting on a sinusoidal boundary lead to a solution which requires evaluation of a single indefinite integral. Closed-form results are given for a uniform pulsating pressure load.

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