Stress Concentration Due to a Hemispherical Pit at a Free Surface

1954 ◽  
Vol 21 (1) ◽  
pp. 57-62
Author(s):  
R. A. Eubanks
Keyword(s):  
Free Surface ◽  
Present Method ◽  
Infinite Medium ◽  
The Body ◽  
Hydrostatic Tension ◽  
Rotationally Symmetric ◽  
Method Of Solution ◽  
In Series ◽  
Axis Of Symmetry ◽  
Plane At Infinity

Abstract This paper contains a solution in series form for the stresses and displacements around a hemispherical pit at a free surface of an elastic body. The problem is idealized by considering a semi-infinite medium which otherwise is bounded by a plane. At infinity the body is assumed to be in a state of plane hydrostatic tension perpendicular to the axis of symmetry of the pit. The present method of solution may be generalized to loadings which are not rotationally symmetric. Numerical results are given for the variation along the axis of symmetry of the normal stress which is parallel to the tractions at infinity; these results are compared with the known corresponding numerical values appropriate to the two-dimensional analog of the present problem.

DIRECT INTERPRETATION OF SELF‐POTENTIAL ANOMALIES CAUSED BY INCLINED SHEETS OF INFINITE HORIZONTAL EXTENSIONS

Geophysics ◽  
1965 ◽  
Vol 30 (3) ◽  
pp. 418-423 ◽  
Author(s):  
M. K. Paul
Keyword(s):  
Free Surface ◽  
Present Method ◽  
The Body ◽  
Direct Interpretation ◽  
Infinite Line ◽  
Self Potential

Self‐potential anomalies caused by inclined sheets of infinite horizontal extension may be interpreted in terms of two infinite line poles situated on the body at positions nearest and furthest from the free surface, respectively. The direct interpretation of such pairs of line poles in terms of their positions and strength is possible from the observed anomaly profile. The solution is unique in its own family, i.e., no pair of line poles other than that arrived at by the present method can give rise to the observed anomaly.

On the Transmission of a Concentrated Load Into the Interior of an Elastic Body

1956 ◽  
Vol 23 (4) ◽  
pp. 541-554
Author(s):  
G. L. Neidhardt ◽  
Eli Sternberg
Keyword(s):  
Exact Solution ◽  
Normal Stress ◽  
Elastic Body ◽  
Half Space ◽  
Circular Cone ◽  
The Body ◽  
Concentrated Load ◽  
In Series ◽  
Stress Functions ◽  
Axis Of Symmetry

Abstract An exact solution in series form is presented for the stresses and displacements in an elastic body bounded by one sheet of a two-sheeted hyperboloid of revolution, subjected to an axial concentrated load at the vertex. The problem is reduced to one governed by finite surface tractions with the aid of a scheme developed in (1), and the solution is based on the Boussinesq stress functions referred to spheroidal co-ordinates. The corresponding known solutions appropriate to the half space and to the circular cone are obtained as limiting cases. Numerical results are given for the normal stress on planes perpendicular to the axis of symmetry, at points on this axis. These values are utilized in a discussion aimed at the influence of the curvature of the boundary at the load point upon the transmission of the load into the interior of the body; the results indicate that this influence may be considerable.

The Second-Order Theory of Heaving Cylinders in a Free Surface

1968 ◽  
Vol 12 (04) ◽  
pp. 313-327
Author(s):  
Choung Mook Lee
Keyword(s):  
Free Surface ◽  
Water Surface ◽  
Vertical Axis ◽  
Order Theory ◽  
Second Order ◽  
The Body ◽  
Two Dimensional ◽  
Forced Motion ◽  
Axis Of Symmetry ◽  
The Waves

A second-order potential solution is sought for a two-dimensional symmetric cylinder placed horizontally in a free surface and forced to oscillate vertically. The forced motion is simple harmonic, and the amplitude is small compared to the beam of the cylinder. The resulting potential-theory problem is solved by placing singularities of all orders at the intersection of the water surface at rest with the vertical axis of symmetry, and by determining their strengths from the boundary condition on the body. The pressure distribution on the cylinder, the force acting upon it, and the waves generated by it are derived through the second order. Numerical computations are made for a circular cylinder and for a U-shaped cylinder, and the results are presented in graphs.

Stress Distribution Around a Circular Inclusion in a Semi-Infinite Elastic Plate

1958 ◽  
Vol 25 (1) ◽  
pp. 129-135
Author(s):  
E. M. Saleme
Keyword(s):  
Elastic Plate ◽  
Elastic Moduli ◽  
Infinite Plate ◽  
Circular Inclusion ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Uniform Tension ◽  
Method Of Solution ◽  
In Series ◽  
Axis Of Symmetry

Abstract This paper contains an exact two-dimensional solution in series form for the stresses and displacements around a circular inclusion perfectly bonded to a semi-infinite elastic plate. At infinity the plate is assumed to be in a state of uniform tension parallel to the straight boundary. It should be emphasized, however, that the method of solution presented may be applied to other types of loading. Numerical results are given for the variation along the axis of symmetry of the normal stress which is parallel to the straight boundary, for a given geometry, and various ratios of the elastic moduli of the plate and the inclusion. Finally, the known solutions corresponding to an infinite plate with a circular inclusion and to a semi-infinite plate with a circular hole are obtained as limiting cases.

On the short cylindrical waves due to a body heaving on water. I

1971 ◽  
Vol 70 (2) ◽  
pp. 311-321 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Free Surface ◽  
Potential Problem ◽  
Vertical Axis ◽  
Short Wave ◽  
The Body ◽  
Dimensional Problem ◽  
Constant Depth ◽  
Force Coefficient ◽  
Cylindrical Waves ◽  
Axis Of Symmetry

AbstractIn this paper we obtain the short-wave asymptotic value of the force coefficient for a heaving body partially immersed in the free surface of water which has finite constant depth. The body is required to intersect the free surface normally and have a vertical axis of symmetry. The motion of the water is thus axisymmetric with short outgoing cylindrical waves at a distance, and these must be calculated. For this we use a non-rigorous argument. The potential problem discussed is analogous to the two-dimensional problem afready investigated involving a heaving surface cylinder. Numerical values are obtained in the case of a half-immersed sphere in conclusion.

ANALYSIS OF THE CREW PART OF THE LOCOMOTIVE TEM23 AND PROPOSALS FOR ELIMINATION OF DISADVANTAGES

2020 ◽  
Author(s):  
Dmitriy Antipin ◽  
Vladimir Vorobev ◽  
Denis Bondarenko ◽  
Gennadiy Petrov
Keyword(s):  
Vertical Plane ◽  
The Body ◽  
Diesel Locomotive ◽  
Design Features ◽  
Bogie Frame ◽  
Spring Suspension ◽  
In Series

The analysis of the design features of the bogie of the TEM23 shunting diesel locomotive is carried out. In the process of analysis, the directions of its improvement are determined. It is proposed to rotate the bogie frame in the vertical plane by reducing the body supports to two and using a pivot with low lowering, equip the bogies with pneumatic spring suspension in the form of two corrugations installed in series with shortened suspension springs. The proposed options for improving the undercarriage of a diesel locomotive will increase the competitiveness of products and reduce costs

Influence of Free Surface Environment on the Shear Zone in Metal Cutting

1966 ◽  
Vol 181 (1) ◽  
pp. 687-705 ◽  
Author(s):  
P. L. Barlow
Keyword(s):  
Free Surface ◽  
Carbon Tetrachloride ◽  
Strain Hardening ◽  
Shear Zone ◽  
Chemical Reaction ◽  
Cutting Forces ◽  
Metal Cutting ◽  
The Body ◽  
Surface Barrier ◽  
Rehbinder Effect

It has previously been suggested that the reduction in cutting forces obtained by the presence of fluids such as CCl4 on the backface or free surface of the forming chip was due to diffusion of the fluid into the body of the chip in the region of the shear zone. In the present work, experiments with carbon tetrachloride tagged with carbon-14 and with carbon tetrachloride tagged with chlorine-36 were performed with the object of assessing the extent of diffusion of lubricants into the chip when present on the free surface only. The results obtained disprove former hypotheses and suggest that the reduced cutting force is due solely to chemical reaction at the surface of the chip. Confirmation of the sensitivity of the surface of the deforming shear zone to change in surface condition was obtained by removing metal from this region by an electropolishing technique during slow speed cutting. By varying the electropolishing conditions increased or decreased cutting forces could be obtained. It is proposed that the result both of chemical reaction at the surface and of surface removal is to reduce the strain-hardening rate of the metal undergoing shear by reducing the surface barrier to the flow of dislocations out of the metal. The association of the surface reaction of carbon tetrachloride with a change in the strain-hardening characteristics of the metal in the shear zone leads to a classification of the backface phenomenon as a Rehbinder effect and enables this effect to be more closely defined than was hitherto possible. Evidence is also presented which indicates that the backface effect does not contribute to the reduction in cutting forces during rakeface lubrication and is therefore unimportant in practice where flood lubrication of the cutting region invariably occurs.

The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

1966 ◽  
Vol 33 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Joseph F. Shelley ◽  
Yi-Yuan Yu
Keyword(s):  
Stress Field ◽  
Uniaxial Tension ◽  
Elastic Solid ◽  
Displacement Function ◽  
Hydrostatic Tension ◽  
Series Form ◽  
Spherical Inclusions ◽  
Spherical Cavities ◽  
In Series ◽  
The Common

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

Boundaries Influence on the Flow Field Around an Oscillating Sphere

2013 ◽  
Author(s):  
Domenica Mirauda ◽  
Antonio Volpe Plantamura ◽  
Stefano Malavasi
Keyword(s):  
Free Surface ◽  
Flow Field ◽  
Boundary Conditions ◽  
Damping Ratio ◽  
Water Channel ◽  
Open Water ◽  
Free Surface Flows ◽  
The Body ◽  
Sphere Diameter ◽  
Oscillating Sphere

This work analyzes the effects of the interaction between an oscillating sphere and free surface flows through the reconstruction of the flow field around the body and the analysis of the displacements. The experiments were performed in an open water channel, where the sphere had three different boundary conditions in respect to the flow, defined as h* (the ratio between the distance of the sphere upper surface from the free surface and the sphere diameter). A quasi-symmetric condition at h* = 2, with the sphere equally distant from the free surface and the channel bottom, and two conditions of asymmetric bounded flow, one with the sphere located at a distance of 0.003m from the bottom at h* = 3.97 and the other with the sphere close to the free surface at h* = 0, were considered. The sphere was free to move in two directions, streamwise (x) and transverse to the flow (y), and was characterized by values of mass ratio, m* = 1.34 (ratio between the system mass and the displaced fluid mass), and damping ratio, ζ = 0.004. The comparison between the results of the analyzed boundary conditions has shown the strong influence of the free surface on the evolution of the vortex structures downstream the obstacle.

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

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