Continuous Bond Failure Due to a Moving Force

1973 ◽  
Vol 40 (2) ◽  
pp. 541-545 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Half Space ◽  
Stationary Solution ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Bond Failure ◽  
Moving Force ◽  
Line Force

Within the framework of the two-dimensional theory of elastodynamics a closed-form, quasi-stationary, solution is given to the problem of continuous failure of bond between an elastic half space and a rigid body. The bond failure is due to a line force moving at the interface.

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.

EFFECT OF IRREGULARITY ON STATIC DEFORMATION OF ELASTIC HALF-SPACE

2008 ◽  
Vol 22 (14) ◽  
pp. 2241-2253
Author(s):  
M. M. SELIM
Keyword(s):  
Fourier Transform ◽  
Closed Form ◽  
Half Space ◽  
Elastic Half Space ◽  
Static Deformation ◽  
Horizontal Distance ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Rectangular Shape

In the present paper, the problem of two-dimensional static deformation of an isotropic elastic half-space of irregular thickness has been studied using the eigenvalue approach, following a Fourier transform. The irregularity is expressed by a rectangular shape. As an application, the normal line-load acting inside an irregular isotropic half-space has been considered. Further, the results for the displacements have been derived in the closed form. To examine the effect of irregularity, variations of the displacements with horizontal distance have been shown graphically for different values of irregularity size, and they are compared with those for the medium with uniform shape. It is found that irregularity affects the deformation significantly.

scholarly journals Contact Response Analysis of Vertical Impact between Elastic Sphere and Elastic Half Space

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yang Yang ◽  
Qingliang Zeng ◽  
Lirong Wan
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Contact Process ◽  
Elastic Half Space ◽  
Metal Plate ◽  
3D Simulation ◽  
Elastic Sphere ◽  
Research Results ◽  
Contact Response ◽  
Vertical Impact

At present, the contact problem between the particle and the plane plate is generally equivalent to the rigid sphere impacting the elastic half space or the elastic sphere impacting the rigid surface. However, in the actual contact process, there will be no rigid body, and both contact and contacted object will deform and absorb energy. The research results obtained from the equivalent of the contact material to the rigid body are less accurate. In order to obtain the accurate mechanical relation and contact response, we took the research of impact between particles and the metal plate as a breakthrough in which the particle is equivalent to an elastic sphere and the metal plate is equivalent to an elastic half space and established the theory of vertical impact contact between elastic sphere and elastic half space by the Hertz contact theory. Through the dynamic simulation of an elastic sphere which has similar properties with rock impacting target in elastic half space in LS-DYNA, the correctness of the established theory and the feasibility of the contact process simulated by LS-DYNA are verified. Based on the established theory and 3D simulation, we studied the influence law of material parameters on the contact response and analyzed the differences of the collision vibration signals caused by the different contact objects. From the above research results, we obtain that the theoretical model is more accurate to predict the maximum contact force and contact displacement in this paper than traditional Hertz theory. And the sphere radius and both contact objects’ elastic modulus have larger influence on the contact response than sphere density, while the Poisson’s ratio has the smallest influence on the contact response results. Different material properties will cause the different contact response. The conclusions of this paper provide a theoretical calculation method for contact and a 3D simulation method for elastic half space and provide theoretical guidance for the differences analysis of the vibration signal.

Rebound of a rigid body falling on an elastic half-space

1969 ◽  
Vol 7 (5) ◽  
pp. 126-128 ◽  
Author(s):  
I. V. Simonov ◽  
L. M. Flitman
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Elastic Half Space

A TWO-DIMENSIONAL STATIC DEFORMATION OF AN IRREGULAR INITIALLY STRESSED MEDIUM

2008 ◽  
Vol 22 (20) ◽  
pp. 3473-3485
Author(s):  
M. M. SELIM
Keyword(s):  
Closed Form ◽  
Initial Stress ◽  
Half Space ◽  
Static Deformation ◽  
Initial Stresses ◽  
Two Dimensional ◽  
Eigenvalue Approach ◽  
Line Load ◽  
Notable Effect ◽  
Approach Method

The paper discusses the problem of a two-dimensional static deformation as the result of normal line-load acting inside an irregular initially stressed isotropic half-space. The eigenvalue approach method has been used. The irregularity is expressed by a rectangle shape. Further, the results for the displacements and stresses have been derived in the closed form. The effect of initial stress and irregularity are shown graphically. It was found that the initial stresses as well as irregularity have a notable effect on this deformation.

Closed-Form Solutions of the Elastic Half Space due to a Line Heat Source

2014 ◽  
Vol 638-640 ◽  
pp. 2082-2091
Author(s):  
John C.C. Lu ◽  
Feng Tsai Lin
Keyword(s):  
Heat Source ◽  
Closed Form ◽  
Half Space ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Line Heat Source ◽  
Closed Form Solutions ◽  
Line Sink ◽  
Vertical Displacements ◽  
Thermoelastic Response

Thermoelastic response due to a line heat source is analog to poroelastic reaction caused by a fluid line sink. In this study, the strata are modeled as a thermoelastic or poroelastic half space bounded by horizontal surface in the mathematical model. Thermomechanics and poromechanics are applied on the formulation of basic governing equations, and an analogy is drawn to show the similarity. Using Hankel transform technique and approaching symbolic integral through Mathematica, the closed-form solutions of the horizontal and vertical displacements due to a fluid line sink are obtained. The displacements produced by the line heat source are described through analog quantities between thermoelasticity and poroelasticity. The solutions can be applied to dewater operations and build waste repository.

To: “The elastodynamic field of N interacting vibrators (two‐dimensional theory).” by T. H. Tan, which appeared in the August 1985 issue of GEOPHYSICS, p. 1229–1252.

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1869-1869
Keyword(s):  
Half Space ◽  
First Integral ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Force Equation

The second sentence in the section “Dynamics of the strips” should read: “Conceptually, the force exerted by the half‐space is the sum of the reacting force and the force…” Equation (6) should read: [Formula: see text]. Equation (49) should read: [Formula: see text] The second exponential in the first integral in equation (77) and (B.9) should be: [Formula: see text].

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