SCATTERING OF TRANSIENT WAVES BY FINITE CRACKS IN AN ANTI-PLANE STRAIN ELASTIC SOLID

1993 ◽  
Vol 01 (01) ◽  
pp. 101-116 ◽  
Author(s):  
YU-CHIUNG TENG
Keyword(s):  
Plane Wave ◽  
Plane Strain ◽  
Elastic Solid ◽  
Transient Problem ◽  
Whole Space ◽  
Crack Tips ◽  
Finite Line ◽  
Energy Sharing ◽  
Analytical Approaches ◽  
Line Crack

The transient problem of finite cracks with vanishing thickness in an anti-plane strain solid is investigated by finite element method. The infinitesimally thin crack with traction free on both faces of the crack is simulated by the energy-sharing-node technique. The following cases are considered: (a) One finite line crack in a whole space subjected to (i) a concentrated line source and (ii) an inclined incident SH plane wave. (b) Two cracks in a whole space subjected to an inclined incident SH plane wave. Emphasis has been laid on the quantitative evaluation of the dynamic disturbances for the problem in the interference stage, which is generally difficult to be obtained by analytical approaches. The synthetic seismograms for displacements along the crack surfaces, which cover a period up to an instant of time during which the second order scattering from crack tips can be observed, are presented. Snapshots of the scattered displacement field for each case are also displayed so that the generations of the scatterings and the processes of the wave propagations can be clearly visualized. The two-dimensional wave propagation for transient acoustic problem and electromagnetic problem with the same nature of boundaries can be analogously obtained.

Stresses Due to Tangential and Normal Loads on an Elastic Solid With Application to Some Contact Stress Problems

1953 ◽  
Vol 20 (2) ◽  
pp. 157-166
Author(s):  
J. O. Smith ◽  
Chang Keng Liu
Keyword(s):  
Plane Strain ◽  
Coefficient Of Friction ◽  
Contact Area ◽  
Normal Load ◽  
Elastic Solid ◽  
Real Variable ◽  
The Body ◽  
Shearing Stress ◽  
Tangential Load ◽  
The Coefficient Of Friction

Abstract The results of two-dimensional approach using real variable method to Hertz’s problem of contact of elastic bodies are presented. Both normal and tangential loads are assumed to be distributed in Hertzian fashion over the area of contact. The magnitude of the intensity of the tangential load is assumed to be linearly proportional to that of the normal load when sliding motion of the body is impending. The stresses in the elastic body due to the application of these loads on its boundary are presented in closed form for both plane-stress and plane-strain cases. A numerical value of f = 1/3 is assumed for the linear proportionality (coefficient of friction) between the tangential and normal loads in order that the distribution of stresses may be illustrated. The significance of the stress distribution, across the contact area and in the body, is also discussed. It is shown that when the combination of loads considered in the paper are applied at the contact area of bodies in contact the maximum shearing stress may be at the surface instead of beneath the surface. For example, for plane strain, if the coefficient of friction is f = 1/3, the maximum shearing stress is at the surface and is 43 per cent larger than the maximum shearing stress, which would be below the surface, that occurs when the normal force acts alone. The effect of range of normal stress and of shearing stress on the plane of maximum shear and on the plane of maximum octahedral shear on failure by progressive fracture (fatigue) is discussed.

scholarly journals Prephase-Based Equivalent Amplitude Tailoring for Low Sidelobe Levels of 1-Bit Phase-Only Control Metasurface under Plane Wave Incidence

2021 ◽  
Author(s):  
Jiexi Yin ◽  
Qi Wu ◽  
Haiming Wang ◽  
Zhining Chen
Keyword(s):  
Plane Wave ◽  
Symmetric Matrix ◽  
Synthesis Method ◽  
Low Sidelobe ◽  
Unit Cells ◽  
Whole Space ◽  
Wave Incidence ◽  
Plane Wave Incidence ◽  
Selection Of ◽  
Degree Step

<p>A prephase synthesis method is proposed for sidelobe level (SLL) suppression of a 1-bit phase-only control metasurface under plane wave incidence. The array factor of the metasurface with N×N unit cells shows that controlling the number of prephases with varying values over the reflective surface realizes equivalent amplitude tailoring. Different from optimizing the prephase distribution, selection of the numbers of 0 and π/2 prephases in specific N regions is used to suppress the SLLs. Therefore, the parameters in the optimization can be dramatically reduced from N<sup>2</sup> to N. The prephase distribution is then designed based on the optimized number of prephases and a symmetric matrix for SLL suppression in the whole space. The SLLs are further suppressed by optimizing some of the unit cell states based on similar equivalent amplitude tailoring. Simulation and measurement of a set of 1-bit reflective metasurfaces with 20×20 unit cells verify that the phase-only control metasurface realizes SLL suppression to -13 dB for multiple beam directions from -30 to 30 degrees with a 10-degree step under normal plane wave incidence.</p>

scholarly journals Noninvasive Vascular Elastography With Plane Strain Incompressibility Assumption Using Ultrafast Coherent Compound Plane Wave Imaging

2015 ◽  
Vol 34 (12) ◽  
pp. 2618-2631 ◽  
Author(s):  
Jonathan Poree ◽  
Damien Garcia ◽  
Boris Chayer ◽  
Jacques Ohayon ◽  
Guy Cloutier
Keyword(s):  
Plane Wave ◽  
Plane Strain ◽  
Wave Imaging

scholarly journals Plane strain problem in microstretch elastic solid

Sadhana ◽  
2003 ◽  
Vol 28 (6) ◽  
pp. 975-990 ◽  
Author(s):  
Rajneesh Kumar ◽  
Ranjit Singh ◽  
T K Chadha
Keyword(s):  
Plane Strain ◽  
Elastic Solid ◽  
Plane Strain Problem

Stress-Intensity Factor for a Three-Dimensional Rectangular Crack

1981 ◽  
Vol 48 (2) ◽  
pp. 309-312 ◽  
Author(s):  
M. K. Kassir
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Plane Strain ◽  
Integral Transform ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Normal Loading ◽  
Rectangular Crack ◽  
Strain Stress

An integral transform solution is developed to reduce the problem of determining the stress-intensity factor of a narrow three-dimensional rectangular crack to the solution of a Fredholm integral equation of the second kind. The crack is assumed to be embedded in an infinite elastic solid subjected to normal loading. Numerical results are presented to indicate a reduction in the value of the stress-intensity factor from the plane strain case. For an elongated rectangular crack the plane-strain stress-intensity factor is recovered.

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