Diffraction of axisymmetric waves in a borehole by bed boundary discontinuities

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1586-1595 ◽  
Author(s):  
W. C. Chew ◽  
S. Barone ◽  
B. Anderson ◽  
C. Hennessy
Keyword(s):  
Scattering Problem ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Mode Spectrum ◽  
The Past ◽  
Symmetric Source ◽  
Discrete Part ◽  
Computational Resources ◽  
Borehole Waves ◽  
The Continuum

This paper presents the calculation of the diffraction of axisymmetric borehole waves by bed boundary discontinuities. The bed boundary is assumed to be horizontal and the inhomogeneities to be axially symmetric. In such a geometry, an axially symmetric source will produce only axially symmetric waves. Since the borehole is an open structure, the mode spectrum consists of a discrete part as well as a continuum. The scattering of a continuum of waves by bed boundaries is difficult to treat. The approach used in the past in treating this class of problem has been approximate in nature, or highly numerical, such as the finite‐element method. We present here a systematic way to approximate the continuum of modes by discrete modes. After discretization, the scattering problem can be treated simply. Since the approach is systematic, it allows derivation of the solution to any desired degree of accuracy in theory; but in practice, it is limited by the computational resources available. We also show that our approach is variational and satisfies both the reciprocity theorem and energy conservation.

Observations of the continuum near the galactic centre

1967 ◽  
Vol 31 ◽  
pp. 405
Author(s):  
F. J. Kerr
Keyword(s):  
Galactic Centre ◽  
The Past ◽  
Centre Region ◽  
The Continuum

A continuum survey of the galactic-centre region has been carried out at Parkes at 20 cm wavelength over the areal11= 355° to 5°,b11= -3° to +3° (Kerr and Sinclair 1966, 1967). This is a larger region than has been covered in such surveys in the past. The observations were done as declination scans.

Investigating Applicability of the Meshfree Method to the Structural Analysis of Tires

2012 ◽  
Vol 40 (2) ◽  
pp. 60-82
Author(s):  
Ken Ishihara ◽  
Takehiro Noda ◽  
Hiroyuki Sakurai
Keyword(s):  
Meshfree Method ◽  
Alternative Methods ◽  
The Finite Element Method ◽  
Tire Industry ◽  
Academic Communities ◽  
The Past ◽  
New Methodologies ◽  
Tire Modeling ◽  
Point Data ◽  
Conducting Research

ABSTRACT In contrast to the finite element method (FEM), which is widely used in the tire industry nowadays, some alternative methods have been proposed by academic communities over the past decade or so. The meshfree method is one of those new methodologies. Originally intended to remove the burden of creating the mesh that is inherent in FEM, the meshfree method relies on the point data rather than the mesh, which makes it much easier to discretize the geometry. In addition to those modeling issues, it has been found that the meshfree method has several advantages over FEM in handling geometrical nonlinearities, continuities, and so forth. In accordance with those emerging possibilities, the authors have been conducting research on the matter. This article describes the results of the authors' preliminary research on the applicability of the meshfree method to tire analyses, which include the theoretical outline, the strategy of tire modeling, numerical results, comparisons with results of FEM, and conclusions.

An analytical model of an I-cored coil located above a conductive material with a hole

2018 ◽  
Vol 82 (2) ◽  
pp. 21001
Author(s):  
Grzegorz Tytko ◽  
Leszek Dziczkowski
Keyword(s):  
Test Object ◽  
Middle Layer ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Cylindrical Coordinate ◽  
Air Space ◽  
Through Hole ◽  
Tree Method ◽  
Good Agreement ◽  
Made In

The paper examines the problem of an axially symmetric I-cored coil located above a three-layered plate with a hole in the middle layer. A cylindrical coordinate system was applied, wherein the solution domain was truncated in the radial direction. The employment of the truncated region eigenfunction expansion (TREE) method resulted in deriving the final formulas for the change of the coil impedance with regard to the air space, and also pertaining to the test object without a flaw. Formulas for various configurations of the test object, among others for a surface hole, a subsurface hole and a through hole, have been presented. For the purpose of defectoscopy, the influence of the hole in the plate on the impedance components was investigated. The calculations were made in Matlab for frequencies from 100 Hz to 50 kHz. The obtained results were verified using the finite element method (FEM) in Comsol Multiphysics package. A very good agreement was observed in the case of both the resistance and reactance.

scholarly journals LOW- TO MID-FREQUENCY SCATTERING FROM ELASTIC OBJECTS ON A SAND SEA FLOOR: SIMULATION OF FREQUENCY AND ASPECT DEPENDENT STRUCTURAL ECHOES

2012 ◽  
Vol 20 (02) ◽  
pp. 1240007 ◽  
Author(s):  
MARIO ZAMPOLLI ◽  
AUBREY L. ESPANA ◽  
KEVIN L. WILLIAMS ◽  
STEVEN G. KARGL ◽  
ERIC I. THORSOS ◽  
...  
Keyword(s):  
Scattering Problem ◽  
Three Dimensional ◽  
Element Model ◽  
Propagation Model ◽  
Target Strength ◽  
Unexploded Ordnance ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Sea Floor ◽  
Spectral Integral

The scattering from roughly meter-sized targets, such as pipes, cylinders and unexploded ordnance shells in the 1–30 kHz frequency band is studied by numerical simulations and compared to experimental results. The numerical tool used to compute the frequency and aspect-dependent target strength is a hybrid model, consisting of a local finite-element model for the vicinity of the target, based on the decomposition of the three-dimensional scattering problem for axially symmetric objects into a series of independent two-dimensional problems, and a propagation model based on the wavenumber spectral integral representation of the Green's functions for layered media.

Numerical Simulation of Combined Forward-Backward Extrusion

2008 ◽  
Vol 367 ◽  
pp. 193-200
Author(s):  
Branko Grizelj ◽  
M. Plancak ◽  
Branimir Barisic
Keyword(s):  
Finite Element ◽  
Close Correlation ◽  
The Finite Element Method ◽  
Forming Process ◽  
Physical Conditions ◽  
Backward Extrusion ◽  
The Past ◽  
Large Numbers ◽  
Element Simulation ◽  
Save Energy

The paper analyses the process of simulation forward-backward extrusion. In metal forming industries, many products have to be formed in large numbers and with highly accurate dimensions. To save energy and material it is necessary to understand the behavior of material and to know the intermediate shapes of the formed parts and the mutual effects between tool and formed party during the forming process. These are normally based on numerical methods which take into account all physical conditions of the deformed material during the process. For this purpose, the finite element method has been developed in the past in different ways. The paper highlights the finite element simulation as a very useful technique in studying, where there is a generally close correlation in the load results obtained with finite elements method and those obtained experimentally.

A micromechanically calibrated numerical model reproducing earthquake cycle in the lab

2021 ◽  
Author(s):  
Guilhem Mollon ◽  
Jérôme Aubry ◽  
Alexandre Schubnel
Keyword(s):  
Acoustic Waves ◽  
Granular Matter ◽  
Fluid Pressure ◽  
Triaxial Tests ◽  
Zone Model ◽  
Geophysical Research ◽  
Stick Slip ◽  
Space And Time ◽  
Discrete Part ◽  
The Continuum

<p>In this communication, we present a novel numerical framework which consists in a direct coupling between a discrete micromechanical modelling of rock damaging processes and a continuous modelling of elastic deformation and acoustic waves. It includes a polygon-based conforming Discrete Element Method (DEM) with a cohesive zone model (CZM, [1]) for the discrete part and a meshfree formulation for the continuum part. This framework is applied to the numerical reproduction of sawcut triaxial tests performed in the lab on marble samples under seismogenic conditions [2]. Realistic boundary conditions (in terms of the elasticity of the loading system, of the absorption of the elastic waves and of the fluid pressure applied on the lateral boundaries) are introduced. Constitutive laws (in the continuum part) and micromechanical parameters (in the discrete part) are calibrated by performing independant simulations based on experimental results found in the literature [3].</p><p>Upon loading, this model provides information on the system behavior that nicely complement the experimental data, such as (i) the progressive damaging of the contacting surfaces, leading to the emission of granular matter in the interface, to the formation of a gouge layer, and to a modification of the interface rheology, (ii) the space and time distribution and statistics and the detailed kinematics of the slip events related to the interface evolution, and (iii) the acoustic wave emission and propagation in the medium associated with such events.</p><p>The model shows that, depending on the experimental conditions (confining pressure, loading rate, surface roughness, etc.), and without relying to any prior choice of slip- or rate-dependent friction laws, a large number of sliding regimes can emerge from this system. This includes large stress drops, regular stick-slip, or stable sliding. This model thus provides an unprecedented view of both local and global phenomena at stake during lab earthquakes, at sampling rates in both space and time which remain out of reach for experimental instrumentation.</p><p>[1]. Mollon, G. (2015). “A numerical framework for discrete modelling of friction and wear using Voronoi polyhedrons”, Tribology International, 90, 343-355<br>[2]. Aubry, J. (2019). “Séismes au laboratoire: friction, plasticité et bilan énergétique”, PhD Thesis, Ecole Normale Supérieure.<br>[3]. Fredrich, J. T.; Evans, B. & Wong, T.-F., (1989). “Micromechanics of the brittle to plastic transition in Carrara marble”, Journal of Geophysical Research: Solid Earth, <span></span></p>

An Evaluation and Comparison of Models for Maximum Deflection of Stiffened Plates Using Finite Element Analysis

2007 ◽  
Vol 44 (04) ◽  
pp. 212-225
Author(s):  
Lior Banai ◽  
Omri Pedatzur
Keyword(s):  
Finite Element ◽  
Orthotropic Plate ◽  
Lateral Pressure ◽  
Stiffened Plates ◽  
Maximum Deflection ◽  
Structural Elements ◽  
The Finite Element Method ◽  
Element Analysis ◽  
The Past ◽  
Different Types

Stiffened plates form the backbone of most of a ship's structure. Today, finite element (FE) models are used to analyze the behavior of such structural elements for different types of loads. In the past, when usage of computers and FE models were not used very much, analytical analysis methods were required. Two well-known methods have been developed for analyses of stiffened plates under lateral loading (uniform pressure), based on two different models, namely, the orthotropic plate model and the grillage model. Both models can give estimations for the maximum plate deflection under uniform lateral pressure. The objective of this paper is to present the two methods, evaluate and compare the methods using the finite element method, and finally implement the methods as a computer program for quick estimations of the maximum deflection of stiffened plates. The degree of accuracy of the two methods when compared to FE is discussed in some detail.

The Strain of a Plane Sampleat the Homogeneous Field of the Strain Rates under the Plane Strain Conditions

2019 ◽  
Vol 945 ◽  
pp. 857-865
Author(s):  
A.L. Grigorieva ◽  
Y.Y. Grigoriev ◽  
A.I. Khromov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Strip Thickness ◽  
Homogeneous Field ◽  
Strain Rates ◽  
The Finite Element Method ◽  
Strain Fields ◽  
Strain Tensors ◽  
The Continuum

In this paper, we obtained analytical solutions of the fields of strain tensors under uniaxial tension of a rigidplasticstrip underthe conditions of a plane stress state.The topicalityof the construction of these solutions is connected with significant difficulties in determining the strain fields by numerical methods (for example, the finite element method).In the construction of these solutions, the change in the geometric characteristics of the strip (thickness, width) was taken into account, which led to the solution of the nonlinear problem of the continuum mechanics.

scholarly journals Quantitative Spectroscopy of Wolf-Rayet Stars

1988 ◽  
Vol 108 ◽  
pp. 133-140
Author(s):  
W. Schmutz
Keyword(s):  
Representative Point ◽  
Dimensional Model ◽  
Model Calculations ◽  
One Dimensional ◽  
The Past ◽  
First Results ◽  
The One ◽  
Expanding Atmospheres ◽  
New Generation ◽  
The Continuum

Advances in theoretical modeling of rapidly expanding atmospheres in the past few years made it possible to determine the stellar parameters of the Wolf-Rayet stars. This progress is mainly due to the improvement of the models with respect to their spatial extension: The new generation of models treat spherically-symmetric expanding atmospheres, i.e. the models are one-dimensional. Older models describe the wind by only one representative point. The older models are in fact ‘core-halo’ approximations. They have been introduced by Castor and van Blerkom (1970), and were extensively employed in the past (cf. e.g. Willis and Wilson, 1978; Smith and Willis, 1982). First results from new one-dimensional model calculations are published by Hillier (1984), Schmutz (1984), Hamann (1985), Hillier (1986), and Schmutz et al. (1987a); more detailed results are presented by Schmutz and Hamann (1986), Hamann and Schmutz (1987), Hillier (1987a,b), Wessolowski et al. (1987), Hillier (1987c) and Hamann et al. (1987). These results demonstrate that the step from zero- to one-dimensional calculations is essential. The important point is that the complicated interrelation between NLTE-level populations and radiation field is treated adequately (Schmutz and Hamann, 1986; Hillier, 1987). For this interrelation it is crucial to model consistently not only the line-formation region, but also the layers where the continuum is emitted. In fact, it is the core-halo approximation that causes the one-point models to fail in certain aspects.

DIRECT CURRENT RESISTIVITY MODELING FOR AXIALLY SYMMETRIC BODIES USING THE FINITE ELEMENT METHOD

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 550-562 ◽  
Author(s):  
H. M. Bibby
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Apparent Resistivity ◽  
Vertical Axis ◽  
Geothermal Field ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Cross Sectional ◽  
Resistivity Anisotropy ◽  
Element Method

The finite element method is used to determine numerically the apparent resistivity anomaly caused by the presence of any body with a vertical axis of symmetry embedded in a uniform half‐space. The potential for a point source of current, and hence the apparent resistivity, is determined in the form of a Fourier series. The use of the finite element method enables certain classes of resistivity anisotropy to be modeled. Several examples of bipole‐dipole apparent resistivity enable us to examine assumptions that are necessarily made when inhomogeneities are approximated by models for which explicit solutions exist for the potential. An application to the Broadlands geothermal field suggests that the horizontal cross‐sectional area of the geothermal reservoir increases with depth, consistent with a decrease in the permeability with depth.

Sign in / Sign up

Export Citation Format

Share Document