Download or read book Heat Conduction Within Linear Thermoelasticity written by William A. Day and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: J-B. J. FOURIER'S immensely influential treatise Theorie Analytique de la Chaleur [21J, and the subsequent developments and refinements of FOURIER's ideas and methods at the hands of many authors, provide a highly successful theory of heat conduction. According to that theory, the growth or decay of the temperature e in a conducting body is governed by the heat equation, that is, by the parabolic partial differential equation Such has been the influence of FOURIER'S theory, which must forever remain the classical theory in that it sets the standard against which all other theories are to be measured, that the mathematical investigation of heat conduction has come to be regarded as being almost identicalt with the study of the heat equation, and the reader will not need to be reminded that intensive analytical study has t But not entirely; witness, for example, those theories which would replace the heat equation by an equation which implies a finite speed of propagation for the temperature. The reader is referred to the article [9] of COLEMAN, FABRIZIO, and OWEN for the derivation of such an equation from modern Continuum Thermody namics and for references to earlier work in this direction. viii Introduction amply demonstrated that the heat equation enjoys many properties of great interest and elegance.
Download or read book Thermoelasticity written by Heinz Parkus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: THERMOELASTICITY-the generalization of elasticity to nonisothermal deformations-has made considerable progress during the last two decades. Its basic theory is now well established, and many applications to problems in engineering have been successfully made. In writing this book it has been my aim to give, in a relatively small volume, an up-to-date presentation of those parts of thermoelasticity which, in my opinion, are of basic importance in the field. The theoretical back ground, together with the corresponding methods of solution, is developed first in each chapter and is followed by 'carefully selected examples intended to serve not only as illustrations of the theory but also as sources for useful results of engineering interest. Following a brief introductory chapter, the linearized, uncoupled theory is presented. Frequent reference is made here to the theory of isothermal elas ticity. A short review of the theory of heat conduction is included. The third and fourth chapters are concerned with special cases: plane thermo elastic stress and strain, and thermal bending and buckling of plates, respec tively. The real function method and the complex function approach are introduced simultaneously in Chapter 3 in order to exhibit and delineate the respective merits of the two procedures. In Chapter 5 the theory of thermo elasticity is developed in its most general form. Several particular cases are considered. This chapter also provides a rigorous foundation for the linearized theory of the preceding chapters.
Download or read book Thermoelasticity written by Witold Nowacki and published by Elsevier. This book was released on 2013-10-22 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Linear Theory of Thermoelasticity written by I.N. Sneddon and published by Springer. This book was released on 2014-05-04 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Thermoelasticity with Finite Wave Speeds written by Józef Ignaczak and published by Oxford University Press. This book was released on 2010 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unique monograph in a fast developing field of generalized thermoelasticity, an area of active research in continuum mechanics, focusing on thermoelasticity governed by hyperbolic equations, rather than on a wide range of continuum theories.
Download or read book Internal Variables in Thermoelasticity written by Arkadi Berezovski and published by Springer. This book was released on 2017-05-05 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material’s reaction to external loading. The basic physical principles provide the primary theoretical information, including the evolution equations of the internal variables. The cornerstones of this framework are the material representation of continuum mechanics, a weak nonlocality, a non-zero extra entropy flux, and a consecutive employment of the dissipation inequality. Examples of thermoelastic phenomena are provided, accompanied by detailed procedures demonstrating how to simulate them.
Download or read book Fractional Thermoelasticity written by Yuriy Povstenko and published by Springer. This book was released on 2015-02-26 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory of Thermoelasticity with Applications written by J.L. Nowinski and published by Springer. This book was released on 1978-06-30 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the theory of thermoelasticity has a long history, its foun dations having been laid in the first half of the nineteenth century by Duhamel and Neumann, wide-spread interest in this field did not develop until the years subsequent to World War Two. There are good reasons for this sudden and continuing revival of interest. First, in the field of aeronautics, the high velocities of modern aircraft have been found to give rise to aerodynamic heating; in turn, this produces intense thermal stresses and, by lowering the elastic limit, reduces the strength of the aircraft structure. Secondly, in the nuclear field, the extremely high temperatures and temperature gradients originating in nuclear reactors influence their design and operation. Likewise, in the technology of modern propulsive systems, such as jet and rocket engines, the high temperatures associated with combustion processes are the origin of unwelcome thermal stresses. Similar phenomena are encountered in the technologies of space vehicles and missiles, in the mechanics of large steam turbines, and even in shipbuilding, where, strangely enough. ship fractures are often attributed to thermal stres ses of moderate intensities. The investigations of these, and similar, problems have brol!ght forth a remarkable number of research papers, both theoretical and experimental, in which various aspects of thermal stresses in engineering structures are described.
Download or read book Moving Heat Sources in Thermoelasticity written by T. Rożnowski and published by Ellis Horwood. This book was released on 1989 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Approximation Theory for the Identification of Linear Thermoelastic Systems written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1990 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: An abstract approximation framework and convergence theory for the identification of thermoelastic systems is developed. Starting from an abstract operator formulation consisting of a coupled second order hyperbolic equation of elasticity and first order parabolic equation for heat conduction, well-posedness is established using linear semigroup theory in Hilbert space, and a class of parameter estimation problems is then defined involving mild solutions, and convergence solutions of the resulting sequence of approximating finite dimensional parameter identification problems to a solution of the original infinite dimensional inverse problem is established using approximation results for operator semigroups. An example involving the basic equations of one dimensional linear thermoelasticity and a linear spline based scheme is discussed and numerical results indicating how our approach might be used in a study of damping mechanisms in flexible structures are presented. (kr).
Download or read book Petroleum Related Rock Mechanics written by Erling Fjær and published by Elsevier. This book was released on 2008-01-04 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and geologists in the petroleum industry will find Petroleum Related Rock Mechanics, 2e, a powerful resource in providing a basis of rock mechanical knowledge - a knowledge which can greatly assist in the understanding of field behavior, design of test programs and the design of field operations. Not only does this text give an introduction to applications of rock mechanics within the petroleum industry, it has a strong focus on basics, drilling, production and reservoir engineering. Assessment of rock mechanical parameters is covered in depth, as is acoustic wave propagation in rocks, with possible link to 4D seismics as well as log interpretation. - Learn the basic principles behind rock mechanics from leading academic and industry experts - Quick reference and guide for engineers and geologists working in the field - Keep informed and up to date on all the latest methods and fundamental concepts
Download or read book Evolution Equations in Thermoelasticity written by Reinhard Racke and published by CRC Press. This book was released on 2000-06-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions remain open, and the field has lacked a comprehensive survey that explores these past results and presents recent developments. Evolution Equations in Thermoelasticity presents a modern treatment of initial value problems and of initial boundary value problems in both linear and nonlinear thermoelasticity, in one- and multi-dimensional spatial configurations. The authors provide the first self-contained presentation of the subject that offers both introductory parts accessible to graduate students and sophisticated sections valuable to experts.
Download or read book A Derivation of Perturbed Equations of Motion and Heat Conduction of a Thermoelastic Solid written by James J. Richardson and published by . This book was released on 1972 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report presents a brief discussion of the finite element method and the derivation of the perturbed equations of motion and heat conduction for an element. The general equations are first derived; then nodal values of displacement, force, stress, entropy, temperature, heat flux, and heat flow are perturbed. Next, the material is assumed to follow anisotropic linear thermoelastic theory throughout its behavioral history. Alternatively, it is allowed to follow an unspecified theory in the gross behavior and anisotropic thermoelasticity only during the perturbations. No geometrical assumptions are made at this point concerning the finite element; therefore, the equations derived in Section II can be adapted to a wide class of finite element approximations. In Section III various aspects of structural stability are considered. First, a number of fundamental definitions and theorems are presented. This is followed by a discussion of the stability of the behavioral expressions formulated in Section II for specific types of systems. (Author).
Download or read book Thermal Stresses Advanced Theory and Applications written by Richard B. Hetnarski and published by Springer. This book was released on 2019-04-11 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Evolution Equations in Thermoelasticity written by Reinhard Racke and published by CRC Press. This book was released on 2000-06-21 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that began in the 80s, we now also understand the basic features of nonlinear systems. Yet some questions r
Download or read book Progress in Thermoelasticity written by Witold Nowacki and published by . This book was released on 1969 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
