Author : B. Das
Publisher : Springer
Page : 112 pages
File Size : 49,64 MB
Release : 2016-11-25
Category : Science
ISBN : 3319488082
This book presents problems and solutions of the mathematical theories of thermoelasticity and magnetothermoelasticity. The classical, coupled and generalized theories are solved using the eigenvalue methodology. Different methods of numerical inversion of the Laplace transform are presented and their direct applications are illustrated. The book is very useful to those interested in continuum mechanics.
Author : W. Nowacki
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 19,37 MB
Release : 1975-12-31
Category : Science
ISBN : 9789028600454
Author : Witold Nowacki
Publisher : Elsevier
Page : 579 pages
File Size : 36,42 MB
Release : 2013-10-22
Category : Science
ISBN : 1483162486
Thermoelasticity, Second Edition reviews advances in thermoelasticity and covers topics ranging from stationary problems of thermoelasticity to variational theorems of stationary thermoelasticity; stresses due to the action of a discontinuous temperature field in an infinite elastic body; the action of heat sources in the elastic space; and thermal inclusions in an infinite disc and semi-infinite disc. Three different sets of differential equations describing the fields of strain and temperature are presented. This book is comprised of 12 chapters and begins with a discussion on basic relations and equations of thermoelasticity. Thermoelasticity is treated as a synthesis of the theory of elasticity and the theory of heat conduction. Some particular cases of thermoelasticity are then investigated, including stationary problems, the theory of thermal stresses, and classical dynamic elasticity. Dynamic effects due to the action of a non-stationary temperature field are examined, along with plane harmonic waves in an elastic space and thermal stresses in plates, shells, and viscoelastic bodies. The final chapter focuses on micropolar thermoelasticity, magnetothermoelasticity, and thermopiezoelectricity. This monograph will be of interest to physicists and mechanical engineers.
Author : Animesh Basu
Publisher :
Page : 111 pages
File Size : 18,20 MB
Release : 1994
Category : Magnetic fields
ISBN : 9780864183125
Author : Robert C. Rogers
Publisher :
Page : 70 pages
File Size : 10,57 MB
Release : 1986
Category :
ISBN :
This paper studies the steady-state behavior of solids that can sustain mechanical, electromagnetic, and thermal effects. The authors examine a class of boundary-value problems for a quasilinear system of functional differential equations that is derived from a very general model for such materials. They propose a physically reasonable constitutive theory which leaves this system amenable to modern methods of partial differential equations. The principal assumption is a modified version of the strong ellipticity condition. Part I proves existence results for the general system under some special physical assumptions (rigidity and hyperelasticity). The formulation admits non-local interactions caused by the magnetic 'self-field' generated by the deformed, conducting body. Part II shows the existence and regularity of solutions of a system of functional ordinary differential equations arising from a semi-inverse problem in a more comprehensive physical situation. Keywords: Smooth solutions; Polyconvex energy functions; Electro-elastic coupling; Magneto-elastic coupling; Conducting rods; Thermo-elastic coupling. (Author).
Author : Witold Nowacki
Publisher :
Page : 246 pages
File Size : 49,95 MB
Release : 1969
Category : Thermoelasticity
ISBN :
Author : Gerard A Maugin
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 45,82 MB
Release : 2013-04-08
Category : Science
ISBN : 9400763530
This overview of the development of continuum mechanics throughout the twentieth century is unique and ambitious. Utilizing a historical perspective, it combines an exposition on the technical progress made in the field and a marked interest in the role played by remarkable individuals and scientific schools and institutions on a rapidly evolving social background. It underlines the newly raised technical questions and their answers, and the ongoing reflections on the bases of continuum mechanics associated, or in competition, with other branches of the physical sciences, including thermodynamics. The emphasis is placed on the development of a more realistic modeling of deformable solids and the exploitation of new mathematical tools. The book presents a balanced appraisal of advances made in various parts of the world. The author contributes his technical expertise, personal recollections, and international experience to this general overview, which is very informative albeit concise.
Author : Richard B. Hetnarski
Publisher : Springer
Page : 636 pages
File Size : 44,8 MB
Release : 2019-04-11
Category : Science
ISBN : 3030104362
This is an advanced modern textbook on thermal stresses. It serves a wide range of readers, in particular, graduate and postgraduate students, scientists, researchers in various industrial and government institutes, and engineers working in mechanical, civil, and aerospace engineering. This volume covers diverse areas of applied mathematics, continuum mechanics, stress analysis, and mechanical design. This work treats a number of topics not presented in other books on thermal stresses, for example: theory of coupled and generalized thermoelasticity, finite and boundary element method in generalized thermoelasticity, thermal stresses in functionally graded structures, and thermal expansions of piping systems. The book starts from basic concepts and principles, and these are developed to more advanced levels as the text progresses. Nevertheless, some basic knowledge on the part of the reader is expected in classical mechanics, stress analysis, and mathematics, including vector and cartesian tensor analysis. This 2nd enhanced edition includes a new chapter on Thermally Induced Vibrations. The method of stiffness is added to Chapter 7. The variational principle for the Green-Lindsay and Green-Naghdi models have been added to Chapter 2 and equations of motion and compatibility equations in spherical coordinates to Chapter 3. Additional problems at the end of chapters were added.
Author : Yuriy Povstenko
Publisher : Springer
Page : 261 pages
File Size : 19,27 MB
Release : 2015-02-26
Category : Science
ISBN : 3319153358
This book is devoted to fractional thermoelasticity, i.e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of the book may also be used as additional reading material for courses on heat and mass transfer, continuum mechanics, thermal stresses as well as in fractional calculus and its applications for graduate and postgraduate students. Extensive references are included in order to stimulate further studies.
Author : D. Iesan
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 48,11 MB
Release : 2013-06-29
Category : Science
ISBN : 9401735174
The theory of thermoelasticity studies the interaction between thermal and mechan ical fields in elastic bodies. This theory is of interest both for the mathematical and technical point of view. Intense interest has been shown recently in this field owing to the great practical importance of dynamical effects in aeronautics, nu clear reactors, and its potential importance in cryogenic applications. This work is concerned mainly with basic problems of the theory of thermoelasticity. Ther moelasticity of polar materials and the theories of thermoelasticity with finite wave speeds are not considered here. The reader interested in these subjects will find a full account in the works of Nowacki [280], Chandrasekharaiah [60] and Ignaczak [195]. Our purpose in this work is to present a systematic treatment of some results established in the theory of thermoelasticity. On the whole, the subject matter is directed towards recent developments. Chapter 1 is concerned mainly with the development of the fundamental equa tions of the theory of thermoelasticity. The kinematics and primitive concepts associated with the basic principles are developed and emphasized only to the ex tent that they are needed in our treatment of the subject. Chapter 2 is devoted to a study of linear thermoelastic deformations for prestressed bodies. We have at tempted to isolate those conceptual and mathematical difficulties which arise over and above those inherent in the problems concerned with unstressed bodies.
