Axisymmetric Inclusion in a Half Space

1990 ◽  
Vol 57 (1) ◽  
pp. 74-77 ◽  
Author(s):  
H. Y. Yu ◽  
S. C. Sanday
Keyword(s):  
General Solution ◽  
Half Space ◽  
Transformation Method ◽  
Dislocation Loops ◽  
Hankel Transformation ◽  
New Approach ◽  
Elastic Fields ◽  
Special Cases

An alternate method of approach for solving the axisymmetric elastic fields in the half space with an isotropic spheriodal inclusion is proposed. This new approach involves the application of the Hankel transformation method for the solution of prismatic dislocation loops and Eshelby’s solution for ellipsoidal inclusions. Existing solutions by other methods for the inclusion with pure dilatational misfit in a half space are shown to be special cases of the present, more general solution.

Distributed Dislocation Method for Determining Elastic Fields of 2D and 3D Volume Misfit Particles in Infinite Space and Extension of the Method for Particles in Half Space

2014 ◽  
Vol 31 (3) ◽  
pp. 249-260
Author(s):  
J. D. Lerma ◽  
T. Khraishi ◽  
S. Kataria ◽  
Y.-L. Shen
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Misfit Strain ◽  
Computational Method ◽  
Dislocation Loops ◽  
Host Matrix ◽  
Elastic Fields ◽  
Numerical Assessment ◽  
Distributed Dislocation ◽  
3D Volume

AbstractA multitude of researchers have utilized a variety of techniques to formulate the stresses and deformations caused by volume misfit inclusions in infinite host media. Few of such techniques can also be extended to derive solutions for inclusions in a half space. In this manuscript we present a novel computational method for determining the elastic fields of two and three-dimensional inclusions of arbitrary shape in an infinite host matrix. The misfit strain is treated by a distribution of prismatic dislocation loops. A systematic numerical assessment illustrates that the discretization can yield excellent agreement with existing analytical solutions for certain particle geometries. This method is then further developed to solve for two-dimensional problems in a half space.

Wave motion in multi-layered transversely isotropic porous media by the method of potential functions

2019 ◽  
Vol 25 (3) ◽  
pp. 547-572 ◽  
Author(s):  
Hamid Teymouri ◽  
Ali Khojasteh ◽  
Mohammad Rahimian ◽  
Ronald Y S Pak
Keyword(s):  
Differential Equations ◽  
Half Space ◽  
Riemann Surfaces ◽  
Closed Form Solution ◽  
Transversely Isotropic ◽  
Transformation Method ◽  
Harmonic Excitation ◽  
Form Solution ◽  
Potential Functions ◽  
Special Cases

Wave propagation in a multi-layered transversely isotropic porous medium has been considered in this paper, which consists of n parallel layers overlying on a half-space. Potential functions are used to solve elastodynamic differential equations of the poroelastic medium. Time-harmonic excitation is assumed and the procedure of solution is performed in the frequency domain. Generalized reflection and transmission matrices are generated for compressional and shear waves separately. By means of the Hankel transformation method, coupled differential equations are altered to ordinary ones and Riemann surfaces are used to establish the path of integrations. A closed-form solution is described to reach Green’s functions of displacements and stresses. Some special cases of excitations are discussed and verification of the solution is presented. The numerical results of a three-layered medium on a porous half-space are determined and discussed.

scholarly journals Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
Kh. Lotfy ◽  
A. Gohaly
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Elastic Layer ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Magnetic Field Effect ◽  
Plane Boundary ◽  
Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

scholarly journals A New Approach for Analyzing the Reliability of the Repair Facility in a Series System with Vacations

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Renbin Liu ◽  
Yong Wu
Keyword(s):  
Renewal Process ◽  
Decomposition Method ◽  
Process Theory ◽  
Series System ◽  
New Approach ◽  
Numerical Examples ◽  
Special Cases ◽  
The Mean ◽  
Repair Facility

Based on the renewal process theory we develop a decomposition method to analyze the reliability of the repair facility in ann-unit series system with vacations. Using this approach, we study the unavailability and the mean replacement number during(0,t]of the repair facility. The method proposed in this work is novel and concise, which can make us see clearly the structures of the facility indices of a series system with an unreliable repair facility, two convolution relations. Special cases and numerical examples are given to show the validity of our method.

scholarly journals Water entry of an expanding wedge/plate with flow detachment

2016 ◽  
Vol 797 ◽  
pp. 322-344 ◽  
Author(s):  
Yuriy A. Semenov ◽  
Guo Xiong Wu
Keyword(s):  
Free Surface ◽  
General Solution ◽  
Water Entry ◽  
Hodograph Method ◽  
Fixed Length ◽  
Pressure Distributions ◽  
Initial Stage ◽  
Special Cases ◽  
Wedge Plate ◽  
Special Case

A general similarity solution for water-entry problems of a wedge with its inner angle fixed and its sides in expansion is obtained with flow detachment, in which the speed of expansion is a free parameter. The known solutions for a wedge of a fixed length at the initial stage of water entry without flow detachment and at the final stage corresponding to Helmholtz flow are obtained as two special cases, at some finite and zero expansion speeds, respectively. An expanding horizontal plate impacting a flat free surface is considered as the special case of the general solution for a wedge inner angle equal to ${\rm\pi}$. An initial impulse solution for a plate of a fixed length is obtained as the special case of the present formulation. The general solution is obtained in the form of integral equations using the integral hodograph method. The results are presented in terms of free-surface shapes, streamlines and pressure distributions.

Defects and Polytype Instabilities

2018 ◽  
Vol 924 ◽  
pp. 147-150
Author(s):  
Jörg Pezoldt ◽  
Andrei Alexandrovich Kalnin
Keyword(s):  
Long Range ◽  
Basal Plane ◽  
Partial Dislocation ◽  
Stacking Faults ◽  
Dislocation Loops ◽  
Elastic Fields ◽  
Basal Plane Dislocation ◽  
The Stability ◽  
Shockley Dislocation ◽  
Polytype Structure

A model based on the generation and recombination of defect was developed to describe the stability of stacking faults and basal plane dislocation loops in crystals with layered polytype structures. The stability of the defects configuration was analysed for stacking faults surrounded by Shockley and Frank partial dislocation as well as Shockley dislocation dipoles with long range elastic fields. This approach allows the qualitative prediction of defect subsystems in polytype structure in external fields.

Implementation of DTM as a numerical study for the Casson fluid flow past an exponentially variable stretching sheet with thermal radiation

2021 ◽  
pp. 2150111
Author(s):  
Khadijah M. Abualnaja
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Numerical Method ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Transformation Method ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Special Cases

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

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