OnLamb's problem: Line load suddenly applied in a magneto-elastic initially stressed conducting half-space

1972 ◽  
Vol 95 (1) ◽  
pp. 34-39
Author(s):  
Ramgopal Roy ◽  
P. R. Sen Gupta
Keyword(s):  
Half Space ◽  
Line Load ◽  
Stressed Conducting

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

Response of a Semi-Infinite Elastic Solid to an Arbitrary Line Load Along the Axis

1971 ◽  
Vol 38 (4) ◽  
pp. 906-910 ◽  
Author(s):  
G. L. Agrawal ◽  
W. G. Gottenberg
Keyword(s):  
Half Space ◽  
Axisymmetric Problem ◽  
Body Force ◽  
Elastic Solid ◽  
Delta Function ◽  
Point Load ◽  
Dirac Delta Function ◽  
Line Load ◽  
Dirac Delta ◽  
Arbitrary Line

The axisymmetric problem of a line load acting along the axis of a semi-infinite elastic solid is solved using Hankel transforms. In this solution the line load is interpreted as a body force loading and by assuming the line load to be of the form of a Dirac delta function the solution of Mindlin’s problem of a point load within the interior of the half space is obtained. Solutions of this problem presented in the literature have been obtained using semi-inverse techniques whereas the solution given here is obtained in a systematic step-by-step manner.

Failure Analysis of a Fibrous Composite Half-Space Subjected to Uniform Surface Line Load

2007 ◽  
Author(s):  
S. Gururaja ◽  
M. Ramulu
Keyword(s):  
Failure Analysis ◽  
Half Space ◽  
Fibrous Composite ◽  
Orthogonal Cutting ◽  
Failure Behavior ◽  
Line Load ◽  
Process Understanding ◽  
Spatial Coordinates ◽  
Edge Trimming ◽  
Cutting Mechanisms

Uni-Directional Fiber-Reinforced Plastic (UD-FRP) laminates have been modeled previously as an equivalent quasi-homogeneous monoclinic half-space subjected to an inclined line load on the surface using Lekhnitskii’s formulation simulating the orthogonal edge trimming loads in UD-FRPs. In continuation, failure analysis of the aforementioned composite half-space has been carried out in the present investigation based on Tsai-Wu criterion. In particular, the failure behavior of the half-space laminate with respect to the fiber orientation, load inclination angle and spatial coordinates has been examined in detail. The motivation behind such a study lies in correlating the failure behavior of the half-space laminate with the damage progression observed during orthogonal edge trimming experiments. The present work strives at identifying this relationship and in the process, understanding the physics of orthogonal cutting mechanisms in UD-FRP laminates.

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.

The Stress Field Due to a Line Load Acting on a Half Space of a Power-Law Hardening Material (A Comparison Between Plane Strain and Plane Stress)

1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Elastic Material ◽  
Plane Stress ◽  
Strain Fields ◽  
Line Load ◽  
Hardening Material

The exact solution is given for a line load acting on a half space of a power-law elastic material under conditions of plane stress. This solution is compared with the corresponding solution under plane-strain conditions; see Aruliunian [1]. A marked difference is found between the plane-stress and plane-strain fields for different values of the hardening exponent.

Moving Load on a Plate Resting on an Elastic Half Space

1967 ◽  
Vol 34 (4) ◽  
pp. 910-914 ◽  
Author(s):  
J. D. Achenbach ◽  
S. P. Keshava ◽  
G. Herrmann
Keyword(s):  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Winkler Foundation ◽  
Bending Moments ◽  
Line Load ◽  
Resonance Effects ◽  
Small Load ◽  
Smooth Contact ◽  
Time Invariant

An elastic plate supported by a semi-infinite elastic continuum is subjected to a moving line load. Both welded and smooth contact between plate and foundation are considered. Dynamic solutions for the bending moments in the plate are presented that are time-invariant relative to a coordinate system moving with the load. Resonance effects at certain critical velocities are discussed. The response of the system depends significantly on the relative stiffness of plate and half space and on the type of contact. For the relatively stiff plate certain resonances occur for smooth contact but not for welded contact. For subcritical load velocities the bending moments are calculated and compared with corresponding bending moments for a plate on a Winkler foundation. The Winkler foundation is adequate for smooth contact and small load velocities.

scholarly journals Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

2021 ◽  
Vol 15 (1) ◽  
pp. 30-36
Author(s):  
Askar Kudaibergenov ◽  
Askat Kudaibergenov ◽  
Danila Prikazchikov
Keyword(s):  
Surface Wave ◽  
Half Space ◽  
Moving Load ◽  
Elastic Half Space ◽  
Elementary Functions ◽  
Material Models ◽  
Line Load ◽  
Transient Regimes ◽  
Surface Wave Field ◽  
Asymptotic Formulation

Abstract The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

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