Boussinesq's problem for a flat-ended cylinder

1946 ◽  
Vol 42 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Ian N. Sneddon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Elastic Medium ◽  
Normal Displacement ◽  
Full Account ◽  
Elastic Stresses ◽  
Special Cases ◽  
Cylindrical Punch ◽  
Distribution Of Stress ◽  
Boussinesq’S Problem

1. In a recent paper(1) expressions were found for the elastic stresses produced in a semi-infinite elastic medium when its boundary is deformed by the pressure against it of a perfectly rigid body. In deriving the solution of this problem—the ‘Boussinesq’ problem—it was assumed that the normal displacement of a point within the area of contact between the elastic medium and the rigid body is prescribed and that the distribution of pressure over that area is determined subsequently. The solutions for the special cases in which the free surface was indented by a cone, a sphere and a flat-ended cylindrical punch were derived, but no attempt was made to give a full account of the distribution of stress in the interior of the medium in any of these cases.

The elastic stresses produced in a thick plate by the application of pressure to its free surfaces

1946 ◽  
Vol 42 (3) ◽  
pp. 260-271 ◽  
Author(s):  
I. N. Sneddon
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Elastic Medium ◽  
Thick Plate ◽  
Normal Displacement ◽  
Plane Boundary ◽  
Free Surfaces ◽  
Boussinesq Problem ◽  
Elastic Stresses ◽  
Distribution Of Stress

In a recent paper (1) an analysis was given of the distribution of stress in a semi-infinite elastic medium deformed by the pressure of a rigid body on part of the plane boundary, the remainder of the plane being free. In that form of the problem—the so-called ‘Boussinesq problem’—the normal displacement of a point within the pressed area was prescribed and the distribution of pressure over that area determined. In this paper the corresponding analysis is given for the case in which the pressed area and the distribution of pressure over it are both prescribed and the normal displacement of a point on the free surface is determined.

Stability Analysis of Hydropower Stations With Complex Flow Patterns in the Tailrace Tunnel

2013 ◽  
Author(s):  
Jianxu Zhou ◽  
Fulin Cai ◽  
Ming Hu
Keyword(s):  
Free Surface ◽  
Stability Analysis ◽  
Flow Patterns ◽  
Normal Operation ◽  
Complex Flow ◽  
Diversion Tunnel ◽  
Implicit Model ◽  
Special Cases ◽  
Tailrace Tunnel ◽  
Hydropower Stations

For some special tailrace tunnels in the hydropower stations, including the changing top-altitude tailrace tunnel and the tailrace tunnel with downstream reused flat-ceiling diversion tunnel, during normal operation and hydraulic transients, the flow patterns inside are relatively complex mainly including the free-surface pressurized flow and partial free flow if the tail water level is lower than the top elevation of tunnel’s outlet. These complex flow patterns have obvious effect on system’s stability, and can not be simulated accurately by the traditional models. Therefore, a characteristic implicit model is introduced to simulate these complex flow patterns for further stability analysis. In some special cases, the characteristic implicit model also fails to completely simulate the mixed free-surface pressurized flow in the flat-ceiling tailrace tunnel. A new method is presented based on both experimental research and numerical simulation, and then, system’s stability is analyzed by compared with traditional ordinary boundary condition. The results indicate that, with different simulation models for the complex water flow in the tailrace tunnel, system’s dynamic characteristic can be actually revealed with the consideration of the effect of complex flow patterns in the tailrace tunnel on system’s stability and regulation performance.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

scholarly journals On the motion of a heavy rigid body in two special cases of S.V.Kovalevskaya’s solution

2018 ◽  
Vol 14 (1) ◽  
pp. 123-138
Author(s):  
Г.В. Горр ◽  
◽  
Е.К. Щетинина ◽  
Keyword(s):  
Rigid Body ◽  
Heavy Rigid Body ◽  
Special Cases

The distribution of stress and velocity in glaciers and ice-sheets

1957 ◽  
Vol 239 (1216) ◽  
pp. 113-133 ◽  
Keyword(s):  
Steady Flow ◽  
Longitudinal Velocity ◽  
Present Theory ◽  
Surface Velocity ◽  
General Flow ◽  
Glacier Valley ◽  
Compressive Flow ◽  
Special Cases ◽  
Flow Law ◽  
Distribution Of Stress

A block of ice resting upon a rough slope forms a theoretical model of a glacier or an ice-sheet, the sides of the glacier valley being ignored. Previous papers have described two types of steady flow in this model: ( a ) laminar flow, in which the longitudinal velocity gradient r is zero, and ( b ) extending or compressive flow, in which r is non-zero, ( a ) was derived under the assumption of a general flow law for ice, but ( b ) was only derived under the assumption of perfect plasticity. In the present paper a general flow law is used throughout, and the equations for steady flow, with r allowed to be non-zero, are found. The previous results ( a ) and ( b ) appear as special cases. Possible variations of density, temperature or flow law with depth are allowed for. If the density and the flow law are known as functions of depth in any region, and if the surface slope, the surface velocity, and the value of r are known, the equations give the stresses and velocity as functions of depth. The borehole experiment on the Jungfraufirn (1948-50) allows an experimental test. From the observed value of r , and Glen’s laboratory flow law for ice, a theoretical curve for the result of the experiment is calculated which is compared with the experimental curve. At a depth of 50 m the effect of ignoring r , as has been done hitherto, is to underestimate the shear rate by a factor of 50; on the present theory it is overestimated by a factor of 1∙33. The remaining discrepancy is probably mainly due to the effect of the glacier sides.

Dynamical Behaviour of Orthotropic Micropolar Elastic Medium

2002 ◽  
Vol 8 (8) ◽  
pp. 1053-1069 ◽  
Author(s):  
Rajneesh Kumar ◽  
Suman Choudhary
Keyword(s):  
Elastic Medium ◽  
Couple Stress ◽  
Normal Force ◽  
Numerical Technique ◽  
Integral Transforms ◽  
Dynamical Behaviour ◽  
Normal Displacement ◽  
Physical Domain ◽  
Elastic Solids ◽  
Eigenvalue Approach

The present paper is concerned with the plane strain problem in homogeneous micropolar orthotropic elastic solids. The disturbance due to continuous normal and tangential sources are investigated by employing eigenvalue approach. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities are given and illustrated graphically.

Validation of Open-Source SPH Code DualSPHysics for Numerical Simulations of Water Entry and Exit of a Rigid Body

2017 ◽  
Author(s):  
Sergei K. Buruchenko ◽  
Ricardo B. Canelas
Keyword(s):  
Free Surface ◽  
Rigid Body ◽  
Stokes Equations ◽  
Offshore Structures ◽  
Water Entry ◽  
Surface Flow ◽  
Rigid Body Dynamics ◽  
Structural Safety ◽  
Entry And Exit ◽  
Momentum Exchange

Water entry and exit of a body is an important topic in naval hydrodynamics as these phenomena play relevant roles both for offshore structures and vessels. Water entry and exit events are intrinsically transient and represent intense topological changes in the system, with large amounts of momentum exchange between phases. At its onset, they can be characterized by highly localized, both in space and time, loads on the vessel, influencing both the local structural safety of the structure and the global loads acting on it. The DualSPHysics code is proposed as a numerical tool for the simulation of fluid and floating object interaction. The numerical model is based on a Smoothed Particle Hydrodynamics discretization of the Navier-Stokes equations and Newton’s equations for rigid body dynamics. This paper examines the water impact, fluid motions, and movement of objects in the conventional case studies of object entry and exit from still water. A two dimensional body drop analysis was carried out demonstrating acceptable agreement of the movement of the object with published experimental and numerical results. The velocity field of the fluid is also captured and analyzed. Simulations for water entry and exit of a buoyant and neutral density cylinder compares well with previous experimental, numerical, and empirical studies in penetration, free surface evolution and object kinematics. These results provide a good foundation to evaluate the accuracy and stability of the DualSPHysics implementation for modeling the interaction between free surface flow and free moving floating objects.

Line Force in a Two-Phase Orthotropic Medium

1982 ◽  
Vol 49 (1) ◽  
pp. 55-61 ◽  
Author(s):  
R. S. Wu ◽  
Y. T. Chou
Keyword(s):  
Free Surface ◽  
Elastic Field ◽  
Space Application ◽  
Orthotropic Medium ◽  
Method Of Images ◽  
Two Phase ◽  
Special Cases ◽  
Line Force ◽  
Technological Interest

Based on the generalized method of images, the elastic field of an in-plane line force acting in a two-phase orthotropic medium is analyzed. Several special cases of technological interest are deduced from the general solution, including the case of a line force applied on the free surface of a half space. Application of the results to the determination of the elastic field of an edge dislocation in a semi-infinite orthotropic medium is illustrated.

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