scholarly journals Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 497 ◽  
Author(s):  
Marin Marin ◽  
Eduard M. Craciun ◽  
Nicolae Pop
Keyword(s):  
Mixed Problem ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Reciprocal Theorem ◽  
General Context ◽  
Main Concern ◽  
Dipolar Bodies ◽  
Uniqueness Of The Solution ◽  
Thermoelastic Body ◽  
Dipolar Structure

The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive.

scholarly journals On the Partition of Energies for the Backward in Time Problem of Thermoelastic Materials with a Dipolar Structure

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 863 ◽  
Author(s):  
M. Marin  ◽  
S. Vlase ◽  
R. Ellahi ◽  
M.M. Bhatti
Keyword(s):  
Mixed Problem ◽  
Temporal Behavior ◽  
Time Problem ◽  
Uniqueness Of The Solution ◽  
Thermoelastic Body ◽  
Dipolar Structure ◽  
Integral Identities

We first formulate the mixed backward in time problem in the context of thermoelasticity for dipolar materials. To prove the consistency of this mixed problem, our first main result is regarding the uniqueness of the solution for this problem. This is obtained based on some auxiliary results, namely, four integral identities. The second main result is regarding the temporal behavior of our thermoelastic body with a dipolar structure. This behavior is studied by means of some relations on a partition of various parts of the energy associated to the solution of the problem.

scholarly journals Existence and uniqueness of a finite energy solution for the mixed value problem of porous thermoelastic bodies

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
M. Marin ◽  
S. Vlase ◽  
C. Carstea
Keyword(s):  
Initial Data ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Finite Energy ◽  
Theory Of Elasticity ◽  
Existence Of A Solution ◽  
Porous Bodies ◽  
Finite Energy Solution ◽  
Uniqueness And Existence ◽  
Dipolar Structure

AbstractWe consider the mixed problem with boundary and initial data in thermoelasticity of porous bodies with dipolar structure. By generalizing some known results developed by Dafermos in a more simple case of the classical theory of elasticity, we prove new theorems in which we address the issues regarding the uniqueness and existence of a solution with finite energy of the respective problem after we define this type of solution.

Study of internal stresses in rock massif within the framework of elastic layered block models with inclusions of the hierarchical structure of the L-rank.

2021 ◽  
Author(s):  
Olga Hachay ◽  
Andrey Khachay
Keyword(s):  
Hierarchical Structure ◽  
Classical Theory ◽  
Acoustic Waves ◽  
Degrees Of Freedom ◽  
Heterogeneous Media ◽  
Theory Of Elasticity ◽  
Rock Massif ◽  
Local Theory ◽  
Internal Stresses ◽  
Non Local

<p>In recent years, new models of continuum mechanics, generalizing the classical theory of elasticity, have been intensively developed. These models are used to describe composite and statistically heterogeneous media, new structural materials, as well as in complex massifs in mine conditions. The paper presents an algorithm for the propagation of longitudinal acoustic waves in the framework of active well monitoring of elastic layered block media with inclusions of hierarchical type of L-th rank. Relations for internal stresses and strains for each hierarchical rank are obtained, which constitute the non local theory of elasticity. The essential differences between the non local theory of elasticity and the classical one and the connection between them are investigated. A characteristic feature of the theory of media with a hierarchical structure is the presence of scale parameters in explicit or implicit form. This work focuses on the study of the effects of non locality and internal degrees of freedom, reflected in internal stresses, which are not described by the classical theory of elasticity and which can be potential precursors of the development of a catastrophic process in a rock massif. Thanks to the use of a model of a layered block medium with hierarchical inclusions, it is possible, using borehole acoustic monitoring, to determine the position of the highest values ​​of internal stresses and, with less effort, to implement the method of unloading the rock massif. If it is necessary to conduct short-term predictive monitoring of geodynamic regions and determine a more accurate position of the source of a dynamic phenomenon using borehole active acoustic observations, it is necessary to use the values ​​of the tensor of internal hierarchical stresses as a monitored parameter.</p>

The Elastic Plane With a Circular Insert, Loaded by a Tangentially Directed Force

1962 ◽  
Vol 29 (2) ◽  
pp. 362-368 ◽  
Author(s):  
M. Hete´nyi ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Elastic Properties ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Elastic Plane ◽  
Elementary Functions ◽  
Explicit Formulas ◽  
Concentrated Force

The problem treated is that of a plate of unlimited extent containing a circular insert and subjected to a concentrated force in the plane of the plate and in a direction tangential to the circle. The elastic properties of the insert are different from those of the plate, and a perfect bond is assumed between the two materials. The solution is exact within the classical theory of elasticity, and is in a closed form in terms of elementary functions. Explicit formulas are given for the components of stress in Cartesian co-ordinates, and also in polar co-ordinates at the circumference of the insert.

scholarly journals The torsion of a semi-infinite elastic solid by an elliptical stamp

1968 ◽  
Vol 9 (1) ◽  
pp. 36-45
Author(s):  
Mumtaz K. Kassir
Keyword(s):  
Field Equation ◽  
Classical Theory ◽  
Cross Sections ◽  
Plane Surface ◽  
Boundary Surface ◽  
Elastic Solid ◽  
Theory Of Elasticity ◽  
Circular Area

The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z ≧ 0) when a part of the boundary surface (z = 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11, and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.

Stiffness of Annular Bonded Rubber Flanged Bushes

2006 ◽  
Vol 79 (2) ◽  
pp. 233-248 ◽  
Author(s):  
J. M. Horton ◽  
G. E. Tupholme
Keyword(s):  
Closed Form ◽  
Finite Length ◽  
Classical Theory ◽  
Theory Of Elasticity ◽  
Numerical Results ◽  
Torsional Stiffness ◽  
Radial Stiffness ◽  
Physical Data

Abstract Closed-form expressions are derived for the torsional stiffness, radial stiffness and tilting stiffness of annular rubber flanged bushes of finite length in three principal modes of deformation, based upon the classical theory of elasticity. Illustrative numerical results are deduced with realistic physical data of typical flanged bushes.

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