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

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.

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Analysis of Deep Beams

Journal of Applied Mechanics ◽

10.1115/1.4010271 ◽

1951 ◽

Vol 18 (2) ◽

pp. 163-172

Author(s):

H. D. Conway ◽

L. Chow ◽

G. W. Morgan

Keyword(s):

Exact Solution ◽

Approximate Solution ◽

Stress Distribution ◽

Finite Difference ◽

Boundary Conditions ◽

Normal Stress ◽

Stress Function ◽

Beam Theory ◽

Deep Beam ◽

Stress Functions

Abstract This paper presents a method of analyzing the stress distribution in a deep beam of finite length by superimposing two stress functions. The first stress function is chosen in the form of a trigonometric series which satisfies all but one of the boundary conditions—that of zero normal stress on the ends of the beam. The principle of least work is then used to obtain a second stress function giving the distribution of normal stress on the ends which is left by the first stress function. By superimposing the two solutions, all the boundary conditions are satisfied. Two particular cases of a given type of loading are solved in this way to investigate the stresses in a deep beam and their deviation from the ordinary beam theory. In addition, an approximate solution by the numerical method of finite difference is worked out for one of the two cases. Results from the two methods are compared and discussed. A method of obtaining an exact solution to the problem is given in an Appendix.

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Stress Concentration Due to a Hemispherical Pit at a Free Surface

Journal of Applied Mechanics ◽

10.1115/1.4010819 ◽

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.

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Supersonic flow past a bluff body with a detached shock Part I Two-dimensional body

Journal of Fluid Mechanics ◽

10.1017/s0022112056000214 ◽

1956 ◽

Vol 1 (4) ◽

pp. 353-365 ◽

Cited By ~ 29

Author(s):

W. Chester

Keyword(s):

Exact Solution ◽

Mach Number ◽

Bluff Body ◽

The Body ◽

Radius Of Curvature ◽

Two Dimensional ◽

Sonic Point ◽

Axis Parallel ◽

Axis Of Symmetry ◽

High Mach

The flow at high Mach number past a body with a rounded nose is considered. Viscosity and heat conduction are neglected, and the body is assumed to be two-dimensional and symmetrical about an axis parallel to the incident stream.An exact solution is first obtained in the case λ → 1, M → ∞, where λ is the adiabatic index and M is the Mach number. This solution is then used as the basis of a double expansion in δ = (λ - 1)/(λ + 1) and M−2, after the exact solution has been modified to make the series expansion converge near the body. The expansion is carried out as far as the terms of order (δ + M−2)2.The results are displayed for various values of δ and M−2; typical results are as follows. With M−2 = 0, δ = 1/6 (λ = 1.4), and for a parabolic body having unit radius of curvature at the nose, the shock is approximately a parabola with radius of curvature 1.822 at the nose. The distance between the body and the shock along the axis of symmetry is 0.323, and the height of the sonic point from this axis is 0.744 both on the shock and on the body. The actual pressure distribution on the body is shown in figure 4, and agrees well with experiment. The pressure falls to zero at a distance 0.86 downstream from the nose of the body, measured along the axis of symmetry. On the assumption that the pressure remains negligible beyond this point, the total drag is 1.39 ρV2, where ρ0 is the density andV is the velocity of the incident stream.

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

PROBLEMS OF APPLIED MECHANICS ◽

10.30987/conferencearticle_5fd1ed03361519.33564687 ◽

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

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Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

Journal of Applied Mechanics ◽

10.1115/1.3564708 ◽

1969 ◽

Vol 36 (3) ◽

pp. 505-515 ◽

Cited By ~ 108

Author(s):

D. C. Gakenheimer ◽

J. Miklowitz

Keyword(s):

Exact Solution ◽

Free Surface ◽

Steady State ◽

Wave Front ◽

Half Space ◽

Displacement Field ◽

Elastic Half Space ◽

Point Load ◽

Limit Case ◽

Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

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Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field

Journal of Fluid Mechanics ◽

10.1017/s0022112066000636 ◽

1966 ◽

Vol 24 (2) ◽

pp. 275-284

Author(s):

R. A. Wentzell

Keyword(s):

Magnetic Field ◽

Exact Solution ◽

Uniform Magnetic Field ◽

Perfect Conductor ◽

Rigid Boundary ◽

Torsional Oscillations ◽

Magnetic Viscosity ◽

Eigen Values ◽

Infinite Conductivity ◽

Axis Of Symmetry

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

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On the Motion of an Elastic Body Rolling/Sliding on an Elastic Substrate

Journal of Tribology ◽

10.1115/1.2831248 ◽

1995 ◽

Vol 117 (2) ◽

pp. 308-314 ◽

Cited By ~ 3

Author(s):

A. Spector ◽

R. C. Batra

Keyword(s):

Elastic Body ◽

Frictional Force ◽

Three Dimensional ◽

The Body ◽

Elastic Substrate ◽

Linear Elastic ◽

Linear Elastic Body ◽

Body Rolling ◽

Applied Forces ◽

Two Phases

The three-dimensional evolutionary problem of rolling/sliding of a linear elastic body on a linear elastic substrate is studied. The inertial properties of the body regarded as rigid are accounted for. By employing an asymptotic analysis, it is shown that the process can be divided into two phases: transient and quasistationary. An expression for the frictional force as a function of the externally applied forces and moments, and inertial properties of the body is derived. For an ellipsoid rolling/sliding on a linear elastic substrate, numerical results for the frictional force distribution, slip/adhesion subareas, and the evolution of the slip velocity are given.

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Human pose estimation based on parallel atrous convolution and body structure constraints

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-212061 ◽

2021 ◽

pp. 1-11

Author(s):

Min Zhang ◽

Haijie Yang ◽

Pengfei Li ◽

Ming Jiang

Keyword(s):

Pose Estimation ◽

The Body ◽

Human Pose Estimation ◽

Spatial Relationships ◽

Body Structure ◽

Convolutional Network ◽

In Series ◽

Human Pose ◽

Ablation Study ◽

View Transformation

Human pose estimation is still a challenging task in computer vision, especially in the case of camera view transformation, joints occlusions and overlapping, the task will be of ever-increasing difficulty to achieve success. Most existing methods pass the input through a network, which typically consists of high-to-low resolution sub-networks that are connected in series. Still, during the up-sampling process, the spatial relationships and details might be lost. This paper designs a parallel atrous convolutional network with body structure constraints (PAC-BCNet) to address the problem. Among the mentioned techniques, the parallel atrous convolution (PAC) is constructed to deal with scale changes by connecting multiple different atrous convolution sub-networks in parallel. And it is used to extract features from different scales without reducing the resolution. Besides, the body structure constraints (BC), which enhance the correlation between each keypoint, are constructed to obtain better spatial relationships of the body by designing keypoints constraints sets and improving the loss function. In this work, a comparative experiment of the serial atrous convolution, the parallel atrous convolution, the ablation study with and without body structure constraints are conducted, which reasonably proves the effectiveness of the approach. The model is evaluated on two widely used human pose estimation benchmarks (MPII and LSP). The method achieves better performance on both datasets.

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Contact Pressures as an Elastic Roller Crosses a Scratch

Journal of Applied Mechanics ◽

10.1115/1.2787326 ◽

1997 ◽

Vol 64 (2) ◽

pp. 425-427 ◽

Cited By ~ 2

Author(s):

J. A. Greenwood

Keyword(s):

Exact Solution ◽

Half Space ◽

Elastic Analysis ◽

Contact Pressures

The Westergaard method of plane elastic analysis is used to obtain an exact solution to the problem of an elastic roller crossing a gap, intended to represent a scratch, on a rigid half-space.

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