Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects

2004 ◽  
Vol 71 (3) ◽  
pp. 409-417 ◽  
Author(s):  
A. I. Kolesnikova ◽  
A. E. Romanov
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Half Space ◽  
Boundary Value ◽  
Free Surfaces ◽  
Elastic Fields ◽  
Surfaces And Interfaces ◽  
Elastic Boundary ◽  
Loop Technique ◽  
Prismatic Dislocation Loop

A technique for elastic boundary value problem solutions for defects in solids is developed. The method is based on the introduction of virtual circular dislocation-disclination loops distributed continuously for satisfying the prescribed boundary conditions at free surfaces and interfaces. The set of dislocation-disclination loops which may be used as virtual ones is considered. The elastic fields and energies of the selected dislocation and disclination loops are presented. The method of the virtual circular dislocation-disclination loops is then applied to obtain the elastic fields and energies of a spherical dilatating inclusion in a plate and a half-space, of a prismatic dislocation loop parallel to free surfaces of a plate and a half-space, and the elastic fields of a twist disclination loop coaxial to a cylinder.

Thermoelasticity of an Anisotropic Half Space

1974 ◽  
Vol 41 (4) ◽  
pp. 935-940 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Half Space ◽  
Boundary Value ◽  
Integral Transforms ◽  
Numerical Results ◽  
Heat Sinks ◽  
Material Anisotropy ◽  
Body Forces

The thermoelasticity of an anisotropic Hookean half space is studied herein. A solution based on successive integral transforms is developed. The solution can handle arbitrary thermal and mechanical boundary conditions together with distributed body forces and heat sinks or sources. To illustrate the substantial effects of material anisotropy, a specific boundary-value problem is solved. Numerical results based on the solution are presented. These illustrate the significant effects of both thermal and mechanical material anisotropy.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

scholarly journals The nonlocal boundary value problem with perturbations of mixed boundary conditions for an elliptic equation with constant coefficients. II

2020 ◽  
Vol 12 (1) ◽  
pp. 173-188
Author(s):  
Ya.O. Baranetskij ◽  
P.I. Kalenyuk ◽  
M.I. Kopach ◽  
A.V. Solomko
Keyword(s):  
Elliptic Equation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Conditions ◽  
Mixed Boundary Conditions ◽  
Multipoint Problem ◽  
Uniqueness Of The Solution

In this paper we continue to investigate the properties of the problem with nonlocal conditions, which are multipoint perturbations of mixed boundary conditions, started in the first part. In particular, we construct a generalized transform operator, which maps the solutions of the self-adjoint boundary-value problem with mixed boundary conditions to the solutions of the investigated multipoint problem. The system of root functions $V(L)$ of operator $L$ for multipoint problem is constructed. The conditions under which the system $V(L)$ is complete and minimal, and the conditions under which it is the Riesz basis are determined. In the case of an elliptic equation the conditions of existence and uniqueness of the solution for the problem are established.

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