scholarly journals THREE-DIMENSIONAL AXISYMMETRIC INVISIBILITY CLOAKS WITH ARBITRARY SHAPES IN LAYERED-MEDIUM BACKGROUND

2011 ◽  
Vol 27 ◽  
pp. 151-163 ◽  
Author(s):  
Yong-Bo Zhai ◽  
Tie-Jun Cui
Keyword(s):  
Layered Medium ◽  
Three Dimensional ◽  
Invisibility Cloaks ◽  
Arbitrary Shapes

Synthetic reflection seismograms in three dimensions by a locked‐mode approximation

Geophysics ◽  
1989 ◽  
Vol 54 (3) ◽  
pp. 350-358 ◽  
Author(s):  
G. Nolet ◽  
R. Sleeman ◽  
V. Nijhof ◽  
B. L. N. Kennett
Keyword(s):  
Finite Difference ◽  
Born Approximation ◽  
Large Scale ◽  
Layered Medium ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Realistic Model ◽  
Three Dimensions ◽  
Acoustic Response ◽  
Many Sources

We present a simple algorithm for computing the acoustic response of a layered structure containing three‐dimensional (3-D) irregularities, using a locked‐mode approach and the Born approximation. The effects of anelasticity are incorporated by use of Rayleigh’s principle. The method is particularly attractive at somewhat larger offsets, but computations for near‐source offsets are stable as well, due to the introduction of anelastic damping. Calculations can be done on small minicomputers. The algorithm developed in this paper can be used to calculate the response of complicated models in three dimensions. It is more efficient than any other method whenever many sources are involved. The results are useful for modeling, as well as for generating test signals for data processing with realistic, model‐induced “noise.” Also, this approach provides an alternative to 2-D finite‐difference calculations that is efficient enough for application to large‐scale inverse problems. The method is illustrated by application to a simple 3-D structure in a layered medium.

Three-Dimensional Finite Element Analysis of Elastic-Plastic Layered Media Under Thermomechanical Surface Loading

2002 ◽  
Vol 125 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N. Ye ◽  
K. Komvopoulos
Keyword(s):  
Finite Element ◽  
Layered Medium ◽  
Numerical Solutions ◽  
Equivalent Stress ◽  
Three Dimensional ◽  
Layered Media ◽  
Thin Layers ◽  
Surface Loading ◽  
Elastic Plastic ◽  
Thermomechanical Surface

The simultaneous effects of mechanical and thermal surface loadings on the deformation of layered media were analyzed with the finite element method. A three-dimensional model of an elastic sphere sliding over an elastic-plastic layered medium was developed and validated by comparing finite element results with analytical and numerical solutions for the stresses and temperature distribution at the surface of an elastic homogeneous half-space. The evolution of deformation in the layered medium due to thermomechanical surface loading is interpreted in light of the dependence of temperature, von Mises equivalent stress, first principal stress, and equivalent plastic strain on the layer thickness, Peclet number, and sliding distance. The propensity for plastic flow and microcracking in the layered medium is discussed in terms of the thickness and thermal properties of the layer, sliding speed, medium compliance, and normal load. It is shown that frictional shear traction and thermal loading promote stress intensification and plasticity, especially in the case of relatively thin layers exhibiting low thermal conductivity.

scholarly journals Stable, high-order computation of impedance–impedance operators for three-dimensional layered medium simulations

2018 ◽  
Vol 474 (2212) ◽  
pp. 20170704 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Applied Sciences ◽  
Numerical Simulations ◽  
Periodic Structure ◽  
Layered Medium ◽  
Three Dimensional ◽  
High Order ◽  
Surface Integral ◽  
Dirichlet Eigenvalues ◽  
Linear Waves ◽  
Spectral Algorithm

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance–impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet–Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

Quadratic wavefront and traveltime approximations in inhomogeneous layered media with curved interfaces

Geophysics ◽  
1982 ◽  
Vol 47 (7) ◽  
pp. 1012-1021 ◽  
Author(s):  
Bjørn Ursin
Keyword(s):  
Taylor Series ◽  
Layered Medium ◽  
Source Region ◽  
Three Dimensional ◽  
Homogeneous Medium ◽  
Quadratic Approximation ◽  
Reference Source ◽  
Layered Model ◽  
Zero Offset ◽  
Receiver Point

A quadratic approximation for the square of the traveltime from a source region to a receiver region is given for a three‐dimensional (3-D) medium consisting of inhomogeneous layers with curved interfaces. The square of the traveltime, being a function of source and receiver coordinates, is developed in a Taylor series around a reference source and receiver point. The relationships of the traveltime parameters to the ray parameters and the wavefront curvature matrices are shown. Using midpoint, half‐offset coordinates gives a simplified traveltime function compared to using source‐receiver coordinates only in the case that the reference source point and the reference receiver point coincide (zero‐offset approximation). For a medium consisting of homogeneous layers with plane dipping interfaces, the traveltime approximation is further simplified. The derived traveltime approximation is shown to be exact for a reflection from a plane dipping interface in a homogeneous medium. Explicit expressions for the traveltime parameters in terms of the layer parameters are derived for a horizontally layered medium. The traveltime errors of two different approximations are compared for a given layered model in a numerical example.

Three-Dimensional Finite Element Analysis of Subsurface Stress and Strain Fields Due to Sliding Contact on an Elastic-Plastic Layered Medium

1997 ◽  
Vol 119 (2) ◽  
pp. 332-341 ◽  
Author(s):  
E. R. Kral ◽  
K. Komvopoulos
Keyword(s):  
Finite Element Analysis ◽  
Material Properties ◽  
Layered Medium ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Element Analysis ◽  
Strain Fields ◽  
Contact Loads ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

A three-dimensional finite element analysis of a rigid sphere sliding on an elastic-plastic layered medium is presented. Results for the subsurface stress and strain fields are given for a perfectly adhering layer with an elastic modulus and yield stress both two and four times that of the substrate, and contact loads 100 and 200 times the initial yield load of the substrate material. Sliding is simulated to distances of approximately two to three times the initial contact radius. The sphere is modeled by contact elements, and the interface friction coefficient is assumed equal to 0.1 and 0.25. The effects of layer material properties, contact friction, and normal load on the sliding and residual stresses in the layer and the substrate are examined. The distributions of tensile stresses in the layered medium and shear stresses at the layer/substrate interface are presented and their significance for crack initiation and layer decohesion is discussed. Reyielding during unloading is also analyzed for different material properties and contact loads.

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